PATTERNS OF TRANSNATIONAL TERRORISM, 1970-99: ALTERNATIVE TIME SERIES ESTIMATES

by

Walter Enders* Department of Economics, Finance, and Legal Studies

University of Alabama Tuscaloosa, AL 35487

and

Todd Sandler

School of International Relations University of Southern California

Von Kleinsmid Center 330 Los Angeles, CA 90089-0043

Revised: October 2001

e-mail of corresponding author: tsandler@usc.edu Authors' Note: Enders is the Lee Bidgood Chair of Economics and Finance, while Sandler is the Robert R. and Katheryn A. Dockson Professor of International Relations and Economics. Sandler is a member of the School of International Relations and the Department of Economics. We have profited from comments from three anonymous referees and from Patrick James.

PATTERNS OF TRANSNATIONAL TERRORISM, 1970-99: ALTERNATIVE TIME SERIES ESTIMATES

Abstract

Using alternative time series methods, this paper investigates the patterns of transnational

terrorist incidents that involve one or more deaths. Initially, an updated analysis of these fatal

events for 1970-99 is presented using a standard linear model with pre-specified interventions

that represent significant policy and political impacts. Next, a (regime-switching) threshold

autoregressive (TAR) model is applied to this fatality time series. TAR estimates indicate that

increases above the mean are not sustainable during high-activity eras, but are sustainable during

low-activity eras. The TAR model provides a better fit than previously tried methods for the

fatality time series. By applying a Fourier approximation to the nonlinear estimates, we get

improved results. The findings in this study and those in our earlier studies are then applied to

suggest some policy implications in light of the tragic attacks on the World Trade Center and the

Pentagon on 11 September 2001.

PATTERNS OF TRANSNATIONAL TERRORISM, 1970-99: ALTERNATIVE TIME SERIES ESTIMATES

On the morning of 11 September 2001, the world watched in horror as 19 hijackers

wreaked death and destruction on the World Trade Center and the Pentagon. The lethality of

transnational terrorism attained a new height, greatly out of line with the experience of the last

three decades where on average 400-500 people lost their lives each year in transnational

terrorist events (US Department of State, 1989-2000). In a matter of an hour, somewhere

between 5000 to 6000 innocent individuals from upwards of 62 nations died in four coordinated

hijackings. This attack underscores that the security threat confronting industrial nations is more

from clandestine groups with perceived grievances than from rogue nations. The reliance of

modern industrialized economies on technology makes them especially vulnerable to terrorist

attacks, as the events of 11 September 2001 sadly demonstrate.

Terrorism is the premeditated use or threat of use of extra-normal violence or brutality by

subnational groups to obtain a political, religious, or ideological objective through intimidation

of a huge audience, usually not directly involved with the policymaking that the terrorists seek to

influence.1 Key ingredients of the definition include the underlying political motive, the general

atmosphere of intimidation, and the targeting of those outside of the decision-making process.

Terrorists choose their targets to appear to be random so that everyone feels at risk, when getting

on a plane, entering a federal building, or strolling a market square. Business people, military

personnel, tourists, and everyday citizens, rather than politicians, are generally the targets of

terrorists attacks. In the case of the World Trade Center, the victims were not directly involved

in the political decision-making process associated with the demand (i.e., the removal of the US

presence from Saudi Arabia and an end to US support of Israel) that may have been behind the

attacks.2 The incident underscores the importance of applying sophisticated analyses to the study

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of international terrorism to better understand its patterns, in the hopes of deriving improved

policies and predictions to protect against future attacks.

Although terrorism has plagued civilization from its inception, there has been a

heightened awareness since the end of 1967 Arab-Israeli War and the start of Israeli occupation

of captured territory, at which point terrorism assumed a greater transnational character.

Whenever a terrorist incident (e.g., a bombing, plane hijacking, and assassination) in one country

involves victims, targets, or institutions of at least one other country, the incident is transnational.

Incidents to protest the Israeli occupation resulted in the hijacking of planes on international

flights, the murder of Israeli athletes at the 1972 Munich Olympics, and attacks throughout

Western Europe, and represented instances of transnational terrorism. Given the perpetrators'

citizenship and the multiple nationalities of the victims, the four simultaneous hijackings on 11

September 2001 were transnational terrorist acts. The ability of terrorist events to capture

headlines demonstrates the consequences of such tactics to others, who later adopt them for their

causes. Terrorism is particularly troublesome for liberal democracies, entrusted with protecting

the lives and property of their electorate.3 If such democracies respond inappropriately to a

terrorist threat by either caving in to terrorist demands or overly restricting freedoms, then they

can lose legitimacy and be defeated at the next election (Wilkinson, 1986, 2001).

With the availability of sufficiently long time series, economists and others have applied

time-series techniques to evaluate anti-terrorism policy effectiveness, to uncover trends and

cycles, and to estimate the effects of terrorist activities. A host of policy decisions have been

examined, including the usefulness of retaliatory raids (Brophy-Baermann and Conybeare, 1994;

Enders and Sandler, 1993), the consequences of UN conventions and resolutions on terrorist

activities (Enders, Sandler, and Cauley, 1990), and the impact of media reporting on future

events (Nelson and Scott, 1992; Scott, 2001). Past studies have decomposed the series of all

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terrorist events into its component series (e.g., assassinations, threats and hoaxes, hostage-taking

events, and bombings) so as to identify any trend or cycles.4 In so doing, it was shown that the

time series for each attack mode displays its own cycle, whose length increases with the

logistical complexity of the action. Apparently, the attack-counterattack interaction between the

terrorists and the authorities give rise to cycles that take longer to play out for more complicated

operations such as skyjackings (Enders et al., 1992). In terms of the estimated effects of

terrorism, studies have examined the relationship of terrorism and tourism as well as that

between terrorism and foreign direct investment.5

When incidents involving casualties (i.e., deaths, injuries, or both) are distinguished from

those with no casualties, there is a striking difference between the two. Namely, casualties series

display more predictability than noncasualties series, which are largely random noise once

detrended (Enders and Sandler, 2000). Thus, estimates and policy evaluation should be based on

a casualty series such as “DEATH,” where one or more deaths among terrorists or victims

resulted from the action, owing to this series’ deterministic factors. This finding suggests that

more intense terrorist events are more predictable than those with less consequence such as

threats, hoaxes, letter bombings, and other small-scale bombings.

This paper carries on the process of improving policy evaluations and estimates of the

patterns of transnational terrorism. At first, time-series-based policy evaluation relied on

intervention analysis, in which dummy variables identifying suspected impact points are tested

for significance for a single series (Cauley and Im, 1988; Enders et al., 1990). This intervention

procedure was later extended to vector-autoregressive (VAR) analysis to capture the

interrelationship among two or more series (Enders and Sandler, 1991, 1993, 1996; Nelson and

Scott, 1992), so that the introduction of, say, metal detectors in airports may curtail skyjackings

but augment hostage-taking events (e.g., kidnappings), not protected by these detectors, as

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terrorists substitute among modes of attacks in response to policy-induced changes in relative

costs. These VAR studies, like their single-series predecessors, assumed linear representations

with no regime-switching possibilities. Hence, the current exercise represents an important

departure where nonlinear techniques are also applied to the DEATH series, which displays the

greatest deterministic factors. These techniques not only allow the mean of the DEATH series to

differ according to the overall intensity of activities, but they also permit the data to indicate

points at which things become different.

In the next section, we present the terrorists' choice-theoretical model that underlies some

of the empirical findings. This is followed by some important intervention points and a

description of the data. The ensuing section distinguishes the dummy-variable intervention

analysis from the nonlinear threshold model. Next, the regime-switching model is introduced,

followed by the actual estimations. The Fourier-approximation model is estimated in the next

section. The next-to-last section addresses the implications of this article and our prior work on

the aftermath of the attacks on the World Trade Center and the Pentagon. Concluding remarks

are then given.

THEORETICAL MODEL

Our application is to transnational terrorism which has become much more prevalent

during the last thirty years as terrorists have taken advantage of improvements in

communication, transportation, and technology to intimidate a global community with threats of

violence unless their political demands are met. Transnational terrorist incidents are examples of

transboundary externalities, because actions by terrorists or reactions by governments in one

country may impose uncompensated costs or benefits on the people or property of another

5

country.6 Thus, a government plagued with terrorism on its soil may spend too much on

deterrence in an effort to transfer the attack elsewhere, or else a terrorist group may achieve

maximum news coverage by staging their attack in a European capital. When an incident is

planned in one country, but executed in another, it is a transnational event. The kidnapping or

assassination of a citizen from another country in a host country is a transnational terrorist act, as

is a bombing directed at one or more foreign citizens. A skyjacking of a flight that originates in

country A, but that ends in country B, is transnational. If, however, the targeted flight has

passengers from two or more countries, the skyjacking is transnational even if it never takes off.

We focus on transnational terrorism not only because of its importance to international studies,

but also because of the availability of a long consistently coded time series. Moreover,

transnational terrorism poses an important threat to the stability of the global community. The

events of 11 September have not only disrupted air travel, but may have pushed the global

economy, already on the brink, into recession. By increasing cross-border interactions,

globalization can augment the ramifications of catastrophic transnational terrorist events.

Like any agent, terrorists' resources in any period are limited and constrain their actions

to pursue satisfaction derived from a political cause. Because our focus is on the entire series of

terrorist events, terrorists are depicted as allocating their resources between terrorist events (t)

and legal actions ( E(U)]. Terrorist events includes

bombings, skyjackings, assassinations, and other actions, while legal activities include

propaganda statements and gaining a foothold within a base country or countries of operation. A

terrorist group is viewed as allocating scarce resources, R, between legal activities with a certain

gain, g, and terrorist activities with an uncertain gain, gt. A terrorist incident may end in at least

two states: success where the incident is completed as planned, or failure where the incident is

either not completed or fails in its goal. Success is a ran

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only two states of the world are permitted for terrorist events, then (1 –

of failure. A terrorist group's expected utility is

( ) ( ) (1 ) ( ),S FE U U W U W= π + − π (1)

where U(W) is the standard von Neumann-Morgenstern utility function. Arguments WS and WF

are the net wealth equivalent measures over the two states of success, S, and failure, F. These

measures equal:

1( ) ( , )S t tW w g R g R e= + + , (2)

2( ) ( , )F tW w g R f R e= + − . (3)

In equation (2), the net wealth derived from a successful terrorist incident includes the group's

current assets net of current earnings, w, the monetary equivalent net gains from legal activities,

and the monetary equivalent net gains from the terrorist act. R represents the resources assigned

to legal actions, and Rt indicates the resources assigned to terrorism actions. In either state of the

world, monetary gains depend directly on the resources (including time) allocated by the

terrorists to either legal activities or the terror campaign, and these gains are assumed to display

diminishing returns.7 In equation (2), e1 represents the environmental factor that also helps

determine gain during a successful outcome. For example, e1 can reflect actions taken by the

authorities (e.g., freezing assets, retaliatory raids, freedom of press) that influence the benefits of

a terrorist success. As such, e1 denotes a shift parameter.

In equation (3), the net wealth for a terrorist failure includes a group's current assets plus

its net gain from legal activities minus the monetary value of the fine or penalty, f, from failure.

If the group fails but escapes, then this penalty includes wasted resources expended on the

unsuccessful event. When, however, the group is captured, the fine refers to the wasted

resources (including murdered terrorists), the opportunity costs of incarceration, and any

monetary penalties assessed. The loss of one or more terrorists results in the costs of training

7

replacements. In f(•), e2 denotes an environmental factor that influences the level of losses

during failed campaigns. This factor includes activities taken by authorities, such as the severity

of sentences and extradition requests. Once again, e2 represents a shift parameter of the model.

The terrorist group's resource constraint,

R = Rt + R, (4)

closes the model and indicates that the group's total resources, R, are divided each period

between legal and terrorist activities. Expected utility in equation (1) can be rewritten in terms

of the choice variables (R, Rt) and the exogenous shift parameters by substituting equations (2)-

(4) into (1). Both the optimal levels of R and Rt are then determined by maximizing the

resulting expression for expected utility. The likely effects of government policy decisions

e1, and e2 are found through comparative-static analysis, where the

assumption of the model are used to determine the influence that changes in these policy

parameters have on the optimal choice of R and Rt. Often, additional assumptions concerning

the terrorist group's risk attitudes can help sign these comparative-static impacts.

Some results are fairly clear-cut without further mathematical analysis. Actions by the

authorities to decrease the terrorists' total resources through raids on their camps, infiltration of

the group, or by freezing their assets will curtail both legal and terrorist activities. If a retaliatory

raid were to increase the terrorists' perceived gains from terrorist attacks as means of protest,8

then the terrorists will shift resources out of legal activities into terrorist acts. During periods of

high terrorist activities, this ability to sustain even a greater level of terrorist acts is limited in

contrast to periods of low activities.

Thus far, we represent the problem as the choice-theoretic decision of a single terrorist

group. From the early 1970s, terrorist groups, engaged in transnational acts, have been tied

either explicitly or implicitly in networks consisting of left-wing terrorist groups (Alexander and

8

Pluchinsky, 1992) united in their goal to overthrow democratic governments, Palestinian groups

united in their aim to establish a homeland or to destroy Israel, and fundamentalist terrorist

groups (Hoffman, 1998; US Department of State, 2001) united in their goal to create nations

founded on fundamentalist principles. Since the start of 1980, the number of religious-based

groups has increased as a proportion of the active terrorist groups: 11 of 48 groups in 1992, 16

of 49 groups in 1994, and 25 of 58 groups in 1995 (Hoffman, 1997:3). Bin Laden's al-Qaida

network includes Islamic extremist organizations in many countries, which are linked through

finances, training, and a common enemy. This network includes such groups as Abu Sayyaf (the

Philippines), Egypt's Islamic Group, Harakat ul-Mujahidin (Pakistan), Islamic Movement of

Uzbekistan, Al-Jihan (Egypt), and Bin Laden's own group (Afghanistan) (US Department of

State, 2001). Even left-wing groups and Palestinian groups have been known to train together

and to have other ties (Wilkinson, 1986, 2001; Hoffman, 1998), so that separate networks have

explicit links to one another. Implicit ties come from copying each other's tactics – the so-called

demonstration effect. These networks' common hatred of the United States and Israel means that

heightened attacks by groups in one part of the world can spark increased attacks in other parts

of the world. This implicit coordination shows up as distinct cycles of peaks and troughs in

transnational terrorist activities (Enders et al., 1992; Enders and Sandler, 1999).

Thus far, we have only considered the terrorist choice between legal and terrorist

activities. Another choice by the terrorists must, however, be made in allocating Rt among

alternative modes of attacks so as to equate the expected marginal gain per dollar spent on

alternative operations. Actions by the government to increase the difficulty (i.e., the price) of

one kind of attack will cause the terrorists to substitute into other types of attacks that now

appear to be relatively cheaper (Sandler, Tschirhart, and Cauley, 1983; Enders and Sandler,

1993). Thus, it is essential for authorities to impose policies that cause the terrorists to substitute

9

into less harmful modes of attacks. Authorities have not always been successful in this aim –

e.g., increased US embassy security led to a decrease in such attacks, which usually resulted in

no injuries, and to an increase of assassinations of embassy personnel as they left secure grounds

(Enders and Sandler, 1993). In light of these substitutions, the authorities must also raise the

difficulty of all modes of attacks – e.g., by limiting terrorist resources or through intelligence on

terrorist operations.

INTERVENTIONS AND THE DATA

Six interventions or suspected changes to the terrorist time series are germane to our

analysis and discussion. These interventions are listed in Table 1 along with their abbreviations,

description, and initiation period. Although our interest is to apply a methodology that allows

for ex post data identification of significant changes in the time series, these ex ante influences,

due to either policy changes (i.e., metal detectors at airports, enhanced embassy security, or a

retaliatory raid) or political events (i.e., the rise of religious fundamental terrorism or the start of

the post-cold era),9 are required for updating the linear intervention-based analysis to 1999 and

for comparing this latter analysis to the nonlinear techniques presented at a later point. In

previous papers, five of these six interventions resulted in significant shifts to the aggregate

terrorist series and its various component series. The sole exception is the US retaliatory raid on

Libya, which resulted in just an immediate impact that dissipated rapidly as the series returned to

its pre-intervention mean.10

Data on transnational terrorism incidents are drawn from International Terrorism

Attributes of Terrorist Events (ITERATE), which records, among other things, the incident date,

its location, type of event, and casualties (i.e., deaths or injuries), if any. ITERATE 2 covers

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1968-77 (Mickolus, 1982), ITERATE 3 covers 1978-87 (Mickolus, Sandler, Murdock and

Fleming, 1989), and ITERATE 4 covers 1988-91 (Mickolus, Sandler, Murdock and Fleming,

1993). To bring the data set up to date, we coded the necessary variables for 1992:1-1999:4

based on written descriptions provided by Mickolus. Coding consistency for ITERATE 2 and its

various updates has been preserved by applying the same criteria for defining transnational

events and associated variables. This consistency was enhanced owing to an overlap among

coders and monitors – e.g., Sandler participated in the coding of the data for 1977:1-1999:4.

ITERATE drew its information from the world print and electronic sources including the

Associated Press, United Press International, Reuter tickers, major US newspapers (e.g., the

Washington Post and the New York Times), and the Foreign Broadcast Information Service

(FBIS). The FBIS Daily Reports, which draws from hundreds of world print and electronic

media sources, served as the single most important source up through the start of 1996.11

ITERATE does not contain information about state sponsorship, because countries keep this

information secret; hence, we cannot distinguish such events in our analysis.

ITERATE does not classify incidents as transnational terrorism that relate to declared

wars or major military interventions by governments (e.g., Chechnyan acts against Russian

military personnel), or guerilla attacks on military targets conducted as internationally

recognized acts of belligency. If, however, the guerilla attacks were against civilians or the

dependents of military personnel in an attempt to create an atmosphere of fear to foster political

objectives, then the attacks are considered terrorism. Palestinian acts in Israel that do not harm

foreigners are not classified as transnational terrorism. While a domestic event may become

transnational if a foreigner is the unintended victim, instances of this are rare. If this randomness

of victims was great, then the large number of US victims, who are the intended target on

average of about 40 percent of all transnational acts (US Department of State, 1989-2001), would

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not consistently characterize the data totals each year. Official government-sanctioned acts in

response to terrorist attacks, such as the US bombing of Libya or US seizure of an Egyptian

plane carrying the terrorists from the Achille Lauro incident, are not themselves coded.

ITERATE also excludes unintended acts from the data set. If, for example, a foreign newspaper

reporter is killed in the cross fire between government troops and guerillas, the reporter's death is

not considered a terrorist assassination. ITERATE, however, does code terrorist acts against

foreign aid workers or UN peacekeepers.

We extract three quarterly time series from ITERATE: (i) a DEATH series, where one or

more individuals died as a result of the incident; (ii) a WOUNDED series, where one or more

individuals were injured, but no one died, as a result of the incident; and (iii) a

NONCASUALTIES series, where no one died or was injured as a result of the incident. We use

terrorist incident “count” data computed on a quarterly, rather than weekly or daily, basis to

eliminate zero-valued observations, inconsistent with the underlying normal distribution

assumption of the various autoregressive (AR) analyses (Harvey, 1989). Based on Enders and

Sandler (2000), we shall focus on the DEATH series, which has the most deterministic factors of

the three series owing to its intensity. This earlier study showed the NONCASUALTIES series

to be essentially random after detrending and the WOUNDED series to be less deterministic than

the DEATH series. Nevertheless, we shall apply our analysis to all three series.

DUMMY VARIABLES VERSUS THE THRESHOLD MODEL

A number of papers have tried to estimate and forecast transnational terrorist events. One

key issue is to ascertain the effects of various policy interventions and political events on the

occurrence of transnational terrorism. For example, Enders and Sandler (2000) estimated the

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following autoregression (with t-statistics in parentheses):

yt = 4.037 + 0.406 yt-1 + 5.62 METALt – 0.26 EMB76t – 5.92 EMB85t (1.77) (3.22) (2.28) (–0.11) (–3.20)

– 7.93 LIBYAt + 4.17 FUNDt + 6.77POSTt (5) (–1.30) (1.89) (3.19) where yt is the quarterly number of incidents with one or more deaths. METALt, EMB76t,

EMB85t, LIBYAt, FUNDt, and POSTt are all dummy variables that represent the various

intervention points as defined previously in Table 1.

The use of dummy variables in this fashion yields some interesting findings. The impact

of metal detectors in airports is estimated to have increased the number of incidents with deaths

by 5.62 incidents per quarter, implying a substitution from skyjackings into more deadly

events.12 The steady-state value of this increase rises to 9.46 [= 5.62/(1 – 0.406) ] incidents per

quarter. Fortification of U.S. embassies in 1985, but not in 1976, is found to decrease the short-

run number of incidents with deaths by 5.92 incidents per quarter, but with a long-run effect of

9.97 fewer incidents per quarter. Moreover, the break-up of the Soviet Union is found to have a

large positive impact on terrorism: the immediate impact effect is estimated to be 6.77 incidents

per quarter rising to a total of 11.4 incidents per quarter. In Figure 1, incidents per quarter are

measured on the vertical axis and the years on the horizontal axis. The dashed line represents the

actual number of fatal incidents, while the vertical lines indicate the four significant intervention

dates. The solid locus with horizontal segments shows the estimated magnitudes of the effects of

the interventions. To depict the impact of each intervention, we set y1 equal to the actual value

of death incidents in 1970:1 and generated the remaining values using equation (5). It is clear

from Figure 1 that the mean number of incidents rose from about 6.5 to about 16 per quarter after

the installation of metal detectors in 1973. The values are shown through only 1996:2 since

equation (5) was estimated using data from 1970:1 to 1996:2.

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Some words are instructive about the political events behind some of the various peaks in

Figure 1. The peaks in 1976 and 1977 are primarily attributed to activities of Palestinian groups

outside of Israel and left-wing European terrorists (Mickolus, 1982). The spikes in 1981, 1983,

and 1985 are due to terrorist activities by left-wing groups in Europe and South America, as well

as from spillover terrorism from the Middle East (Mickolus et al., 1989). The Libyan retaliatory

raid by the United States and the backlash it caused are behind the peak in 1986. Numerous

Middle-East-motivated deadly terrorist attacks, coupled with Afghan rebel attacks in Pakistan,

led to the spike in 1988 (US Department of State, 1989). Finally, the peaks in the early 1990s

are rooted in religious fundamentalism (by HAMAS and others) and in separatism (in Sri Lanka)

(US Department of State, 1990-96). Actions by the Kurdish Workers Party in Turkey and by

narcoterrorists in Colombia also contributed to these totals. The Afghanistan War trained many

individuals with fundamentalist views, who account for many lethal events in the 1990s and

beyond.

The use of multiple dummies, however, raises a number of concerns as follows:

1. There is a danger of ex post fitting if the break points’ dates are chosen as a result of

an observed change in the variable of interest, then test statistics lose their importance. Clearly,

with enough dummy variables, any series can be fitted to any degree desired. The problem is

reinforced by the fact that the starting dates for the FUND and POST variables were found by a

grid search method, for which the two starting dates were those that maximized the overall fit of

the regression (Enders and Sandler, 1999, 2000). There is, however, less of a problem if

interventions are chosen ex ante based on hypothesized changes to the data that are then tested

for significance.

2. Other incidents that roughly coincide with the break point dates may, in part, be

responsible for the observed change in the series. For example, events surrounding the demise of

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the Soviet Union (as measured by POST) came about the time of the war in Kuwait. As

recognized by Enders and Sandler (2000), it is exceedingly difficult to distinguish between the

influences of two near, but distinct, events.

3. The efficacy of the estimates cannot rely on the usual asymptotic properties of an

autoregression. If there is a single break point, Lutkepohl (1991) showed that the standard

asymptotic properties hold if it is assumed that observations on both sides of the break increase

as sample size increases, but that a “logical problem” arises in the presence of multiple breaks.

Given that there are a fixed number of observations lying between EMB76 and EMB85,

increasing the sample size does nothing to increase the number of points lying between these two

break points. Lutkepohl (1991:410) stated that “… the large sample χ2-distribution … may be

used if the periods between the interventions is reasonable large. Since no small sample results

are available it is not clear, however, how large is large enough to obtain a good approximation

to the asymptotic χ2-distribution.”

4. The interventions need not be modeled as [0, 1] dummy variables; for example, Enders

et al. (1990) used an alternative form for the METAL dummy. Although the United States began

installing metal detectors in its airports in the first quarter of 1973, it took almost a full year for

installation to be completed internationally at major airports. As such, they used an intervention

variable equal to 1/4 in 1973:1; 1/2 in 1973:2; 3/4 in 1973:3; and 1 in 1973:4. More generally,

interventions can have temporary or permanent effects on a series that may grow or fade over

time. The standard way to determine the ‘best’ form of the intervention variable is to use the one

that provides the best in-sample fit.

5. The effects of the different dummies may overlap each other. This could be especially

problematic if there is any misspecification in the way that each dummy is allowed to affect the

system. For example, instead of being a 0 versus 1 dummy, suppose that the importance of

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Islamic fundamentalism has grown over time. The POST variable will then capture some of this

effect, leading some of the subsequent increase in terrorism resulting from FUND to be wrongly

attributed to POST.

6. The effects of the interventions are allowed to affect only the mean of the series, even

though the autoregressive coefficient(s) may themselves be affected by the changes.

7. Finally, there may be other events that influence terrorism, not included in the model –

e.g., political events in the Middle East or Latin America may have had profound effects on the

terrorism series.

Some of the problems with multiple dummy variables are apparent when we re-estimate

equation (5) using an updated version of ITERATE with observations for 1996:3-1999:4. After

incorporating these 14 additional observations into the data set, we obtain the following

regression estimates of the DEATH series:

yt = 4.10 + 0.423 yt-1 + 4.71 METALt – 0.479 EMB76t – 4.91 EMB85t (2.10) (4.98) (1.89) (–0.201) (–2.65)

– 8.64 LIBYAt + 4.02 FUNDt + 2.50 POSTt, AIC = 1008.2, SBC = 1030.4, (6) (–1.37) (1.82) (1.48) where AIC is the Akaike Information Criteria and SBC is the Schwartz Bayesian Criteria.13 If

we omit EMB76t and LIBYAt we obtain:

yt = 4.15 + 0.417 yt-1 + 4.54 METALt – 5.29 EMB85t + 3.80 FUNDt + 2.87 POSTt, (7) (2.13) (4.93) (1.99) (–2.88) (2.11) (1.72)

AIC = 1006.3, SBC = 1022.9.

Even if we use equation (7), it is striking that METALt is barely significant at the 5% level

and POSTt is not significant at the 5% level. Moreover, the absolute values of the magnitudes of

the coefficients and the associated t-statistics for EMB85t and FUNDt are all closer to zero than

in equation (5). Thus, when we use the updated data, it appears that the interventions were not

that important for the DEATH series after all. To explain the erosion in the coefficients and their

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significance, we note that the number of incidents with deaths declined throughout the updated

sample period (see the extended portion of the dashed line in Figure 1), so that the magnitude of

the jump in incidents attributed to the demise of the Soviet Union was not sustained. Moreover,

the decrease in the overall mean of the incident series pushed the t-statistics for the previously

significant interventions closer to zero. Quite simply, the recent decline in the number of

DEATH incidents makes it difficult to interpret the importance of the previous interventions.

Perhaps, the importance of POSTt had just a temporary effect lasting only a few years (see our

previous point 4); there may have been other influences not captured by the interventions (see

point 7); or the original effect of POSTt was due to overfitting (see point 1). Of course, it would

be possible to capture the decline in terrorism with yet another dummy for the 1996:3-1999:4

period, but, this simply compounds the problems encountered when using multiple interventions.

A word of caution and clarification is in order before we present some nonlinear time

series methods for addressing these issues. Linear intervention analysis has its place if

intervention points are chosen ex ante based on theoretical priors. For a skyjacking time series,

the significant of metal detectors would remain even with the addition of another few years of

data because these detectors had such a large and sustained impact on skyjackings. The

influence of metal detectors on the DEATH series, which includes all incidents and not just

skyjackings, is apt to be more tenuous as equations (6)-(7) indicate. Thus, our exploration of

alternative time series methods is not intended to dismiss intervention analysis when used with

theoretical priors in the proper setting.

REGIME-SWITCHING ESTIMATION

One way to circumvent some of the above problems is to estimate the DEATH series

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using a type of regime-switching model. Intuitively, there may be several states of the world and

the severity of terrorism may differ in each. Suppose, for example, that a political event or

policy intervention occurs that causes the amount of terrorism to switch into the high state.

Since terrorists are using relatively large amounts of their scarce resources, it would be

surprising to find that attacks exhibit a high degree of persistence in the high state. Terrorism

could persist in this high state for a while until another event takes place that switches the system

into the low state. Terrorism could then remain low until yet another political or policy shock of

sufficient magnitude occurs that switches the system back into the high state. If our theoretical

model about resource allocation is correct, then we anticipate that activity levels above the

estimated mean of the series for the high state cannot last for long, unlike the low-state scenario

where terrorist resources are not stretched and departures from the mean can persist. The cause

of the shock sufficient to switch the system could be unknown to the researcher; nevertheless, it

is possible to estimate the behavior of the terrorist incidents in the various states.

Consider a two-regime version of the threshold autoregressive (TAR) model developed

by Tong (1983, 1990):

ε+

ββ−

αα= ∑∑

=−

=− t

p

iitit

p

iititt y + I+y + Iy

10

10 )1( , (8)

where yt is the series of interest, the αi, and βi are coefficients or constants to be estimated, τ is

the value of the threshold, p is the order of the TAR model, and It is the Heaviside indicator

function:

τ<τ≥

=−

−

.0

1

1

1

t

tt yif

yifI (9)

The nature of the system is that there are two states of the world. In the high-terrorism

state, yt-1 exceeds the value of the threshold τ so that It = 1 and (1 – It ) = 0, where yt follows the

18

autoregressive process, α0 + Σαiyt-i. Similarly, in the low-terrorism state, yt-1 falls short of the

threshold τ, so that It = 0 and (1 – It ) = 1, where yt follows the autoregressive (AR) process,

β0 + Σβiyt-i. There are essentially two attractors or potential “equilibrium” values: the system is

drawn toward α0/(1 – Σαi) in the high state and toward β0/(1 – Σβi) in the low state. Moreover,

the degree of autoregressive decay will differ across the two states if for any value of i, αi ≠ βi.

The key feature of the TAR model is that a sufficiently large εt shock can cause the system to

switch between states.

The momentum threshold autoregressive (M-TAR) model used by Tong and Lim (1980)

and Enders and Granger (1998) allows the regime to change according to the first-difference of

yt-1. Hence, equation (9) is replaced with

τ<∆τ≥∆

=−

−

.0

1

1

1

t

tt yif

yifI (10)

The M-TAR model is useful in capturing situations in which the degree of autoregressive decay

depends on the direction of change in yt. For example, Enders and Granger (1998) showed

that interest rate adjustments to the term-structure relationship display M-TAR behavior. If,

however, all αi = βi, then the TAR and M-TAR models are equivalent to an AR(p) model.14

!"-TAR models is straightforward.

Simply set the indicator function according to equations (9) or (10) and form the variables Ityt-i

and (1 – It )yt-i. The coefficients of equation (8) can be estimated using ordinary least squares

(OLS), and the lag length p determined as in an AR model.15#$%&''(

showed how to obtain a super-consistent estimate of the threshold parameter. For a TAR model,

the procedure is to order the observations from smallest to largest such that:

y1 < y2 < y3 ... < yT. (11)

For each value of yj)yj, set the Heaviside indicator according to equation (9), and estimate

19

an equation in the form of equation (8). The regression equation with the smallest residual sum

of squares contains the consistent estimate of the threshold. In practice, the highest and lowest

15 percent of the yj values are excluded from the grid search to ensure an adequate number of

observations on each side of the threshold. For the M-TAR model, equation (11) is replaced by

the ordered first-differences of the observations.

Notice that the TAR model overcomes a number of the problems involved with the use of

dummy variables. Most importantly, the dates of the regime switch at which the series passes

the threshold are not specified ex ante by the researcher; instead, the data itself determine

whether the series is in the high- or low-terrorism state. Since there are no specific intervention

points, the standard asymptotic properties of the estimates hold. For example, the asymptotic

properties of the estimates are such that individual coefficients can be tested using standard t-

statistics and joint restrictions – such as the symmetry restriction that all αi equal all βi – can be

tested using an F-test. Obviously, there are no overlapping dummy variables and the alternative

regimes are allowed to affect the degree of autoregressive decay as well as the mean of each

series. If, therefore, the goal is to determine the magnitude of any specific intervention, such as

the effect of the end of the Cold War, then the TAR model is not especially useful, because it

includes no exogenous variables. This again emphasizes that alternative time series methods can

fulfill different purposes making them complementary.

THE ESTIMATED THRESHOLD MODEL

We begin by estimating the DEATH series as a threshold autoregressive process with a

single lagged value. As indicated by equation (7), we search over all potential thresholds to

obtain (with t-statistics in parentheses):

20

yt = [ 19.95 + 0.07yt-1 ] It + [ 7.09 + 0.47yt-1 ] (1 – It ), (12) (4.63) (0.38) (3.10) (2.39)

where the estimate of the threshold is τ = 18. If we purge the model of the insignificant lagged

coefficient occurring whenever yt-1 ≥ 18 and re-estimate the model, we obtain:16

yt = [ 21.53 ] It + [ 7.09 + 0.47yt-1 ] (1 – It ), (13) (23.02) (3.12) (2.41) AIC = 1005.4, SBC = 1016.5.

Diagnostic checking indicates that the model is appropriate. For example, the first eight

autocorrelations of the residuals are less than 0.13 in absolute value and the Ljung-Box Q-

statistics for 4, 8, and 12 lags indicate that there are no significant residual correlations at

conventional levels. We also estimate the model setting p = 2, and find that the coefficients of

yt-2It and yt-2 (1 – It) are both insignificant. We set the indicator function using the M-TAR

specification. Our estimated models never fit the data as well as the TAR models reported

above.17 Finally, Tsay’s (1989) method of arranged autoregressions do not yield any evidence of

multiple thresholds.

For comparison purposes, we estimate the DEATH series as a linear autoregression. The

best-fitting model is the following AR(1) equation:

yt = 6.81 + 0.56yt-1, AIC = 1012.1, SBC = 1017.7. (14) (5.03) (7.25) Notice that AIC and SBC both select the TAR model over the linear model. In addition, as

measured by either criteria, the TAR model fits better than either intervention model reported in

equations (6) and (7). This is particularly important since the TAR model makes no use of the

“explanatory” variables employed in the intervention model. In fact, the SBC actually selects the

linear model over either of the intervention models!

The threshold model yields very different implications about the behavior of the terrorism

DEATH series than the linear models. The linear AR(1) model indicates that the sequence

21

convergences to the long-run mean of approximately 15.5 incidents per quarter [ 6.81 ÷ (1.0 –

0.56) ≈ 15.5 ]. Moreover, the degree of autoregressive decay is always constant. Regardless of

whether the number of incidents is above or below the mean, the degree of persistence is

estimated to be 56%. In contrast, the estimated threshold model in equation (13) suggests there

is no single long-run equilibrium value for the number of incidents, since there are high- and

low-terrorism regimes or states. In the low state, the system gravitates toward 13 incidents per

quarter [ 7.09 ÷ (1.0 – 0.47) ≈ 13 ]. The point estimates of this low-state regime are similar to

those of the linear AR(1) model. When the number of incidents exceeds the 18-incident

threshold, there tends to be an immediate jump to 21.53 incidents per quarter. Whenever the

number of incidents exceeds 21.53, we estimate that there will be an immediate decline to 21.53

incidents in the subsequent quarter, so that, there is no persistence for terrorist activity exceeding

the key value of 21.53 incidents.18 The high-incident state can be maintained until a shock of

sufficient magnitude causes a switch of regime; but, the number of events in this high-incident

state cannot be maintained at more than 21.53 incidents. Since the estimated standard deviation

*t is equal to 6.14, the magnitude of a typical shock is likely to cause a regime switch. In

fact, we uncover a number of short-lived terrorist campaigns of heightened activity (including

one immediately following POST) – see Figure 1.

We also examine other incident series for threshold autoregressive effects. We find no

evidence of any autoregressive behavior in the non-causality series, which is dominated by

threats, hoaxes, letter bombs, and other low-intensity activities. As these incidents use few

resources, it is to be anticipated that they contain no predictable pattern. The number of

incidents containing wounded individuals (but no deaths) appeared to be a symmetric AR(2)

process. One explanation is that a TAR specification is not appropriate to capture the form of the

non-linearity in this series. Another is that these incidents use few resources relative to incidents

22

with deaths, so that there may not be any important differences in the persistence of this type of

terrorism.

THE FOURIER APPROXIMATION

As indicated above, the TAR model cannot ascribe the effects of a regime switch to any

particular event. An alternative way to capture any potential non-linearity's in the data is to use

the methodology of Ludlow and Enders (2000), where a simple modification of the

autoregressive framework allows the autoregressive coefficient to be a time-dependent function

%t). For simplicit !%& %t) is

an absolutely integral function, for any desired level of accuracy, then it is possible to write:19

yt)%t)yt-1+t, (15)

with sin coss

0 k kk=1

2 k 2 k(t)= + t + t A A B

T T

π π α • • ∑ ,

where s refers to the number of f , %t).20

The key point is that the behavior of any deterministic sequence can be readily captured

by a sinusoidal function even though the sequence in question is not periodic. As such, non-

linear coefficients may be represented by a deterministic time-dependent coefficient model

without first specifying the nature of the asymmetry. The nature of the approximation is such that

the standard ARMA model emerges as a special case. If the actual data-generating process is

linear, all values of Ak and Bk in equation (15) should be zero. Thus, instead of positing a

specific model, the specification problem is transformed into one of selecting the proper

frequencies to include in equation (15). Ludlow and Enders (2000) called the approximation in

equation (15) an F-ARMA process. Since the value of s can be large, the estimation problem is

23

to determine the particular Fourier coefficients to include in the analysis.

More generally, both the intercept and the degree of autoregressive decay may fluctuate

over time and it is possible to apply the method to both coefficients. Because the nonlinear

estimation may be quite complicated, we restrict ourselves to only two frequencies for the

intercept and only one (possibly different) frequency for the degree of autoregressive decay. We

use nonlinear optimization methods to obtain the maximum-likelihood estimates of:

1 1 2 20 1 2 3 4sin cos sin cost

2 k 2 k 2 k 2 k = c c ( t) + c ( t) c ( t) + c ( t) y

T T T T

π π π π+ • • + • •

3 31 1 2 3sin cos .tt t -1 t -1

2 k 2 ka y a ( t) + a ( t) + y y

T T−π π+ + • • ε (16)

The interpretation of equation (16) is that the magnitudes of any fluctuations in the

intercept term are captured by nonzero values of c1 through c4. Similarly, fluctuations in the

degree of autoregressive decay are captured by nonzero values for a2 and a3. The frequencies of

the fluctuations in the intercept are given by k1 and k2, while the frequency of the fluctuations in

the autoregressive parameter is given by k3. Clearly, the linear AR(1) model is the special case

of equation (16) where the c1 = c2 = c3 = c4 = a2 = a3 = 0. Because we are not interested in the

very high frequency changes, we limited the analysis to frequencies no greater than 10. With

100 observations, Ludlow and Enders (2000) found that the critical values for a2 and a3 are each

2.06, 2.39, and 3.02 at the 10%, 5%, and 1% significance levels, respectively. Similarly, Davies

(1987) found that the critical values for the F-statistic of c1 = c2 = 0 (c3 = c4 = 0) are 10.66,

12.18, and 15.63 at the 10%, 5%, and 1% significant levels.

The Fourier approximation in equation (16) is something quite different from the

standard Spectral Analysis. The periodiogram used in Spectral Analysis is obtained from the

Fourier expansion:

[ ] t

T

kkkt TktcTktccy ε+π+π+= ∑

=

2/

10 )/2cos()/2sin( . (17)

24

In particular, Spectral Analysis uses all possible integer frequencies in the interval k = [1, T/2] in

order to assess relative contribution of high, medium, and low frequencies to the total variation

of yt. Instead, equation (16) uses only the two most significant frequencies in order to

approximate a time-varying intercept term. This is supplemented by a (possibly) third frequency

to approximate a time-varying degree of autoregressive decay. Estimating (16) and eliminating

the coefficient with t-values less than 1.96 in absolute value, we obtain:21 c0 = 11.84 (11.77), c1

= –3.24 (–5.63), c3 = –2.85 (–5.31), a1 = 0.24 (4.05) and a3 = –0.14 (–2.96), where t-statistics are

in parentheses. In addition, the frequencies are k1 = 2.105, k2 = 3.23, and k3 = 6.80.

Given that there are two frequencies for the intercept and that the degree of

autoregressive decay oscillates, the time path for the estimated series is highly nonlinear. In

order to depict the estimated movements of yt, we set y1 equal to the actual number of

incidents in 1970:1 and generated the values through 1999:4 using our estimated coefficient

values. The resulting series is shown as the fluctuating solid line in Figure 2.22 For comparison

purposes, we also include the actual number of incidents and the effects of the interventions

(now updated through 1999:4) that were shown in Figure 1.

The intervention and the F-ARMA models both suggest (i) an increase in DEATH

incidents after the installation of metal detectors in 1973 (METAL), (ii) an increase near 1979

(around the time of FUND), (iii) a sharp decline at the time of embassy fortifications in 1985

(EMB85), and (iv) a relatively constant time profile through 1992. Overall, the F-ARMA model

tracks the actual series much better than the intervention model. There are, however, some

interesting comparisons to be drawn from the different estimates of the intervention and Fourier

models. As displayed in Figure 2, the intervention model in equation (7) estimates that metal

detectors had a long-run impact of 7.79 incidents per quarter with the full impact on the DEATH

series being attained almost immediately. The Fourier model tells a different story. Beginning

25

in 1973:1, the estimated number of DEATH incidents rose steadily until the third quarter of

1976. If all of this increase can be ascribed to the deployment of metal detectors, the estimated

long-run impact is 14 DEATH incidents per quarter (22 estimated incidents for 1976:3 minus

eight estimated incidents in 1972:4). Part of the discrepancy between the two estimates might be

that the installation of the detectors was not immediate. The installation of these detectors in US

airports was immediate in 1973:1, while their installation in non-US airports took place more

gradually (Enders et al., 1990).

A very interesting comparison emerges with respect to the POST variable. The

intervention results in equation (7) give the long-run impact of POST to be 4.92 additional

DEATH incidents per quarter. In contrast, the Fourier model estimates that the DEATH series

gradually rose from approximately 11 to 27 incidents throughout the 1991-94 period. Thereafter,

DEATH incidents steadily declined until the end of the sample period.

IMPLICATIONS AND POLICY RECOMMENDATIONS

In this section, we shall draw some implications and policy recommendations in regards

to the events of 11 September 2001, based on the analysis of this paper and our cumulative work

on examining terrorist time series. The attack on the World Trade Center and the Pentagon came

during a time when transnational terrorism was in a relatively low-activity period. Retaliatory

strikes typically produce a shock to the time series that generates higher levels of attacks as

terrorists protest the action (Enders and Sandler, 1993). An intertemporal substitution occurs as

terrorists move attacks planned for the future into the present to demonstrate their displeasure.

The TAR analysis findings indicate that this heightened activity can be sustained for a long

period, because it will be coming during a low-activity period when resources can be shifted

26

from nonterrorist activities of these terror networks. Thus, nations associated with the alliance

forged by the United States must be vigilant for these increased attacks not only during the

period of military action begun on 7 October 2001, but also well after this period. This means

that national guard at US airports may need a longer deployment than originally planned (i.e.,

longer than six months).

All time series associated with terrorist events display cyclical behavior (Enders et al.,

1992; Enders and Sandler, 1999). This is also true of the time series with one or more casualties

(i.e., death or injuries). In Enders and Sandler (2000:322), the length of the cycles for the

casualties time series is just under two years. Thus, the trough in Figure 2 at the end of 1999 is

anticipated to be followed by a peak toward the end of 2001, which proved to be an accurate

prediction. Our work23 on the relationship between the rise of fundamentalist terrorism and

heightened casualties from terrorist attacks suggests that terrorist attacks as a reaction to

retaliatory strikes will involve a greater number of casualties than, say, the increased terrorism

following the US retaliatory raid on Libya in April 1986.

If there is a basic message from our work on the effects of policy interventions, it is that

piecemeal policy is ineffective.24 That is, efforts to secure US airports and borders will cause

terrorists to stage their attacks at other venues and in other countries against Americans. Quite

simply, terrorists respond to “higher prices” for one mode of attack stemming from a policy

intervention (e.g., better metal detectors and security screening at airports) by substituting into an

alternative mode where measures have not been taken. The installation of metal detectors in

airports cut down on skyjackings but was associated with an increase in other kinds of hostage-

taking events (Enders and Sandler, 1993). Despite recent events in New York and Washington,

DC, Americans are still most vulnerable abroad. Consider the statistics for 2000, during which

there were 423 transnational terrorist attacks worldwide. Although not a single such attack

27

occurred in the United States, 200 of these attacks were against US people or property (US

Department of State, 2001:1). This poses a real dilemma for the United States, because security

measures abroad cannot be dictated to other countries. Actions by the United States to protect its

diplomatic and military personnel abroad will make its unprotected citizens more inviting

targets.

The kinds of actions that work best accomplishes one of two outcomes: a reduction in

the resources of terrorists or an increased difficulty associated with all modes of attack.

Coordinated strikes to hit the al-Qaida network throughout the world are required to attain the

first outcome. Cooperative efforts worldwide to freeze al-Qaida’s assets would also foster the

first outcome. To raise the “price” of all modes of terrorist attacks, countries would have to

increase security throughout society, which impinges on personal freedoms in liberal

democracies. Moreover, such massive actions would be prohibitively costly to countries. A

cheaper means for accomplishing the second outcome would be better field intelligence so that

any kind of planned terrorist incidents can be stopped in the planning stage.

The fight against transnational terrorism presents a serious collective action problem to

nations confronting the threat of terrorist acts. Destroying a global terrorist network represents a

pure public good to all targeted nations, because its destruction yields benefits that are both

nonrival and nonexcludable among nations (Sandler, 1997:129-138). As such, nations are apt to

free ride on the efforts of the country or countries that perceive the greatest benefits from such

actions. Given the events of 11 September 2001, the country with the most at stake from

destroying this network is the United States, followed by the United Kingdom, which lost the

second greatest number of its citizens in the World Trade Center attack. The US interest is

bolstered by it being the primary target of transnational terrorism for the last couple of decades

(US Department of State, 1989-2001). Despite the invocation of Article 5 of the NATO Treaty,

28

the rooting out of the al-Qaida and other networks is anticipated to be primarily an American

operation. There is an irony here, because collective action among terrorist groups in sharing

training and financing has been quite substantial. To date, this suggests that terrorists are more

united in their common goals than are countries in addressing the transnational terrorist threat.

Perhaps, the recent horrors will change this collective action failure.

In the terrorists’ attempt for greater brutality and casualties to capture media attention, it

will be difficult to outdo the carnage or terror of 11 September. The casualties from the four

simultaneous skyjackings are equal to the cumulative deaths from all transnational terrorist

events between 1985 and 2000 (US Department of State, 1989-2001). This suggests that

symbolic targets at home and abroad that rival the World Trade Center or the Pentagon may be

chosen for the annual spectacular event that has characterized transnational terrorism over the

last 30 or so years. Another means for achieving greater casualties would be to resort to

weapons of mass destruction (e.g., biological or chemical agents) as portended by the Sarin

attack on the Tokyo subway on 20 March 1995 by Aum Shinrikyo.25 Clearly, transnational

terrorism has taken on a new threat level since 11 September.

This heightened threat level suggests that this date should be investigated as an

intervention point in future time series studies as time progresses. Have the events of this day

changed the pattern of transnational terrorism? For example, do future attacks involve greater

numbers of casualties? Has the mix of attack modes or where terrorist incidents are staged

changed since 11 September? These are questions for future time series investigations. Another

issue concerns the war on terrorism coordinated by the United States that started on 7 October

2001. The effectiveness of this war can be evaluated using intervention analysis, intervention-

VAR techniques, and TAR methods. Given its greater objective to root out terrorist networks,

this retaliatory war might have a more permanent impact than past episodic retaliations.

29

CONCLUDING REMARKS

Each advance in the study of time series provide a new method that can be applied to the

analysis of transnational terrorism. In the current paper, we have used a regime-switching model

to find turning points in the time series of events, for which one or more persons die. The so-

called DEATH series is used because it is more predictable than less-intense series where

individuals are either injured or unscathed. A regime-switching model offers a better fit than

either a linear AR(1) representation or an intervention representation, with one or more dummy

variables for policy changes. With the regime-switching depiction, increases in activity above

the mean are not sustainable during high-terrorism eras, while there is a 56% persistence for

changes around the mean during low-terrorism eras. This finding has implications for policy or

political decisions that may result in either a regime switch or else a shock, insofar as the

persistence of such shocks depends on whether terrorist activities are already running high or

low.

We also applied a Fourier approximation to the nonlinear estimates of the DEATH series

for 1970:1-1999:4. In so doing, we derive better estimates than those that characterize earlier

articles. Our Fourier-series-based estimates are superior in identifying recent downturns in the

lethality of transnational terrorism in the post-cold war era.

The appropriate technique depends on the issue under investigation – there is no time

series method best for all issues. The TAR model is best applied to a single time series at a time

in contrast to the VAR model. If, for example, the effectiveness of a policy intervention – e.g.,

heightened security measures at US airports in the wake of the 11 September attacks – is under

scrutiny, then intervention analysis applied to the study of multiple time series is the preferred

30

methodology. When a single time series is pertinent, TAR and intervention analysis can be both

applied to determine which results have the better statistical properties. In the case of the

DEATH series, TAR appeared to be the more appropriate representation.

31

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35

Footnotes

1. This definition captures the essential features of those in the literature. See Hoffman

(1988, chap. 1), Mickolus (1982), and Schmid and Jongman (1988).

2. Since no claim of responsibility or demands have been made in wake of the attacks,

no one knows for sure what these atrocities were intended to achieve. If the attacks were

directed by Osama Bin Laden, as the evidence suggests, then his demands are the ones listed in

parentheses.

3. The seminal study on the terrorist dilemma confronting a liberal democracy is

Wilkinson (1986).

4. Articles that analyze trends and cycles include Cauley and Im (1988), Enders, Parise,

and Sandler (1992), and Enders and Sandler (1999). A pioneering analysis by Midlarsky,

Crenshaw, and Yoshida (1980) was the first to employ the autocorrelation function in the study

of terrorist time series.

5. The causality between transnational terrorism and Spanish tourism was investigated

by Ender and Sandler (1991), whereas the relationship between terrorism and foreign direct

investment for a few select countries was studied by Enders and Sandler (1996).

6. On these transboundary externalities, see Sandler and Lapan (1988).

7. Diminishing returns to terrorists’ resources are reflected by 0, 0, 0,t tR R RRg g g> > <

and 0,RRg < where subscripts on the respective gain function indicate first- and second-order

partial derivatives. These partials indicate that resources have a positive, but declining, marginal

impact on gain.

8. Studies on the aftermath of retaliatory raids have consistently found an heightened

level of terrorism following such raids (Enders and Sandler, 1993; Brophy-Baermann and

Conybeare, 1994).

36

9. With the start of the post-cold war era, there is a ratcheting down of the number of

terrorist events as state-sponsors reduced their support of transnational terrorism, and Russia and

the United States had few faceoffs (Enders and Sandler, 1999, 2000; Hoffman, 1998).

10. The impact of these interventions was shown in Enders and Sandler (1993, 1999,

2000) and Enders et al. (1990).

11. For a more in-depth description of the sources for ITERATE, consult Mickolus,

Sandler, and Murdock (1989, vol. 1, pp. ix-xxvi). This source also has the working definition for

transnational terrorism that the coders were instructed to apply.

12. This substitution into more deadly events is also shown in Enders and Sandler

(1993).

13. AIC is calculated as T•rss + 2•k, where T = number of usable observations, rss =

residual sum of squares, and k = number of parameters estimated. SBC is calculated as T•rss +

ln(T)•k. Note that the SBC tends to select the more parsimonious model since it heavily

penalizes the inclusion of additional coefficients (k).

14. AR(p) refers to an autoregressive model with a lag length of p periods.

15. To allow for the different intercepts, we must include It and (1 – It) as regressors.

16. For the TAR model, the value of τ has to be estimated. Hence, we include it as a

parameter when calculating the AIC and the SBC (i.e., we add 1 to the value of k ).

17. To save space, we do not report the estimated M-TAR models. Moreover, Tsay’s

(1989) method of arranged autoregressions do not yield any evidence of multiple thresholds or of

a delay parameter other than unity. Details are available from the authors on request.

18. Similarly, when there are more than 18, but less than 21.53 incidents, we estimate

that there will be a jump to 21.53 units in the subsequent period. Thus the skeleton of the system

is such that there are two long-run equilibria: 13 and 21.53 DEATH incidents per quarter.

37

Because the equilibrium value in the high-terrorism state is close to the threshold value of 18,

shocks are more likely to cause the system to shift from the high to the low state than from the

low to the high state.

&'-%t) have the Fourier expansion:

••∑

∞

tT

k2 B + t

T

k2 A + = (t) kk

=1k0

ππαα cossin

and define Fs(t) to be the sum of the Fourier coefficients:

•π•π∑ t

T

k2 B + t

T

k2 A = (t)F kk

s

1=k

s cossin .

Then, for any arbitrary positive number h, there exists a number N such that:

| – Fs(t) | .h for all s / N.

20. The Fourier approximation can also be applied to any changes in the intercept term

and/or any moving-average terms.

21. Davies (1987) provides critical values for the F-statistic but does not provide critical

values for the individual t-statistics. The eliminated coefficients for the mean (i.e., c2 and c4)

each had a t-statistics of less than 1.4 in absolute value. As these coefficients are small relative

to their standard error, the time path of the Fourier model, later shown in Figure 2, is virtually

unaffected by the exclusion.

22. Note that these are not 1-step ahead forecasts – instead, they are analogous to the

fitted values from the intervention model. The series shown represents the fitted values of yt if

*t had been equated to zero.

23. Enders and Sandler (2000) showed that in recent years, each incident is almost 17

percentage points more likely to result in death or injuries. This increased lethality was related

to the shift away from left-wing terrorism to fundamentalist terrorism.

38

24. For a theoretical model on the ineffectiveness of piecemeal policy, see Sandler and

Lapan (1988).

25. During rush hour, eleven sarin-filled bags planted on five subway trains created

terror, pandemonium, and injuries at fifteen Tokyo subway stations, resulting in the deaths of

twelve people and the hospitalization of more than 5,000.

Interventions Actual

Figure 1: Effects of the InterventionsEstimated through 1996:2

years

Inci

den

ts p

er q

uar

ter

70 73 76 79 82 85 88 91 94 970

5

10

15

20

25

30

35

40

Fourier Actual Intervention

Figure 2: The F-ARMA and Intervention Models

years

Inci

den

ts p

er Q

uar

ter

70 73 76 79 82 85 88 91 94 970

5

10

15

20

25

30

35

40

Table 1. Interventions

Abbreviation Description Starting Date

METAL Metal detectors installed in US airports on 5 January 1973, followed shortly thereafter by their installation in airports worldwide.

1973:1

EMB76 A doubling of the spending to fortify and secure US

embassies beginning in October 1976. 1976:4

FUND The rise of religious fundamentalist-based terrorism

starting with the 4 November 1979 takeover of the US embassy in Tehran. Intervention date established statistically in Enders and Sandler (2000).

1979:4

EMB85 Further increases in spending to secure US embassies by

Public Law 98-533 in October 1985. 1985:4

LIBYA US retaliatory raid against Libya on the morning of 15

April 1986 for its alleged involvement in the terrorist bombing of La Belle Discothèque in West Berlin on 5 April 1986.

1986:2

POST The start of the post-cold war era with the official demise

of the Warsaw Pact on 1 July 1991 and the breakup of the Soviet Union on 20 December 1991.

1991:4

* For just LIBYA, the dummy variable for the intervention is 1 for the quarter beginning the intervention and 0 thereafter. For the other five interventions, the dummy variable remains at the value of 1 for all periods after the intervention

AN ECONOMIC PERSPECTIVE ON TRANSNATIONAL TERRORISM

by

Todd Sandler School of International Relations University of Southern California

Von Kleinsmid Center 330 Los Angeles, CA 90089-0043

tsandler@usc.edu 213-740-9695

213-742-0281 (fax)

and

Walter Enders* Department of Economics, Finance, and Legal Studies

University of Alabama Tuscaloosa, AL 35487 wenders@cba.ua.edu

205-348-8972 205-348-0590 (fax)

February 2002

*Walter Enders is the Lee Bidgood Chair of Economics and Finance in the School of Business at the University of Alabama. Todd Sandler is the Robert R. and Katheryn A. Dockson Professor of International Relations and Economics. He is a member of the School of International Relations and the Department of Economics at the University of Southern California. Sandler acknowledges research support from the Center for International Studies, University of Southern California to update the ITERATE data for 1999-2000. The authors have profited from helpful comments from Daniel Arce.

AN ECONOMIC PERSPECTIVE ON TRANSNATIONAL TERRORISM

On 11 September 2001, the world watched aghast as two commercial airliners toppled the

twin towers of the World Trade Center and a third airliner plowed into the Pentagon. Yet a

fourth hijacked plane landed short of its intended Washington, DC target as passengers took

matters into their own hands. Economic methods – both theoretical and empirical – have been

applied by a small group of economists to understand a host of issues associated with such

terrorist events. These issues concern the policy effectiveness of alternative responses (e.g.,

toughening punishments, retaliatory raids, installing technological barriers), negotiation

responses in hostage incidents, the terrorists’ choice of target, the economic impacts of terrorism,

and others.

Terrorism is the premeditated use, or threat of use, of extranormal violence to obtain a

political objective through intimidation or fear directed at a large audience. An essential aspect

of this definition concerns the presence of a political objective (e.g., getting the United States out

of the Persian Gulf states) that the terrorist acts or campaigns of terror are designed to achieve.

Incidents that have no specific political demand are criminal rather than terrorist acts – e.g.,

extortion for profit. Another crucial ingredient is the use of extranormal violence or brutality to

capture news headlines. As the public becomes numb to their acts of violence, terrorists respond

with more ghastly actions to recapture media attention. Thus, the escalation experienced on 11

September 2001 came as no surprise to those who study terrorism. Moreover, terrorists often

direct their violence and threats toward a vulnerable target group, not immediately involved with

the political decision-making process that they seek to influence. The two planes that were

crashed into the World Trade Center fit this pattern, while the planes that were intended for

targets in Washington, DC do not fit this pattern. In a deliberate attempt to create a general

atmosphere of fear, terrorists strike at a variety of targets with alternative modes of operations

2

(e.g., assassinations, bombings, kidnappings), thus making it difficult for the authorities to

anticipate the venue of the next incident. Such actions make attacks appear to be random, so that

a targeted society must expend large amounts of resources to protect a wide range of

vulnerabilities. This simulated randomness provides terrorists with a cost advantage over the

stronger authorities who must defend against the threat that they pose (Hirshleifer, 1991).

Because people tend to overrespond to unlikely catastrophic events while ignoring more likely

daily dangers (e.g., dying in a car accident), terrorists succeed in achieving society-wide anxiety

with a minimal amount of resources.

When a terrorist incident in one country involves victims, targets, institutions,

governments, or citizens of another country, terrorism assumes a transnational character. In the

World Trade Center tragedy, citizens from over 80 countries lost their lives at the hands of

terrorists who crossed into the United States from abroad. Obviously, the four hijackings on 11

September constitute transnational terrorist attacks. The kidnappings of foreigners in Lebanon

during the 1980s, as a protest against Israeli-occupied territory, also represent transnational

terrorism. Transnational terrorist incidents are transboundary externalities, insofar as actions

conducted by terrorists or authorities in one country may impose uncompensated costs or

benefits on people or property of another country. As such, myriad market failures are

associated with collective actions to curb international terrorism.

The application of economic methods to the study of terrorism began with Landes (1978),

who applied the economics of crime and punishment to the study of skyjackings in the United

States. Economic methodology is particularly well-suited to provide insights over and beyond

those from a political science approach, the latter of which has stressed definitions, institutional

factors, and case studies in an inductive framework (see, e.g., Crenshaw, 1992; Hoffman, 1998;

Wilkinson, 1986; Wilkinson and Stewart, 1987). First, economic analysis can account for the

3

strategic interactions among opposing interests – e.g., the terrorists and the authorities, between

two targeted countries. Second, rational-choice models, based on microeconomic principles, can

be applied to ascertain how terrorists are apt to respond to policy-induced changes to their

constraints. The same methods can be used to analyze how governments react to terrorist-

induced changes to their policymaking environment. Third, the theory of market failures can

underscore how independent pursuits of well-being by the agents may be at odds with socially

efficient outcomes. Thus, governmental failures may result from well-intentioned policies.

Fourth, various economic empirical methods can be applied to evaluate theoretical predictions

and policy recommendations.

The primary purpose of this article is to demonstrate novel insights already gained from

applying an economic perspective to a political problem. A second purpose is to highlight the

role of game theory and other modern economics tools in the study of transnational terrorism. A

third purpose is to present some new applications of economic methods to this crucial problem

area.

A Look at the Data

To provide a perspective of the nature of the transnational terrorist threat, we compile

Table 1 based on data from the US Department of State (1988-2001). This table indicates the

annual number of transnational terrorist events, the associated deaths, the number of wounded,

and the number of attacks against US people and/or property. A number of essential facts can be

drawn from these numbers. First, transnational terrorism on average results in relatively few

deaths, especially when compared with the annual 40,000 people killed on US highways, so that

the events on 11 September are clear outliers. In fact, the deaths on this single day is

approximately equal to all transnational terrorist-related deaths recorded during the entire 1988-

4

2000 period. Second, transnational terrorism appears to follow a cyclical pattern with much of

the 1990s being a relatively calm era. Something that cannot be seen from Table 1 is that a high

proportion of total casualties for a given year is typically associated with a couple of

“spectacular” events – e.g., the simultaneous bombings of the US Embassies in Nairobi, Kenya

and Dar es Salaam, Tanzania account for 291 deaths and almost 5,000 injuries in 1998 (US

Department of State, 1999). Third, attacks against US interests account for a relatively high

proportion of events. This is particularly noteworthy from an externality viewpoint, because

relatively few incidents take place on US soil – in 1998 and 2000, there were no such events,

while, in 1999, there was just one such event (US Department of State, 1999-2001).

By having relatively secure borders, the United States must rely on foreign governments

to protect US citizens and property while abroad. Terrorists that target US interests – e.g.,

Revolutionary Organization 17 November in Greece – may operate with impunity if the risks to

foreigners are of little concern to the local government.1 This leads to underdeterrence of

terrorism from a multi-country viewpoint (Lee, 1998). If, instead, much of the threat is to a host

country’s interests, then overdeterrence may result as the country does not account for the

transference externality of causing the terrorists to switch their attacks to another less-protected

country. In the overdeterrence scenario, each country engages in a Prisoners’ Dilemma “arms

race” to deflect the common terrorist threat to an alternative venue (Sandler and Lapan, 1988).

Unless such actions decrease the overall level of attacks, each country expends resources without

reducing the overall threat or securing their citizens’ safety, which is particularly relevant when

these citizens are targeted in other countries. This is a real concern for the United States, which

has deflected almost all attacks on its interests to foreign soil.

Data

5

Except for some annual totals, government-collected data sets have not been made

available to researchers. RAND also maintains data on significant transnational terrorist

incidents and has made it available to some researchers. Edward Mickolus (1980, 1982)

developed a data set, International Terrorism: Attributes of Terrorist Events (ITERATE) for

1968-77. This incident-based data set was extended to cover 1978-87 and 1988-91 by Mickolus,

Sandler, Murdock, and Fleming (1989, 1993). More recently, Fleming (2001) has updated some

40 variables for 1992-98, while Sandler has updated select variables for 1999-2000. ITERATE

uses a host of sources for its information, including the Associated Press, United Press

International, Reuters tickers, the Foreign Broadcast Information Service (FBIS) Daily Reports,

and major US newspapers (e.g., the Washington Post, New York Times).

ITERATE poses a number of shortcomings that researchers must take into account when

testing theories. By relying on newspaper accounts, ITERATE is better at chronicling the

actions of terrorists (e.g., number of terrorists in a hit squad, terrorists’ actions during

negotiations) than in recording those of the authorities. In select instances, government strategy

is revealed by newspapers and is coded by ITERATE. Because ITERATE is an events data set,

researchers must rely on event counts rather than on continuous measures of intensity unless

casualty counts are used (Enders and Sandler, 2000, 2001). ITERATE picks up newsworthy

transnational terrorist incidents, so that there is some bias, which must be recognized. The bias

is worsened since mid-1996 when the FBIS Daily Reports was no longer available to ITERATE

coders.

Despite these difficulties, ITERATE is suited to a wide range of empirical tasks. For

example, it can display trends and cycles for newsworthy events for forecasting purposes (e.g.,

Cauley and Im, 1988; Enders, Parise, and Sandler, 1992). The data have even been used to

investigate terrorist and government bargaining behavior in hostage-taking events – i.e.,

6

kidnapping, skyjackings, and takeover of facilities (barricade and hostage-taking events) – by

Atkinson, Sandler, and Tschirhart (1987). This latter study applied a time-to-failure model,

where the length of an incident is related to choice variables of the adversaries – e.g., sequential

release of hostages, allowing deadlines to pass uneventfully, number of hostages secured.

Based on ITERATE data, we display two quarterly time series – all transnational

incidents and bombings – in Figure 1 for 1970-2000. From Figure 1, we can see that

transnational terrorism displays peaks and troughs. Bombings are the favorite mode of operation

of terrorists, accounting for about half of all transnational terrorist incidents on average in any

given year. Additionally, the bombing time series tracks the all-incident series rather well. The

latter half of the 1990s represents a downturn in transnational terrorism due, in large part, to

fewer states sponsoring terrorism in the post-Cold War era (Enders and Sandler, 1999). In

Figure 2, the quarterly time series for assassinations and hostage-taking events are displayed for

1970-2000. Cycles are again prevalent. The two time series display far fewer incidents per

quarter than bombings. If terrorists are rational actors, as we suppose, then they should respond

to risk and engage less frequently in those events that are more risky and logistically complex,

such as assassinations and hostage taking (Sandler, Tschirhart, and Cauley, 1983). Insofar as

terrorists must allocate scarce resources from a budget (resource) constraint to alternative tactics,

choices among attack modes are interdependent.

In Figure 3, we display the quarterly percentage of incidents with casualties (i.e., deaths

or injuries) for the 1970-2000 period. This time series is noteworthy because it indicates that

since the early 1990s, transnational terrorist incidents, although down in number, are more likely

to end in injuries or death for targeted individuals. Terrorist experts have documented a change

in the makeup and motivation of the general perpetrators of terrorism since the takeover of the

US Embassy in Tehran in November 1979 (Hoffman, 1998). From the late 1960s until the latter

7

1980s, transnational terrorism has been primarily motivated by nationalism, separatism, Marxist

ideology, and nihilism (Wilkinson, 1986). In the 1990s, the motivation of terrorism has changed

with “the emergence of either obscure, idiosyncratic millennium movements” or religious-based

fundamentalist groups (Hoffman, 1997, p. 2). Since the beginning of 1980, the number of

religious-based groups has increased as a proportion of the active terrorist groups: 2 of 64

groups in 1980, 11 of 48 groups in 1992, 16 of 49 groups in 1994, and 25 of 58 groups in 1995

(Hoffman, 1997, p. 3).

With the earlier prevalence of leftist-based organizations that wanted to win the hearts

and minds of the people, such terrorist groups avoided casualties except of individuals

characterizing the establishment or the “enemy.” Today, fundamentalist terrorist groups

purposely seek out mass casualties, viewing anyone not with them as a legitimate target. Thus,

the events of 11 September with their massive casualties of innocent people of all ages came as

no surprise to those of us who study terrorism and warned of an ominous changing nature of

transnational terrorism. In a recent time-series-based study, Enders and Sandler (2000) show

that a significant rise in casualties from transnational incidents can be traced back to the takeover

of the US Embassy in Tehran, as speculated by Hoffman (1998). In recent years, an incident is

almost 17 percentage points more likely to result in death or injury compared with the earlier

eras of leftist terrorism.

Trends and Cycles

Judging by the public’s and media’s reaction to 11 September, one might conclude that

international terrorism is on the rise, but Figures 1 and 2 (displayed earlier) indicate just the

opposite trend. This misperception may be due to the increasing likelihood of an incident

resulting in casualties, making incidents on average more newsworthy. The standard procedure

8

for ascertaining the form of a deterministic trend is by fitting a polynomial in time (t), where

additional trend terms (i.e., t, t2, t3) are added until the associated coefficient is no longer

statistically significant. For 1968-2000, we investigate trends for six time series extracted from

ITERATE: hostage taking, bombings (of all types), threats and hoaxes (i.e., threatened future

incidents or a false claim for a concurrent incident – a bomb aboard a plane, when there is no

bomb), assassinations, incidents with casualties, and all transnational terrorist incidents. Table 2

indicates the polynomial trend estimates for these six series (where time = t), all of which are

characterized by a nonlinear trend. The t-ratios associated with the coefficient estimates are

indicated in parentheses beneath the constant and the time trend terms. Five of the six series are

represented by a quadratic trend with a negative coefficient for the squared time term. This

characterization reflects the fact that series tended to rise in the late 1960s and to decline in the

late 1990s. Only the threats and hoaxes series is represented by a more complicated cubic trend;

nevertheless, this series also displays a similar inverted U-shaped pattern.

In Table 2, the next-to-the-last column on the right reports the F-statistics and their

“prob” values in brackets, representing the statistical significance of the overall regression.

These significance levels are all zero to three digits, which are strongly supportive of the fitted

nonlinear trend equations. Such fitted trends are not useful for very long-term forecasting,

because there is little reason to believe that the number of incidents will continue to decline.

Instead, the fit of the nonlinear trend cautions against simple statements about a decidedly

upward or downward trend to any form of international terrorism. Such proclamations are

common in the media and the political science literature.2 The trend analysis suggests that there

is persistence in each of the incident series – high and low levels of terrorism come in waves or

cycles. Shocks to any incident series are not permanent, so that there is a reversion toward a

long-run mean.

9

Cycles in terrorism data have been attributable to a number of factors. Alexander and

Pluchinsky (1992) explain fluctuations in terrorism using demonstration and copycat effects.

Heightened public sensitivity following a successful terrorist attack induces other terrorists to

strike when media reaction is likely to be great. The anthrax attacks following the events of 11

September appear to correspond to this pattern. Economies of scale in planning terrorist

incidents by terrorist groups or networks may also lead to the bunching of attacks. Cycles may

also stem from the attack-counterattack process between the terrorists and authorities. Public

opinion following a spate of attacks can prompt governments’ periodic crackdowns that

temporarily create a lull in transnational terrorism. These downturns are subsequently followed

by countermeasures and recruitment by the terrorists as they prepare for a new offensive. Chalk

(1995) indicates that cycles based on public-opinion pressure swings are in the three to five year

range, insofar as time is required for the public to unite and successfully make their demands on

officials to do something – a prediction borne out by time series investigations (Enders and

Sandler, 1999).

In our past work, we find that each type of terrorist series has its own characteristic cycle

that hinges on the logistical complexity of the attack mode. Enders and Sandler (1999) and

Enders, Parise, and Sandler (1992) argue that logistically complex events such as skyjackings,

large suicide car bombings, and assassinations will have longer cycles than less sophisticated

events as the attack-counterattack interaction among adversaries takes longer. Such complex

missions utilize relatively large amounts of resources as compared to small explosive bombings,

threats, and hoaxes. Given their resource constraints, terrorists can more easily gear up for a

campaign dominated by small bombs than one relying on more resource-intensive events.

The theory of Fourier series allows a wide class of functions to be expressed in terms of

sine and cosine components. To uncover the underlying cycles in a series, a researcher must

10

regress the detrended values of a series on all frequencies in the interval [1, T/2], where T is the

number of observations. The frequency of a series indicates how fast the underlying cycle is

completed – a low (high) frequency implies a long (short) cycle. A graph depiction the

proportionate variation explained by each frequency (called the periodogram) has large peaks

representing the crucial underlying frequencies. Some series with obvious cycles, like sunspots

or average daily temperatures, will display a periodogram with a single focal frequency. Given

the stochastic behavior of terrorists and the measures applied to curb terrorism, there is unlikely

to be one deterministic frequency that dominates the periodicity for any of the six series. Thus,

we use a different approach than trying to identify one particular frequency. Series with long

periods will have most of their variance explained by the low frequencies, whereas series with

short periods will have most of their variance explained by high frequencies.

In accordance with spectral analysis, we detrended each series using the fitted polynomial

trends in Table 2. The last two columns of Table 2 report the total variance of each series and

the proportion of this variance accounted for by the lowest 15 percent of the frequencies.3 We

anticipate that the logistically complex incident types will have relatively large amounts of this

proportion attributable to the low frequencies. The all-events series has a large variance of

1335.56 with just 25.2 percent corresponding to the relatively low frequencies. In marked

contrast, the more complex events of assassinations and those involving casualties have smaller

variances with more of this variance (41.1 and 52.7 percent, respectively) attributed to low

frequencies. Threats and hoaxes display the greatest evidence of short cycles with just 24.7

percent of the variance explained by the longest cycles. The variance results for hostage taking

and bombing events imply moderately short cycles. Only in the case of hostage taking are our

priors not realized.

11

Game Theory and Hostage Taking

To date, there have been seven economic analyses of hostage-taking events – i.e.,

Atkinson, Sandler, and Tschirhart (1987), Lapan and Sandler (1988), Selten (1988), Islam and

Shahin (1989), Sandler and Scott (1987), Scott (1991), and Shahin and Islam (1992). The first

three studies stress game-theoretic aspects, while the latter four studies do not. We focus our

remarks around the Lapan and Sandler (1988) study, which is the most general of these three

game-theoretic studies. The question posed by their investigation is whether or not a stated

policy by which a government precommits never to negotiate with hostage takers will have the

intended consequence of keeping terrorists from ever taking hostages. The conventional wisdom

states that if terrorists know ahead of time that they have nothing to gain that they will never

abduct hostages. This belief has become one of the four pillars of US policy with respect to

addressing transnational terrorism – i.e., “make no concessions to terrorists and strike no deals”

(Malvesti, 2001; US Department of State, 2001, p. iii).

The underlying game tree is displayed in Figure 4, where the government goes first and

chooses a level of deterrence, D, which then determines the likelihood, θ, of a logistical failure

(i.e., failure to secure hostages). Because deterrence expenditure (equivalent to D) must be paid

by the government in all states of the world, it is analogous to an insurance premium and is,

hence, part of the cost to the government’s payoff, listed above that of the terrorists, at the four

endpoints to this simple game in Figure 4. More risk-averse governments choose higher

deterrence levels and experience less hostage taking at home. Once deterrence is decided, the

terrorists must then choose whether or not to attack. The probability of an attack, Ω, depends on

whether the terrorists’ expected payoffs from a hostage-taking attack are positive.4 If hostages

are apprehended (i.e., logistical success occurs), then the government must decide whether or not

to capitulate to terrorists’ demands, where p is the likelihood of government capitulation. The

12

probability of a hostage-taking incident increases with the likelihood of a logistical success, the

probability of a government capitulation (if hostages are secured), and the benefit of a successful

operation, m. In contrast, the likelihood of an attack decreases with smaller terrorist payoffs

associated with logistical and negotiating failures – i.e., smaller |c| and .m!

The conventional wisdom for the never-to-capitulate policy hinges on at least four

implicit assumptions: (i) the government’s deterrence is sufficient to stop all attacks; (ii) the

government’s pledge is fully credible to all would-be hostage takers; (iii) the terrorists’ gains

from hostage taking only derives from the fulfillment of their demands; and (iv) there is no

uncertainty concerning the payoffs. Each of these assumptions may not hold in practice.

Deterrence will not stop all attacks if the terrorists perceive that there is a positive expected

payoff from taking hostages.5 Even if the government’s pledge is believed by the terrorists (i.e.,

p = 0), conditions on m! exists, so that the terrorists can derive a positive gain from securing

hostages when getting no concessions.6 This may arise when media exposure from holding the

hostages is sufficient reward in itself. If, however, the government’s pledge is not completely

credible (i.e., p > 0) owing to past concessions, then the terrorists’ expected payoff is greater than

in the case of a credible governmental pledge, and so an attack becomes more imminent.7 When

a terrorist group is sufficiently fanatical that it views failure as having a positive payoff (i.e.,

m! > –c > 0), then the expected payoff is always positive even when θ = 1 and deterrence is

insufficient to make failure a certainty.

At the endpoints of the game, the payoffs may themselves be uncertain. In this regard,

we focus on the payoffs to government from the four possible outcomes to the game. With no

attack, the government incurs only the cost of deterrence. If an attack ensues but fails (i.e., no

hostages are taken), then the government incurs the cost of a (> 0) in addition to deterrence

expense; if, however, an attack succeeds, then the government experiences an added cost of h for

13

capitulating and n for not capitulating. The game is more interesting (and realistic) by allowing

either h or n, or both to be uncertain. When, instead, h and n are known beforehand, the

government’s response would be to not capitulate provided that h > n. In the latter case,

conventional wisdom applies. Next, suppose that n is a random variable, which may assume a

large value for some hostages (e.g., a soldier or member of parliament). The government is now

guided by comparing h with the expected value of n, and then choosing the smallest, which may

involve conceding to terrorist demands (e.g., the Israeli release of 1,150 Arab prisoners in a

negotiated swap for three Israeli soldiers in May 1985)8 when the expected value of n exceeds h.

For the scenario when both h and n are random, the choice then hinges on choosing the

negotiation response that minimizes the expected cost. A precommitment strategy to never

concede to hostage takers’ may be time inconsistent when a government later discovers that the

cost of holding firm is too high owing to cost randomness. Although the government has every

intention to fulfill its pledge, its inability to deter all incidents and the terrorists’ ability to capture

the “right” hostage means that a government may, at times, renege on its pledge.

The game representation can be made more realistic by allowing multiple periods and

reputation costs. A government concession in one period to hostage takers makes terrorists raise

their belief about future concessions. As p increases for future periods, more hostages will be

taken, so that there is an added cost to conceding in any period. This cost is denoted by R for

loss of reputation, and results in capitulation costs to the government, becoming h + R + D(θ) in

Figure 4. Even when reputation cost is included, conceding may not be eliminated unless h + R

exceeds n for all realizations of n. Such a scenario may be achieved through rules – e.g., a

constitutional amendment that imposes sufficiently severe punishment to eliminate any

discretion of government negotiators.

The game can be made still more realistic by including additional sources of uncertainty

14

in terms of the terrorists’ payoffs. Hostage-taking incidents involve asymmetric information and

uncertainty on the part of both terrorists and governments.9 The beauty of game theory is that it

permits the evaluation of policies while accounting for uncertainty and strategic interactions of

opposing interests. In so doing, easy fixes may not be so straightforward.

Game Theory and Governmental Responses

We have already discussed the transference externality when terrorists target two

different countries and each independently chooses a level of deterrence that fails to account for

associated external cost/benefit. External costs are present when deterrence at home displaces

the attack abroad, while external benefits are relevant when deterrence at home either protects

foreigners or reduces the level of attacks globally. Depending on the opposing external effects,

and there may be others not listed, there may result too much or too little deterrence (Sandler and

Lapan, 1998). The overdeterrence/underdeterrence problem is heightened when a terrorist

network (e.g., al-Qaida) operates in upwards of 60 countries and stages their attacks worldwide

(US Department of State, 2001). Underdeterrence is particularly acute in countries sympathetic

to a group’s grievances when the group focuses their attack on foreigners. As the number of

potential targets increase, transference efforts may be especially large. By forming a global

network, terrorists limit the effectiveness of countries’ efforts to thwart terrorism as externalities

are maximized through countries’ uncoordinated decisions. Terrorists will naturally seek out the

weakest link – i.e., the country with the least security – for the venue for their next attack. To

address these weaknesses, prime targets, such as the United States, have instituted programs to

assist such weakest-link countries in bolstering their counterterrorist capabilities. In fact, this

assistance is another of the four pillars of US antiterrorism policy (US Department of State,

2001; Mavesti, 2001). Ironically, US efforts to induce other countries to secure their airports and

15

public places make the United States a more attractive target, as 11 September sadly

demonstrated.

If the terrorist networking advantage is to be countered, then targeted nations must learn

to coordinate their own efforts at counterterrorism. This poses a special problem because nations

are loathed to sacrifice their autonomy over security matters to a supranational collective. With

this in mind, terrorist experts have often called for piecemeal policy where intelligence is shared

but not deterrence decisions (e.g., Kupperman, 1987, p. 577; Wilkinson, 1987). Such piecemeal

responses may be inadvisable when the strategic incentives are taken into account. Suppose that

a terrorist network targets three countries, each of which are engaged in overdeterrence to

transfer the attack abroad. Further suppose that intelligence allows the targeted countries to

better judge the marginal effectiveness of diverting attacks by revealing the terrorists’ preference

for alternative targets. As these nations acquire this information, they become better adept at

diverting attacks, thereby augmenting the negative transference externality. The net impact of

this information sharing may be to heighten the “transference race” without providing more

security, so that the added deterrence cost simply makes the three countries worse off. This

results in a second-best outcome in which the change in one policy parameter (i.e., increased

information sharing) which would, under full cooperation, improve efficiency, may worsen

inefficiency when a second policy (i.e., coordination of deterrence) is not chosen optimally. A

similar second-best scenario may characterize other partial responses – e.g., greater actions to

apprehend terrorists without coordinating efforts to increase punishments. The failure to

coordinate retaliatory responses until 7 October 2001 is another piecemeal response that may

have led to inefficiencies. Thus, the application of game theory again raises policy concerns

previously ignored in the terrorism literature.

16

Building a Coalition against Terrorism

Actions to coordinate retaliation against either a terrorist organization or a state-sponsor

of terrorism has typically been characterized as a Prisoners’ Dilemma (e.g., Lee, 1988) with all

countries playing their dominant strategy to sit back and do nothing. This representation follows

because a country’s own cost of retaliating is often greater than its perceived benefit (Sandler,

1997, p. 133). That is, the cost is private to the retaliator but the benefit is purely public –

nonexcludable and nonrival – to potential targeted countries. Perceived retaliation cost may be

higher than the retaliator’s derived benefit, since the retaliator often attracts subsequent terrorist

attacks as protests for its actions (Brophy-Baermann and Conybeare, 1994; Enders and Sandler,

1993). In the past, a targeted country responds to maintain its political legitimacy in a liberal

democracy (Wilkinson, 1986) – i.e., to be viewed as trying to protect lives and property. For a

targeted country, these political benefits may offset the net negative economic gains associated

with retaliation,10 so that it acts alone. Countries not directly in the terrorists’ cross hairs will

only weigh the net negative economic benefits and free ride.

The forging of an alliance to wage war on terrorism in Afghanistan after 11 September

2001 appears to abide by a different underlying game form than the Prisoners’ Dilemma for

select countries that have participated in the retaliatory response against the Taliban and Osama

bin Laden. We shall focus on the two most ardent participants – the United States and the

United Kingdom. In Figure 5, we represent an underlying retaliation game in ordinal form,

where payoffs are rank ordered from highest (4) to lowest (1). The payoffs for the row player –

the US – are listed first, followed by those of the column player – the UK – in each of the four

strategic combinations. The ordinal payoffs displayed indicate that the highest payoffs come

from these two countries jointly retaliating, followed by the next-largest payoff for free riding

when the other country retaliates. The worst payoff corresponds to retaliating on one’s own,

17

followed by the second-worst payoff when neither country retaliates. This game differs from the

standard Prisoners’ Dilemma by having the ordinal payoffs of the 3s and 4s switched. That is,

the heinous nature of the 11 September attacks and its human toll on American and British

citizens at the World Trade Center increased the ordinal payoff for joint retaliation and decrease

this payoff from free riding, as compared with earlier terrorist incidents, including the downing

of Pan Am Flight 103 over Lockerbie, Scotland on 21 December 1988.11

For the assurance game displayed in Figure 5, there is no dominant strategy that gives

higher payoffs no matter what the other country does, but there are two pure-strategy Nash

equilibria, where either both countries retaliate or both do nothing. In this scenario, an alliance

can be forged provided that one country leads and begins to retaliate, which was the role that the

United States assumed. Other countries that have come along once the retaliatory strikes were

well underway were Japan, Germany, and Italy. US leadership, coupled with initially successful

operations, brought these others into the alliance by more than name only. Still other alliance

members would only go along with US actions through private inducements that made being an

ally a dominant strategy.

Rational-Choice Representations

Beginning with the Landes (1978) study of skyjackings, economists characterize

terrorists as rational actors who maximize expected utility or net payoffs subject to constraints.

Arguments in these constraints may consist of terrorists’ resource endowments or actions taken

by the authorities to thwart terrorism. In the Landes (1978) model, potential hijackers will

engage in a hijacking provided that the associated expected utility exceeds other nonskyjacking

means of furthering their goals. Based on this utility comparison, Landes (1978) specifies an

offense (i.e., number of skyjackings) function, whose independent variables include the

18

hijackers’ subjective estimate of the likelihood of apprehension, their estimate of the conditional

probability of imprisonment (if apprehended), and other actions by the authorities (e.g., the

presence of US sky marshals on flights). Using data on US hijackings for 1961-76, Landes

demonstrates that greater prison sentences and enhanced likelihood of apprehension are

significant deterrents. He also indicates that the installation of metal detectors on 5 January 1973

led to between 41 and 50 fewer hijackings in the United States during 1973-76.

In a subsequent analysis, Enders and Sandler (1993) examine a wide range of policy

interventions, including metal detectors, fortification of embassies, retaliatory raids, and the

Reagan “get-tough-on-terrorists” laws. The theoretical model for the terrorists that underlies

their study is analogous to the consumer-choice model. Terrorists maximize utility or expected

utility derived from the consumption of basic commodities, produced from terrorist and

nonterrorist activities. For example, al-Qaida terrorists may gain utility from a reduced political

resolve on the part of the United States to remain in the Persian Gulf as Americans lose their

lives in terrorist attacks (e.g., the destruction of the Al Khubar Towers housing US airmen and

others on 25 June 1996 near Dhahran, Saudi Arabia). This weakening of US resolve is the basic

commodity that can be produced with a number of alternative attack modes. Substitution

possibilities among terrorist tactics arise when alternative modes of operations produce the same

basic commodities (e.g., political instability, media attention) in varying amounts. Substitution

is enhanced when attack modes possess closely related outcomes and are logistically similar.

This is clearly the case for hijackings and other kinds of hostage events. Complementarity

results when combinations of attack modes are required to produce one or more basic

commodities. When threats follow real attacks, both actions assume a heightened effectiveness

and are then complementary.

To produce these basic commodities, a terrorist group must choose between nonterrorist

19

and terrorist activities, while being constrained by resources. In the latter choice, terrorists must

further choose between different modes of terrorist attacks based on the perceived “prices”

associated with alternative operations. Choices are many and include the intended lethality of

the act, its country of location, and whom or what to target. The expenditure on any activity

consists of the activity’s per-unit price times the activity’s level. Each mode of operation has a

per-unit price that includes the value of time, resources, and anticipated risk to accomplish the

act. The securing and maintenance of a kidnapping victim in a hidden location is logistically

more complex and requires more resources than leaving a small bomb in a trash bin in a railroad

station, so that the former has a greater per-unit price. In choosing a venue, the price is

anticipated to differ based on security measures taken by the authorities, so that a country with

more porous borders will be the staging ground for attacks against targets from other more

secure countries. The prices confronting the terrorists for each tactic are determined, in large

part, by the government’s allocation of resources to thwart various acts of terrorism. If, for

example, embassies are fortified, then attacks against embassy personnel and property within the

mission’s ground become more costly for the terrorists – i.e., there is a rise in the price of such

attacks. Similarly, metal detectors in airports increase the relative price of skyjackings as

compared with other kinds of terrorist acts, including kidnappings.

Government policies aimed at a single type of terrorist event (e.g., the installation of

bomb-sniffing equipment in airports) adversely changes its relative price and results in a

substitution into now less expense modes of attack. Thus, Landes’ (1978) measure of the

success of metal detectors, in terms of fewer skyjackings, does not go far enough, because the

application of this technology may have induced a large number of other kinds of events.

Similarly, to judge the success of embassy fortification, a researcher must also examine

assassinations and other attacks against embassy personnel once outside of the compound.

20

To account for these substitutions, Enders and Sandler (1993) apply vector autoregression

(VAR) analysis to allow for the potential interactions among various terrorist time series (e.g.,

skyjackings and other hostage events) in response to government policies. They find that metal

detectors decreased skyjackings and threats, but increased other kinds of hostage incidents, not

protected by detectors. The trade-off between events were about one for one (also see Enders,

Sandler, and Cauley, 1990; Im, Cauley, and Sandler, 1987). Both substitutions and

complementarities are uncovered. Fortification of US embassies and missions reduced attacks

against such installations, but were tied to a disturbing increase in assassinations of officials and

military personnel outside of protected compounds. In addition, Enders and Sandler (1993)

establish that the US retaliatory raid against Libya on April 1986 (for its suspected involvement

in La Belle Discothèque in West Berlin on 4 April 1986) was associated with an immediate

increase in terrorist attacks against US and UK interests. This increase was shortly followed by a

temporary lull as terrorists built up depleted resources. Apparently, the raid caused terrorists to

intertemporally substitute attacks planned for the future into the present to protest the retaliation.

Within a relatively few quarters, terrorist attacks resumed the same mean number of events.12

There are a number of ways to institute antiterrorist policies that address these likely

substitutions and complementarities. First, the government must make the terrorists substitute

into less harmful events. Second, the government must go after the terrorists’ resource

endowment (i.e., its finances, its leadership, its membership) if an overall decrease in terrorism is

to follow. Efforts to infiltrate groups or to freeze terrorist finances have this consequence.

Third, the government must simultaneously target a wide range of terrorist attack modes, so that

the overall rise in the prices of terrorist attacks becomes analogous to a decrease in resources.

Success in raising the price of all modes of terrorist attacks would induce terrorists to shift into

legal protests and other nonterrorist actions to air grievances. Based on the above, we can

21

conclude that a reliance on technological barriers merely causes a substitution into other attack

modes in the short run. In the long term, terrorists will develop ingenuous countermeasures (i.e.,

plastic guns, bottles of flammable liquid) to circumvent the technology. Thus, there is a dynamic

strategic interaction present, where authorities must be ever vigilant to be improving the

technology by anticipating ways of circumventing such barriers. This vigilance must lead to

periodic upgrades in the technology prior to the terrorists exposing the technology’s weakness

through a successful attack. Unfortunately, authorities have been reactive in practice by only

responding after a technological barrier’s weakness has been exploited, so that the public

remains vulnerable until a new technological fix is found and installed.

Other Kinds of Substitutions

Substitution effects abound in the study of terrorism and involve not only actions of the

terrorists, as described above, but also actions of the targets. For targets, the economic literature

addresses two kinds of substitutions. First, there are studies that examine the tourists’ choice of

vacation spot based on the perceived threat of terrorism and other costs. An alteration in travel

risks, arising from increased terrorist incidents in a country, raises the price of a holiday there in

comparison to other vacation venues, not confronted with terrorism. In a study of Spain, Enders

and Sandler (1991) employ VAR analysis to demonstrate that a typical transnational terrorist

incident is estimated as scaring away just over 140,000 tourists when all monthly impacts are

combined. Companion studies by Enders, Sandler, and Parise (1992) and Drakos and Kutan

(2001) establish and quantify terrorism-induced substitutions in tourism for Greece, Austria,

Italy, Turkey, Israel, and other terrorism-ridden countries. Countries, like Greece, that have not

addressed transnational terrorist attacks directed at foreigners lose significant foreign-exchange

earnings as a consequence. The cost of terrorism comes in many forms.

22

Second, target-based substitutions involve foreign direct investment (FDI). Investors

decide where to invest based on their perceived economic risks, political risks, and monetary

returns. An increase in transnational terrorism directed at FDI (e.g., attacks on Euskadi ta

Askatasuna (ETA) in the Basque region of Spain) is sure to divert such investment. Enders and

Sandler (1996) show that an “average” year’s worth of terrorism reduced net FDI in Spain by

13.5 percent annually, and it reduced net FDI in Greece by 11.9 percent annually. These

reductions translated into declines in real net FDI of $488.9 million and $383.5 million,

respectively, or the equivalent of 7.6 percent and 34.8 percent of annual gross fixed capital

formation in Spain and Greece. Transnational terrorism displayed significant economic cost, not

counting the billions spent on barriers and deterrence.

Toward a Benefit-Cost Analysis of Terrorist-Thwarting Policies

As a future research project, economists should assess the benefits and cost of specific

policies to thwart terrorism. Such an exercise has not been adequately done and poses some real

challenges. The cost side is much easier than the benefit side for measurement purposes since

figures are available in, say, the United States as to what is paid to fortify our embassies and

missions, or to guard US airports. Consider the cost associated with airport security. To the cost

of guards and screening equipment must be added the value of lost time as travelers are screened

at US airports.

On the benefit side, calculations are less transparent and more cleverness is needed on

behalf of the researcher. One way to estimate a portion of this benefit would be to compute the

reduced loss of life attributable to airport security measures – i.e., fewer people killed in

skyjackings. If the net number of such lives saved, after adjusting for substitutions into other

23

life-threatening terrorist actions, can be measured, then the average “value of a statistical life”

can be applied to translate these lives into a monetary figure. To this figure, a researcher must

also compute and add the reduced losses in property values (i.e., from destroyed planes)

attributable to the fewer hijackings. In addition, a portion of the value of net air travel revenues

must be considered as a benefit arising from a heightened sense of security stemming from

security upgrades. The events of 11 September clearly underscore that there is a cost to a breach

in airport security as the public loses its confidence in air travel. Any of these components are

fraught with measurement difficulties, because there may be other intervening factors at work –

e.g., air travel was already in a slump prior to 11 September.

Every policy to thwart terrorism would entail its own stream of benefits and costs.

Invariably, the benefit calculations are problematic. The US-led retaliation against al-Qaida and

the Taliban in Afghanistan has well-defined costs in terms of deployed soldiers, ordnance,

diplomacy, and side payments to “allies.” But the true savings or benefits from fewer future acts

of terrorism, in terms of lives and property saved, is so much more difficult to calculate. Time-

series techniques, engineered by Enders and Sandler to measure losses to tourism or to FDI from

terrorism, can be utilized following the retaliation to roughly estimate the decline in terrorist

incidents and their economic value.

Concluding Remarks

Although economic methods have enlightened the public on a number of issues

concerning transnational terrorism, not addressed by the political science literature, there are

many other issues to analyze. For instance, there is a need for applying more dynamic game

methods – i.e., differential game theory – if the waxing and waning of terrorist organizations

(e.g., Red Brigades, Red Army Faction) are to be understood. Clearly, past successes and

24

failures determine the size of these groups over time. The terrorists try to increase their

organization’s size through enhanced resources, successful operations, and recruitment, while the

government tries to limit the group’s size through raids, intelligence, group infiltration, and

actions to thwart successes. This dynamic strategic interaction needs to be modeled and

empirically tested. In addition, researchers must better assess the role of information and

intelligence on behalf of the terrorists and the authorities. Given how little governments really

know about the strength of the terrorists that they confront – e.g., the US government has almost

no clue about the size of al-Qaida,13 asymmetric information characterizes efforts to thwart

terrorism. Similarly, the terrorists are ill-informed about the resolve of the government and the

amount of resources that it is willing to assign to curbing terrorism. Additionally, there is a need

to model terrorist campaigns – i.e., the choice of the sequence and composition of attacks used

by terrorists. As researchers better understand these choices, more effective policy responses can

be devised that adjust for the strategic interaction.

25

Footnotes

1. Since 1973, the 17 November group has engaged in over 140 attacks and 22

assassinations yet no member has been brought to justice (Wilkinson, 2001, p. 54).

2. In fact, there is reasonable evidence to support the claim that each of the incident

series is stationary. Using an augmented Dickey-Fuller unit-root test, we can reject the null

hypothesis of a unit-root in all series, but that of threats and hoaxes, at the .05 level. For this

latter series, we can reject the null of a unit-root at the .10 level.

3. We report the proportion of the variance explained by the frequencies in the interval

[1, 0.15•T/2]. Since we are somewhat skeptical of the fitted polynomial trends, we also obtained

results using only demeaned data. These results are very similar to those discussed below.

4. If * [(1 ) ] [ (1 ) ],c c pm p m< = − θ θ • + − ! then the terrorists are better off attacking even

though they receive –cθ for a logistical failure and (1 )[ (1 ) ]pm p m− θ + − ! for a logistical success.

We have c < c* when the expected payoff from a logistical success, which accounts for

negotiation success or failure, exceeds the expected payoff from a logistical failure. In Figure 4,

Ω corresponds to *

0( ) ,

cf c dc∫ where f(c) is the probability density for c which reflects the

unknown resolve of the terrorists.

5. The terrorists’ perceived net expected payoff equals: (1 ) [ (1 ) ] .pm p m c− θ • + − − θ!

6. The condition is that (1 ) .m c− θ > − θ!

7. When p > 0, expected benefits increase by (1 )( )pm pm− θ − ! compared with the p = 0

case. A reasonable assumption is that ,m m> ! so that winning concessions is better than not

gaining concessions.

8. The Arab prisoners released included Kozo Okomato, a Japanese Red Army Faction

member, who was the sole surviving terrorist in the Lod Airport massacre of 1972, which left 27

26

people dead and 78 injured.

9. On asymmetric information models of terrorism, see Lapan and Sandler (1993) and

Overgaard (1994).

10. Economic benefit refers to the direct benefit derived from retaliation, while

economic cost refers to the expenditure of resources to carry out the retaliation and other

subsequent losses associated with the retaliation. We use the term economic benefit to

distinguish it from political benefit stemming from maintaining legitimacy.

11. Britain lost the second greatest number of citizens of any country at the World Trade

Center. Despite Pan Am 103 flying out of Heathrow Airport and crashing in the United

Kingdom (Lockerbie, Scotland), Britain lost relatively few of its citizens in this incident.

12. Analogous results are found in Brophy-Baermann and Conybeare (1994) for

retaliations by Israel against Palestinian terrorists.

13. In the latest Patterns of Global Terrorism, al-Qaida strengths is given as “may have

several hundred to several thousand members” (US Department of State, 2001, p. 69).

27

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Table 1 Transnational Terrorism: Events 1968-2000

Year Number of Events Deaths Wounded Attacks on US Interests 2000 423 405 791 200 1999 392 233 706 169

1998 273 741 5,952 111 1997 304 221 693 123

1996 296 314 2,652 73 1995 440 163 6,291 90

1994 322 314 663 66

1993 431 109 1,393 88 1992 363 93 636 142 1991 565 102 233 308

1990 437 200 675 197

1989 375 193 397 193 1988 605 407 1,131 185

1987 665 612 2,272 149 1986 612 604 1,717 204

1985 635 825 1,217 170 1984 565 312 967 133

1983 497 637 1,267 199 1982 487 128 755 208

1981 489 168 804 159 1980 499 507 1,062 169

1979 434 697 542 157

1978 530 435 629 215 1977 419 230 404 158

1976 457 409 806 164 1975 382 266 516 139 1974 394 311 879 151

1973 345 121 199 152

1972 558 151 390 177 1971 264 36 225 190

1970 309 127 209 202 1969 193 56 190 110

1968 125 34 207 57

Source: US Department of State, Patterns of Global Terrorism (1988-2001) and tables provided to Todd Sandler in 1988 by the US Department of State, Office of the Ambassador at Large for Counterterrorism.

Table 2 Trend and Other Statistical Properties of Transnational Terrorist Incidents

Incident Type Constanta Time (Time)2 (Time)3 F–statb Variance Percentc

Hostage taking 5.901 0.219 –0.001 13.11 32.223 0.278 (3.832) (4.093) (–3.202) [0.000] Bombings 34.449 1.139 –0.010 15.87 842.470 0.314 (4.442) (4.230) (–5.021) [0.000] Threats & Hoaxes 8.595 –0.276 0.010 –0.000 11.34 87.170 0.247 (2.540) (–1.256) (2.572) (–3.340) [0.000] Assassinations –1.521 0.400 –0.003 43.49 21.472 0.411 (–1.229) (9.299) (–8.830) [0.000] Casualties 9.726 0.579 –0.004 10.74 119.479 0.527 (2.441) (4.497) (–4.635) [0.000] All Events 41.689 2.435 –0.019 30.79 1335.560 0.252 (4.270) (7.185) (–7.743) [0.000] a t-ratios are in parentheses. b Prob values are in brackets under the F-statistics. c Proportion of variance of the detrended, fitted-polynomial series that is accounted for by the lowest

15 percent of the frequencies (i.e., the longest cycles).

Figure 1

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Figure 5 Ordinal Game Matrix for Retaliation

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Retaliate Do Nothing

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Do Nothing 3, 1 2, 2

WHAT DO WE KNOW ABOUT THE SUBSTITUTION EFFECT IN TRANSNATIONAL TERRORISM?

by

Walter Enders* Department of Economics, Finance, and Legal Studies

University of Alabama Tuscaloosa, AL 35487 wenders@cba.ua.edu

Todd Sandler School of International Relations University of Southern California

Von Kleinsmid Center 330 Los Angeles, CA 90089-0043

tsandler@usc.edu

April 2002

*Walter Enders is the Lee Bidgood Chair of Economics and Finance in the School of Business at the University of Alabama. Todd Sandler is the Robert R. and Katheryn A. Dockson Professor of International Relations and Economics. He is a member of the School of International Relations and the Department of Economics at the University of Southern California. Sandler acknowledges research support from the Center for International Studies, University of Southern California to update the ITERATE data for 1999-2000.

The success of the terrorist attacks on the World Trade Center and the Pentagon on 11

September 2001 (henceforth, 9/11) has resulted in profound economic and social consequences

for the United States. In addition to the loss of life and property, total costs of the attacks are

staggering. With the economy already on the brink of recession, the unemployment rate rose by

almost 1%.1 Some sectors bore the brunt of the loss in business and consumer confidence. Wall

Street closed for a week; on its re-opening, various stock market indices fell substantially and

investment funds seemed to dry up. The airline industry was temporarily shut down, the tourism

industry was especially hard-hit, and several airlines never recovered. The opportunistic anthrax

attacks that followed caused major disruptions of the mail.

The worldwide response to fighting terrorism has been equally dramatic. The U.S.-led

coalition known as “Operation Enduring Freedom” quickly achieved its aim of eliminating the

Taliban regime in Afghanistan. In total, seventeen nations contributed more than 16,500 troops

to the initial operation. Other efforts included the enhancement of airport security and directives

from nearly 150 countries to freeze terrorist assets totaling at least $104.8.

Within the United States, President Bush created the Office of Homeland Security and

the National Defense Authorization Act (S. 1438, 8 December 2001). This Act earmarked funds

for extending the war on terrorism, which includes countermeasures against potential biological

and chemical attacks. Future years promise even greater anti-terrorism measures. President

Bush’s proposed budget for 2003 directs $37.7 billion to homeland security (an $18.2 billion

increase over 2002). In particular, the budget proposal includes $11 billion for border security,

$6 billion to defend against bioterrorism, $3.5 billion (a 1,000-percent increase) for police,

firefighters and Emergency Medical Teams, and $700 million to coordinate the antiterrorism

1 All data used in this section were obtained from the official website of the President of the United States: www.whitehouse.gov.

2

measures of the various branches of government.

Undoubtedly, a massive anti-terrorist campaign will reduce the overall level of terrorism.

Nevertheless, an important strategic question remains, since some anti-terrorism policies are apt

to be more successful than others. As surveyed in this paper, economists and political scientists

have investigated the effectiveness of alternative policy responses (e.g., toughening punishments,

retaliatory raids, installing technological barriers). Each anti-terrorism policy can influence a

terrorist group’s choice of operations by either affecting their resources or the relative costliness

of different kinds of attacks. Such policies can have an “income effect” or “substitution effect”

or both. The income effect involves the overall level of available resources – e.g., freezing

terrorists’ assets reduces their “war chest” and their overall ability to conduct a campaign of

terror. If a government action increases the resource outlays necessary to undertake a particular

type of operation, then there is a motive to substitute into some less costly operation that

achieves a similar outcome at less cost. For example, the installation of screening devices in US

airports in January 1973 made skyjackings more difficult, thus encouraging terrorists to

substitute into other kinds of hostage missions or to stage a skyjacking from an airport outside of

the United States.

Unlike the two examples above, the income and substitution effects of an anti-terrorism

policy are often interrelated. For example, the seizure of a cache of explosive devices has a clear

income effect (since resources decline) and a substitution effect (since terrorists are less likely to

stage incidents that rely on explosives). The essential point is that the overall effectiveness of

any anti-terrorism policy depends on the direct and indirect effects that arise through various

substitutions. The purpose of this chapter is to provide a careful examination of the terrorists’

decision-making process, so as to understand and predict the likely responses.

1. Transnational Terrorism

3

Since the events of 9/11, the popular press has run articles arguing over the precise

meaning of “terrorism.”2 We define terrorism as the premeditated use, or threat of use, of

extranormal violence to obtain a political objective through intimidation or fear directed at a

large audience. An event, no matter how brutal, is not a terrorist incident unless it involves the

presence of a political objective. Incidents that have no specific political motive are criminal

rather than terrorist acts: a barroom shooting is a criminal act, while the assassination of an

ambassador to coerce political change is a terrorist act. Another fundamental ingredient in the

definition is the creation of widespread intimidation or fear. Unlike warfare, where the aim is to

destroy opposing combatants, terrorists also seek to affect those not immediately involved with

the political decision-making process. The 9/11 attack on the World Trade Center clearly fits

this pattern.

As part of the attempt to create a general climate of intimidation, terrorists strike at a

variety of targets using attack modes ranging from skyjackings to simple threats and hoaxes.

The mix of operations makes it difficult for the authorities to predict the nature and location of

the next incident. From the perspective of the authorities, terrorist incidents appear to be

random, so that society must expend relatively large amounts of resources to protect against all

forms of potential attacks.

Most terrorist events directed against the United States do not occur on U.S. soil. The

kidnapping and murder of reporter David Pearl in Pakistan, the destruction of the Al Khubar

Towers housing US airmen in June 1996 near Dhahran, Saudi Arabia, and the bombs destroying

the U.S. embassies in Kenya and Tanzania in August 1998 are but three gruesome examples of

transnational terrorism. Terrorism is transnational when an incident in one country involves

2 Carr (2002) raises a number of issues concerning the appropriate definition of terrorism. Slate (http://slate.msn.com//?id=2062267) contains a discussion of the premise that terrorism necessitates that the victims be non-combatants.

4

perpetrators, victims, targets, institutions, governments, or citizens of another country.

Obviously, the four skyjackings on 9/11 constitute transnational terrorist attacks since the events

were staged by individuals who crossed into the United States from abroad and because victims

came from many countries. However, the bombing of the Murrah Federal Building in Oklahoma

City by Timothy McVeigh in April 1995 was not a transnational terrorist incident.

From the late 1960s until the late 1980s, transnational terrorism was primarily motivated

by nationalism, separatism, Marxist ideology, anti-racism, nihilism, and the desire for economic

equality (Wilkinson 1986). In the 1990s, a driving motivation of terrorism has changed with "the

emergence of either obscure, idiosyncratic millennium movements" or religious-based groups

(Hoffman 1997, 2; 1998, 185-99). When religion provides the dominant objective of a group

that employs terrorist tactics, it is identified as a religious terrorist group (e.g., Hamas, Algerian

Armed Islamic Group (GIA), Hezbollah, Egyptian Gamat al-Islamiya). Since the start of 1980,

Hoffman (1997) reports that the number of religious-based groups has increased as a proportion

of the active terrorist groups: 2 of 64 groups in 1980; 11 of 48 groups in 1992; 16 of 49 groups in

1994; and 25 of 58 groups in 1995. This increase can be attributed to a growth of religious

fundamentalism worldwide, the diffusion of the Islamic revolution from Iran, and the approach

of the millennium. With this motivational change for some terrorists, Hoffman (1997, 1998) and

Juergensmeyer (1997) view the new generation of terrorists as posing a more deadly threat than

earlier groups.

The demise of many leftist groups in the late 1980s and 1990s is attributable to at least

three factors: (i) domestic efforts by some terrorism-prone countries (e.g., France, Germany,

Spain, the United Kingdom) to capture and to bring to justice group members; (ii) reduced state

sponsorship of left-wing groups by East European and Middle Eastern countries (Chalk 1995;

Clutterbuck 1994; Jongman 1992); and (iii) the reduced interest in Marxism following the

5

collapse of many communist regimes. These factors were bolstered by collective initiatives by

the European Union to foster cooperation in terms of extradition, shared intelligence, and

accreditation of foreign diplomats (Chalk 1995; Wilkinson 1992; Zagari 1992). In recent years,

NATO has also begun a program to address collectively the risks posed by transnational

terrorism (Wilcox 1997). Another recent development in terrorism has been the increase in

“splinter” groups that are less disciplined, often more violent, and more nebulous than the parent

group (Hoffman 1997, 1998). The IRA splinter group responsible for the Omagh bombing in

Northern Ireland on 15 August 1998 is a clear-cut example. They did not follow standard IRA

procedures and issued a warning that herded people nearer to the subsequent blast. Some days

later, the group apologized and ceased operations. If members’ actions are not constrained, then

a few fanatical individuals can cause great carnage.

The greater prevalence of religious groups has apparently increased the lethality of post-

Cold War terrorism, because such groups view civilians as legitimate targets of a "decadent"

society. Religious groups that declare a Jihad or holy war against another nation consider its

people, not just its officials, as the enemy. Moreover, religious terrorist groups act out of a

desire to satisfy their own goals (e.g., ascend to heaven) rather than to win favor with an external

constituency. Violence may be viewed as a purifying act. Although it is tempting to attribute

the increased casualties per incident, documented below, to better technology available to

terrorists, most of the incidents have not really relied on new technologies. Old-fashioned bombs

were used at Oklahoma City, Nairobi, and most other targets. The difference today is that these

bombs are set to explode where and when maximum carnage will result.

2. The Choice-Theoretic Model of Terrorism

The choice-theoretic model of rational terrorists considers a terrorist group as choosing

how to allocate scarce resources to maximize the expected value of its objective function. The

6

model developed by Landes (1978) considers a potential skyjacker contemplating the forcible

diversion of a commercial aircraft for political purposes. A simplified version of the Landes’

model considers three states of the world: there is no skyjacking, the skyjacking is successful,

and the skyjacking fails.

In order to highlight the risky nature of terrorism, we assume that utility in the no-

skyjacking state is certain; if the terrorist decides not to attempt to undertake the skyjacking,

utility is given by U N. If, however, the skyjacking occurs, the outcome is uncertain. Expected

utility can be represented by:

EU SKY = π U S + ( 1 – π )U F, (1)

where EU SKY = expected utility if there is a skyjacking;

π = skyjacker’s subjective estimate of the probability of a successful skyjacking;

1 – π = skyjacker’s subjective estimate of the probability of a failed skyjacking;

U S = utility if the skyjacking is successful;

U F = utility if the skyjacking fails.

The terrorist will attempt the skyjacking if the expected utility derived from undertaking

the skyjacking exceeds the utility level UN when there is no skyjacking:

U N < EU SKY = π U S + ( 1 – π )U F. (2)

Thus, anything that lowers U N or raises EU SKY increases the probability of a skyjacking.

Landes’ model is useful for understanding the choice between legal and illegal terrorist

activities. Given that utility from success exceeds utility from a failure [ i.e., U S > U F ], it

follows that an increase in the probability of a success will make it more likely that the

skyjacking will occur. Formally, the change in expected utility from a skyjacking due to a

change in π is:

7

/ 0.SKY S FdEU d U U= − >π (3)

Hence, if the authorities undertake a policy (such as enhanced airport security) that

reduces the probability of a successful skyjacking (lowering π), the Landes’ model predicts that

the terrorists will be more likely to forego the skyjacking, owing to the associated reduction in

EU SKY. Policies that lower the utility from a skyjacking failure, such as longer jail sentences,

also reduce the expected utility from skyjackings, thus decreasing the likelihood of such events.

Moreover, policies that limit the utility from success, such as reduced media coverage, also

reduces the number of skyjackings.

Although some Hamas and al-Qaida terrorists engage in suicide missions, the vast

majority of terrorists do not resort to such attacks and respond predictably to security

enhancements and other policy actions. Nevertheless, the model is capable of addressing suicide

attacks. If a terrorist is concerned with living, then U F is likely to be low, thereby inhibiting

EU SKY from exceeding U N – the necessary requirement for an attack. A fanatical terrorist, who

does not fear death and may welcome it, has a higher U F, which makes an attack more likely in

(2). Fanaticism brings U F closer to U S in (3); thus the policy effectiveness of lowering the

success probability diminishes. If, for example, U F = U S in (3), then efforts to lower π have no

effect on EU SKY. Consequently, policy becomes completely ineffective. Fanatical terrorists

must be apprehended or killed for attacks to stop.

Landes presented two regressions for US skyjackings based on US Federal Aviation

Administrative data on skyjackings for the 1961-1976 period. The first regressed the quarterly

total of skyjackings on the probability of apprehension, the probability of conviction, sentencing,

and other policy efforts. The second regressed the time interval between skyjackings and the

same set of variables. Both regressions found the length of sentence and the probability of

apprehension to be significant deterrents. For most regressions, the probability of conviction

8

was marginally significant. Landes also estimated that between 41 and 50 fewer skyjackings

occurred in the U.S. from the start of 1973 following the installation of metal detectors in US

airports.

More generally, substitutions can be analyzed with a household production function

(HPF) approach for which the utility of a terrorist group is a function of a shared political goal.

The HPF model was first applied to transnational terrorism by Enders and Sandler (1993). Given

the groups’ budget constraint, this shared goal is produced from a number of basic commodities

that may include both terrorist and non-terrorist activities. To be more specific, basic

commodities may include political instability, media publicity, an atmosphere of fear, or

extortion. Alternative terrorist attack modes can be substitutable if they produce the same basic

commodities. Substitution possibilities are augmented when attack modes are logistically similar

and yield the same basic commodities in nearly identical proportions. An assassination of a key

public official or a skyjacking might be substitutes if they provide a terrorist group with similar

amounts of media attention. Complementarity results when a combination of attack modes is

required to produce one or more basic commodities or when the success of one type of attack

reinforces the effects of a second type of attack. For example, in the wake of 9/11, the anthrax

mailings had an especially demoralizing (complementary) effect on a public already sensitized to

terrorism.

The advantage of the HPF approach is that it allows for substitutions between legal and

illegal activities and for substitutions within the set of illegal terrorist activities. Choices within

the set of terrorist activities are many and include the intended lethality of the act, its country of

location, and whom or what to target (Sandler and Lapan, 1988). In each period, an overall

resource constraint limits the terrorist group’s expenditures to a magnitude not exceeding its

monetary and non-monetary resource endowments. The expenditures on any activity consist of

9

the product of the activity’s level and its per-unit price. Each terrorist and non-terrorist tactic has

a per-unit price that includes the value of time, the use of personnel, funding and capital

equipment, including weapons. A skyjacking is a high-priced incident because it is logistically

more complex to plan and execute and thus requires more resources than do many other types of

incidents. At the other extreme, threats and hoaxes require few resources and are low-priced

incidents. Nevertheless, such incidents can add to the overall level of fear and intimidation. The

recipients of various powders disguised as anthrax felt the same initial fear and undertook the

same precautions as did the recipients of the real thing.

In addition to such technological considerations, the prices terrorists pay for each tactic

are influenced by anti-terrorism policies. If, for instance, the government were to secure its

embassies or military bases, then attacks against such facilities would become more costly on a

per-unit basis. If, moreover, the government were not at the same time to increase the security

for embassy and military personnel when outside their facilities, then attacks directed at these

individuals (e.g., assassinations) would become relatively cheaper.

The HPF approach yields a number of important predictions concerning the substitution

phenomenon. The critical result is that a government policy that increases the relative price of

one type of terrorist tactic produces a substitution out of the now-more-costly tactic into those

terrorist and non-terrorist activities whose prices are now relatively less costly. If, for example,

embassies are fortified, then attacks against embassy personnel and property within the mission’s

ground become more costly for the terrorists – i.e., there is a rise in the price of such attacks.

Similarly, in choosing a venue, the price is anticipated to differ based on security measures taken

by the authorities; therefore, a country with more porous borders will be the staging ground for

attacks against targets from other, more secure, countries. A further prediction of the model is

that complementary tactics would respond in a similar fashion to relative price changes. For

10

example, assassinations and bombings tend to be substitutes, while bombings and threats are

complementary. Thus, the model predicts that a policy that makes it more costly to obtain

assault weapons (an important input in an assassination) will reduce the number of assassinations

but increase the number of bombings and threats. In contrast, government interventions that

raise the price of all terrorist tactics or that reduce terrorists’ resources will cause non-terrorist

activities to increase relative to terrorist actions. However, there is no reason to suppose that this

type of policy will induce substitutions among the various attack models.

To be more formal, suppose that a group only uses two kinds of operations – hostage

taking (h) and bombings (b). Further, suppose that the per-unit costs of each kind of operation

are Ph and Pb for hostage taking and bombings, respectively. In general, these unit costs will

depend on the level of operations and on the anti-terrorism expenditures of the authorities:

Ph = Ph(h, gh) , 0and 0h h hP h P g∂ ∂ ≥ ∂ ∂ ≥ (4)

Pb = Pb(b, gb) , 0and 0b b bP b P g∂ ∂ ≥ ∂ ∂ ≥ (5)

where gh and gb are the government’s anti-terrorism expenditures on hostage-takings and

bombings, respectively.3

Taking as given the government’s anti-terrorism expenditures and their own total level of

resources (R), the terrorists choose h and b to maximize their utility

U(h, b), (6)

subject to:

R = Ph(h, gh) h + Pb(b, gb) b. (7)

Under the standard assumptions, it is possible to show that hostage taking and bombings

3 Notice that in our 2-incident example, we abstract from direct substitutability and complementarity. In a more general setting, we could allow the price of bombings to depend on the number of hostage takings and the price of hostage-takings to depend on the number of bombings. Moreover, anti-terrorism spending directed towards one type of incident might be expected to increase the price of the alternative incident types.

11

decrease when the authorities manage to limit the terrorist’s resource base R. Moreover, actions

by the authorities to increase the unit cost of, say, hostage taking cause terrorists to switch some

operations to the now relatively cheaper bombing events.

A third choice of terrorists involves an intertemporal allocation of resources. Analogous

to other investors, terrorists can invest resources to earn a rate of return, r, per period. When

terrorists want to augment operations, they can cash in some of their invested resources.

Suppose that terrorists have a two-period horizon and must decide terrorist activities today (T0)

and tomorrow (T1) based on resources today (R0) and tomorrow (R1). The intertemporal budget

constraint is:

1 1 0 0(1 )( ),T R r R T= + + − (8)

where tomorrow’s terrorism equals tomorrow’s resource endowment plus (minus) the earnings

on savings (the payments on borrowings) from the initial period. Terrorists maximize an

intertemporal utility function, 0 1( , ),U T T subject to (8) and, in so doing, decide terrorist activities

over time. Thus, terrorists can react to shocks by augmenting operations not only from curbing

non-terrorist activities, but also through an intertemporal substitution of resources.

Unlike a standard intertemporal optimizing framework, the capital market is not perfect –

terrorist groups cannot fully borrow against their expected future income levels. As such, there

may also exist a liquidity constraint. If high-terrorism periods are to be supported by an

intertemporal substitution, it may be difficult for terrorists to maintain a prolonged campaign. As

such, particularly long and intense terrorist campaigns are not as readily sustained as lower levels

of conflict. This prediction may not characterize non-resource-using threats and hoaxes.

We can summarize some of the key predictions and implications of the household

production approach as follows:

12

Substitutions across attack modes: An increase in the probability of success, a decrease in the relative price, or an increase in the payoff of any one type of attack mode will increase that type of attack.

Effects of government policies: Government policies aimed at a single type of terrorist

event (e.g., the installation of bomb-sniffing equipment in airports) adversely changes its relative price and results in a substitution into now less expense modes of attack. Thus, Landes’ (1978) measure of the success of metal detectors, in terms of fewer skyjackings, does not go far enough, because the application of this technology may have induced a large number of other kinds of events.

Substitutions across countries: A decrease in the probability of success or a reduction in

the payoff in successfully attacking any one country will reduce the number of attacks on that country. Given their available resources, terrorists wll move planned attacks into similar, relatively less-protected countries. Intertemporal Substitutions: High-terrorism states deplete resources and so are followed by low-terrorism states. Particularly long and intense terrorist campaigns are not as readily sustained as are lower campaign levels.

3. Evidence of the Substitution Effect

The data we use is constructed from the source files of ITERATE (International

Terrorism: Attributes of Terrorist Events). ITERATE was originally developed by Edward

Mickolus (1982) and has been extended by Mickolus, Sandler, Murdock, and Fleming (1989,

1993) and Fleming (2001). Todd Sandler updated select variables through 1999-2000.

ITERATE uses information from publicly available sources to construct a chronology of

transnational terrorist events. The sources for ITERATE include the Associated Press, United

Press International, Reuters tickers, the Foreign Broadcast Information Service (FBIS) Daily

Reports, and major US newspapers (e.g., the Washington Post, New York Times).

Figure 1 displays the quarterly totals of all transnational terrorist events over the 1968:1 -

2000:4 period. In contrast to the impression cast by the media, the number of transnational

terrorist incidents has been declining since 1993. Bombings are the favorite mode of operation

of terrorists, accounting for about half of all transnational terrorist incidents on average in any

13

given year. As is evident from the figure, transnational terrorism displays a number of sharp

peaks and troughs. Some of the fluctuations are due to landmark political events. The jump in

1979 can be attributed to the political ramifications surrounding the takeover of the U.S. embassy

in Tehran (Enders and Sandler, 2000). The spike in 1986 is associated with the U.S. retaliatory

raid against Libya that occurred on 15 April 1986. The latter half of the 1990s represents a

downturn in transnational terrorism due, in large part, to fewer states sponsoring terrorism in the

post-Cold War era (Enders and Sandler, 1999).

Substitutions and religious based terrorism

Despite the decline in overall terrorism, Figures 2 and 3 paint a grim picture. Figure 2

shows the number of individuals KILLED per quarter in all transnational events, and Figure 3

shows the quarterly proportion of incidents with CASUALTIES and the proportion with deaths.

Notice that the values of the KILLED series have generally increased since 1993. Over the

entire sample period, an average of 63 individuals have been killed in each quarter. Beginning in

1993, the average number of deaths has increased to 79 per quarter. This pattern is reinforced by

the data shown in Figure 3. The proportion of incidents with CASUALTIES (the dashed line in

the figure) has remained fairly stable since 1973; however, the proportion of incidents with

deaths has more than doubled over the same period. In fact, the proportion of casualty incidents

without deaths (i.e., those with only wounded individuals) has declined. In recent years, there

has been little difference between the proportion of incidents with casualties and the proportion

of incidents with deaths. The strong impression from Figures 1-3 is that the number of incidents

has been declining while the typical incident is becoming much more lethal. The increase in the

proportion of deadly incidents is consistent with the HPF model. Enders and Sandler (2000)

trace the increase in the severity of a typical terrorist incident to the takeover of the US Embassy

in Tehran. The change in the composition of terrorists from less leftist groups to more religious

14

groups means that terrorists no longer fear death. Moreover, fundamentalist terrorist groups

purposely seek out mass casualties, viewing anyone not with them as a legitimate target. As

such, the typical incident is more likely to involve the death of a terrorist and/or the public.

The assassination series shown in Figure 4 includes both successful and failed

assassinations. As such, the values shown exceed the number of assassinations resulting in

deaths. Notice that the overall pattern of the series follows the pattern of transnational incidents

shown in Figure 1. The disturbing feature is that assassinations are declining while the number

of incidents with deaths is increasing; as such, more KILLED incidents involve non-protected

persons and multiple victims.

Substitutions and government policy interventions

Enders and Sandler (1993, 1995) apply vector autoregression (VAR) analysis to capture

the potential interactions among various terrorist attack modes (e.g., skyjackings and other

hostage events) in response to government policies. They find that the installation of metal

detectors in airports (begun in 1973) decreased skyjackings and threats, but increased other kinds

of hostage incidents, not protected by detectors. Specifically, metal detectors were estimated to

reduce skyjackings and threats and hoaxes by 13 and 9.5 incidents per quarter, respectively.

However, the number of other hostage-taking incidents and assassinations rose by almost 10

incidents per quarter. The measured trade-off between skyjacking and other logistically complex

events was nearly one for one (also see Enders, Sandler, and Cauley, 1990; Im, Cauley, and

Sandler, 1987). In terms of the HPF approach, the installation of metal detectors in US airports

increased the relative price of a skyjacking. Skyjackings fell and so did the complementary

threats and hoaxes. This policy intervention had primarily a substitution effect, because it did

not deplete the resources, knowledge, or wherewithal of the terrorists. Substitutions across

attack modes were also found to be important when the United States fortified its embassies in

15

1985 in accord with public law 98-533. Although direct attacks on embassies were reduced, an

indirect consequence was that the number of political assassinations was increased by 5.4

incidents per quarter.

Intertemporal Substitutions

Both Brophy-Baermann and Conybeare (1994) and Enders and Sandler (1993) examine

the effects of retaliatory raids on intertemporal substitutions. Brophy-Baermann and Conybeare

(1994) find that retaliations by Israel against Palestinian terrorists had no lasting effects on the

level of terrorism. They posit a model such that rational terrorists select a long-run or ‘natural’

rate of attacks. The actual level of attacks will differ from the ‘natural’ level only in the presence

of an unanticipated event. In 1972, Israel conducted nine air raids against PLO camps in Syria in

retaliation for Black September’s attack on Israeli athletes in the 1972 Munich Olympic games.

These attacks were estimated as increasing the number of PLO attacks against Israel by 9.39

incidents on impact. After three quarters, the PLO attacks were only 0.5 incidents above the

natural rate. Five other Israeli attacks were found to have no long-run statistical effect on PLO

terrorism.

Similarly, Enders and Sandler (1993) establish that the US retaliatory raid against Libya

on April 1986 (for its suspected involvement in the bombing of the La Belle Discothèque in

West Berlin on 4 April 1986) was associated with an immediate increase in terrorist attacks

against US and UK interests. The raid involved eighteen US F-111 fighter-bombers being

allowed to take off from UK airbases in Lakenheath and Upper Heyford. The planes were

deployed from UK airbases because European nations, geographically closer to Libya, refused to

allow the United States to use their airbases or their airspace. This endangered the raid since it

forced the US fighters to refuel in midair after flying through the Strait of Gibraltar.

As a result of the raid, terrorist attacks against US and the UK interests were estimated to

16

have increased by 39 incidents. However, the attacks had very little persistence as there was a

temporary lull while terrorists built up depleted resources. In the long run, the mean number of

attacks directed against US and UK interests was found to be unchanged. The evidence seems to

be that retaliatory raids induce terrorists to intertemporally substitute attacks planned for the

future into the present to protest the retaliation. Within a relatively few quarters, terrorist attacks

resumed the same mean number of events.

However, the Israeli raids against the PLO and the US raid against Libya did destroy

some of the terrorists’ resource base, so that one must wonder why overall terrorism did not

diminish as a result. One answer is that the retaliations were not sufficient to destroy a

significant portion of the terrorists’ bases or personnel. A second answer is that the raids

actually made it easier for terrorists to recruit new members and to raise funds. A third answer is

that Libya was not responsible for a lot of transnational terrorism.

Enders and Sandler (2002) find additional evidence of intertemporal substitutions using a

threshold autoregressive (TAR) model. The HPF model implies that high-terrorism states are

difficult to maintain if there are important liquidity constraints. In the midst of an intense

terrorist campaign, weapons, funds, and personnel may be depleted. In contrast, a low-terrorism

state can be maintained almost indefinitely; during this time, terrorists can recruit individuals,

raise funds, and acquire weapons. As such, low-terrorism states should be more persistent than

high-terrorism states. Enders and Sandler (2002) let yt denote the number of incidents with

deaths over the 1970:1-1999:4 period and estimate the TAR model (with t-statistics in

parenthesis):

yt = [ 21.53 ] It + [ 7.09 + 0.47yt-1 ] (1 – It ), (9) (23.02) (3.12) (2.41)

17

where: 1

1

1 18

0 18.t

tt

if yI

if y−

−

≥= <

The threshold model suggests that there is no single long-run equilibrium value for the

number of incidents; instead, there are high- and low-terrorism regimes or states. In the low state

(i.e., when the number of incidents is less than 18), the system gravitates toward 13 incidents per

quarter [7.09 ÷ (1.0 – 0.47) ≈ 13]. If, however, the number of incidents exceeds the threshold,

there tends to be an immediate jump to 21.53 incidents. Whenever the number of incidents

exceeds this threshold due to a shock or event, there will be an immediate decline to 21.53

incidents in the subsequent quarter. The high-incident state can be maintained until a shock of

sufficient magnitude causes a switch of regime; however, the number of events in this

heightened state cannot be maintained at more than 21.53 incidents. Insofar as the estimated

standard deviation of is equal to 6.14, the magnitude of a typical shock is likely to cause a regime

switch.

Policy Implications

The findings that substitution effects are important have a number of implications for

government policymaking. Clearly, governments must act to reduce the terrorists’ resource

endowments (i.e., their finances, leadership, and membership) if an overall decrease in terrorism

is to follow. Efforts to infiltrate and undermine terrorist groups and to freeze their assets have

the consequence of reducing the overall amount of terrorism.

Even some piecemeal policies that cause substitutions by focusing on only part of the

overall terrorism problem may have some net positive impacts. To the extent that the National

Defense Authorization Act leads to a reduction in the likelihood of biological terrorism,

substitutions into other attack modes will occur. The desirability of such policies is that they

may force terrorists to substitute into less harmful events. Anti-terrorist policies can be most

18

effective when the government simultaneously targets a wide range of terrorist attack modes, so

that the overall rise in the prices of terrorist attacks becomes analogous to a decrease in

resources. A government must maintain the resolve to fight terrorism. Terrorists do not have the

same ability as governments to maintain a sustained offensive. A short-lived governmental

effort to fight terrorism will afford the group time to regroup and replenish its resources.

Success in raising the price of all modes of terrorist attacks and/or in reducing terrorists’

resources would induce them to shift into legal protests and other nonterrorist actions to air

grievances.

Similarly, the development of technological barriers to thwart terrorism causes a

substitution into other attack modes in the short run. In the long term, terrorists will develop

ingenious countermeasures to circumvent the technology. Immediately after airport vigilance

was increased as a result of 9/11, Richard Reid (aka Tariq Rajah) was discovered on a flight from

Paris to the United States with an explosive device in his shoes. Now that airport security

routinely inspects shoes, plastic guns, electronic jamming equipment, bottles of flammable liquid

or other explosive devices are predicted to be hidden on (or in) the terrorist or in carry-on

luggage. Thus, there are dynamic strategic interactions; authorities must be vigilant to improve

technology by anticipating ways of circumventing current technological barriers. This vigilance

must lead to periodic upgrades in the technology prior to the terrorists exposing the technology’s

weakness through a successful attack.

4. What We Do Not Know About the Substitution Effect

ITERATE poses a number of shortcomings that researchers must take into account when

testing theories. First, since it relies on public sources such as newspaper accounts, ITERATE

picks up only newsworthy transnational terrorist incidents. However, what is deemed

19

“newsworthy” changes over time as the public becomes desensitized to terrorism. For example,

ITERATE contains the following incident:

November 5, 1985— GREECE — Police discovered a bomb in a suspicious-looking cloth bag planted between the first and second floors of an Athens building at 8 Xenophon Street. The building housed the offices of Trans World Airlines. Bomb experts removed the bomb and detonated it without mishap.

Given the increased severity of terrorist events, such an attempted bombing might not be

prominently reported in the newspapers. Thus, ITERATE might suggest that certain types of

terrorist events may have declined simply because they are no longer reported. Of course, this

bias is more likely for threats, hoaxes, and bombings without casualties than for incidents with

deaths. The bias has worsened since mid-1996, when the FBI’s Daily Reports became

unavailable to ITERATE coders. Moreover, by relying on newspaper accounts, ITERATE is

better at describing the actions of terrorists than of the authorities. In some instances,

government strategies are revealed and coded in ITERATE. However, anti-terrorism initiatives

may have been undertaken in secret in response to an undisclosed terrorist threat. To circumvent

such limitations of ITERATE, the US government should give proven researchers access to the

unclassified portions of its more inconclusive data sets. The same is true of the RAND-St.

Andrews data set on incidents, which we have tried unsuccessfully to acquire. The true biases in

these data sets can only be ascertained by testing the same hypothesis with alternative data sets.

Clearly, there is much to learn about the substitution effect. Only a portion of the problem

concerns data limitations. Instead of presenting a “laundry list” of unknowns, we conclude with

three useful directions for future research involving substitutions associated with terrorist

negotiations, terrorist recruitment, and terrorist networks.

Atkinson, Sandler, and Tschirhart (1987), Sandler and Scott (1987), Lapan and Sandler

20

(1988), Selton (1988), Islam and Shahin (1989), Scott (1991), and Shahin and Islam (1992)

examine the effects of negotiating with terrorists. If terrorism becomes successful, the HPF

model predicts that terrorists will devote more of their resources to terrorist activities and that

new terrorist groups will emerge. However, the extent to which a concession to one terrorist

group induces additional terrorist incidents needs to be satisfactorily established.

As posited, the HPF model treats the resources of a group as given. Nevertheless, groups

can obtain resources through publicity. An extremely heinous or highly visible attack may

provide a signal that the responsible group is particularly influential or powerful. Such attacks

may lower recruiting costs so that major campaigns become more sustainable. This means that

the recruiting decisions are not independent of the mode of attack.

The HPF model analyzes the choice-theoretic decision of a single terrorist group. If

terrorists are tied together implicitly through similar hatreds (e.g., of Israel and the United

States), then multiple terrorist groups may simultaneously act as a unified whole. However,

there may be important network externalities or interdependencies not directly captured by the

HPF model of a single group. Since attack modes may be complementary, the actions of one

group may affect the behavior of other groups. For example, attacks by al-Qaida may make it

more desirable for a second terrorist group to also attack the US interests. Moreover, strikes

against terrorists in Afghanistan may make it easier for terrorists elsewhere to recruit individuals

and resources. Such complementarities may induce terrorists worldwide to take on the

appearance of a single group even though they have no direct links with each other.

21

References

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Framework.” Journal of Law and Economics. 30:1, pp. 1-21.

Brophy-Baermann, Bryan and John A.C. Conybeare . 1994. “Retaliating Against Terrorism:

Rational Expectations and the Optimality of Rules versus Discretion.” American Journal

of Political Science. 38:1, pp. 196-210.

Carr, Caleb. 2002. The Lessons of Terror: A History of Warfare Against Civilians, Why It Has

Always Failed and Why It Will Fail Again. New York: Random House.

Chalk, Peter. 1995. “The Liberal Democratic Response to Terrorism.” Terrorism and Political

Violence. 7:4, pp. 10-44.

Clutterbuck, Richard. 1992. “Keeping track of terrorists after 1992.” Terrorism and Political

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Enders, Walter and Todd Sandler. 1993. “The Effectiveness of Anti-Terrorism Policies:

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Enders, Walter and Todd Sandler. 1995. “Terrorism: Theory and Applications” in Handbook

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213 - 49.

Enders, Walter and Todd Sandler. 1999. “Transnational Terrorism in the Post-Cold War

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Enders, Walter and Todd Sandler. 2000. “Is Transnational Terrorism Becoming More

Threatening.” Journal of Conflict Resolution. 44:3, pp. 307-32.

Enders, Walter and Todd Sandler. 2002. “Patterns of Transnational Terrorism, 1970-99:

Alternative Time Series Estimates.” International Studies Quarterly. forthcoming.

22

Enders, Walter, Todd Sandler, and Jon Cauley. 1990. “UN Conventions, Technology and

Retaliation in the Fight Against Terrorism: An Econometric Evaluation.” Terrorism

and Political Violence. 2:1, pp. 83-105.

Fleming Peter. 2001. International Terrorism: Attributes of Terrorist Events 1992-1998

(ITERATE 5 update). Personal communication.

Hirshleifer, Jack. 1991. “The Paradox of Power.” Economics and Politics. 3:3, pp. 177-200.

Hoffman, Bruce. 1997. “The Confluence of International and Domestic Trends in Terrorism.”

Terrorism and Political Violence. 9:2, pp. 1-15.

Hoffman, Bruce. 1998. Inside Terrorism. New York: Columbia University Press.

Im, Eric I., Jon Cauley, and Todd Sandler. 1987. “Cycles and Substitutions in Terrorist

Activities: A Spectral Approach.” KYKLOS. 40:2, pp. 238-55.

Islam, Muhammad Q. and Wassim N. Shahin. 1989. “Economic Methodology Applied to

Political Hostage-Taking in Light of the Iran-Contra Affair.” Southern Economic

Journal. 55:4, pp. 1019-24

Jongman, Albert J. 1992. “Trends in International and Domestic Terrorism in Western

Europe.” 1968-1988. Terrorism and Political Violence 4, pp. 26-76.

Juergensmeyer, Mark. 1997. “Terror mandated by God.” Terrorism and Political Violence 9,

pp. 16-23.

Lapan, Harvey E. and Todd Sandler. 1988. “To Bargain or Not to Bargain: That Is the

Question.” American Economic Review. 78:2, pp. 16-20.

Landes, William M. 1978. “An Economic Study of US Aircraft Skyjackings, 1961-1976.”

Journal of Law and Economics. 21:1, pp. 1-31.

Mickolus, Edward F. 1982. International Terrorism: Attributes of Terrorist Events, 1968-

1977. (ITERATE 2). Ann Arbor, MI: Inter-University Consortium for Political and

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Social Research.

Mickolus, Edward F., Todd Sandler, Jean M. Murdock, and Peter Fleming. 1989.

International Terrorism: Attributes of Terrorist Events, 1978-1987. (ITERATE 3).

Dunn Loring, VA: Vinyard Software.

Mickolus, Edward F., Todd Sandler, Jean M. Murdock, and Peter Fleming. 1993.

International Terrorism: Attributes of Terrorist Events, 1988-1991. (ITERATE 4).

Dunn Loring, VA: Vinyard Software.

Sandler, Todd and Harvey E. Lapan. 1988. “The Calculus of Dissent: An Analysis of

Terrorists’ Choice of Targets.” Synthese. 76:2, pp. 245-61.

Sandler, Todd and John L. Scott. 1987. “Terrorist Success in Hostage-Taking Incidents.”

Journal of Conflict Resolution. 31:1, pp. 35-53.

Scott, John L. 1991. “Reputation Building in Hostage Incidents.” Defence Economics. 2:3,

pp. 209-18.

Selten, Reinhard. 1988. “A Simple Game Model of Kidnappings,” in Reinhard Selten (ed.),

Models of Strategic Rationality (Boston, MA: Kluwer Academic).

Shahin, Wassim N. and Muhammad Q. Islam. 1992. “Combating Political Hostage-Taking:

An Alternative Approach.” Defence Economics. 3:4, pp. 321-7.

Wilcox, Phillip C., Jr. 1997. “The Western Alliance and the Challenge of Combating

Terrorism.” Terrorism and Political Violence 9, pp. 1-7.

Wilkinson, Paul. 1986. Terrorism and the Liberal State, rev. ed. London: Macmillan.

Wilkinson, Paul. 1992. “The European Response to Terrorism: Retrospect and Prospect.”

Defence Economics 3, pp. 289-304.

Zagari, M. 1992. “Combating terrorism: Report to Committee of Legal Affairs and Citizen’s

Rights of the European Parliament.” Terrorism and Political Violence 4, pp. 288-300.

24

Figure 1: All Incidents

0

50

100

150

200

250

300

350

1968 1972 1976 1980 1984 1988 1992 1996 2000

Qu

arte

rly

To

tals

Figure 2: Individuals Killed

0

50

100

150

200

250

1968 1972 1976 1980 1984 1988 1992 1996 2000

Qu

arte

rly

To

tals

25

Figure 3: Proportions of Casualty and Death Incidents

0%

5%

10%

15%

20%

25%

1968 1972 1976 1980 1984 1988 1992 1996 2000

Casualties Deaths

Figure 4: Assassinations

0

5

10

15

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30

35

1968 1972 1976 1980 1984 1988 1992 1996 2000

Qu

art

erl

y T

ota

ls

AN EVOLUTIONARY GAME APPROACH TO FUNDAMENTALISM AND CONFLICT

by

Daniel G. Arce M. and Todd Sandler*

Final Version: July 2002

Abstract

This paper investigates the evolutionary equilibria of a clash of cultures game where conflict results from failures to share social power in individual pairings. Members of a general subpopulation are matched with those of a fundamentalist subpopulation, the latter being more cohesive and insistent that their identity traits define the norms for, and outcomes of, social, economic, and political interaction. Simulations of the evolutionary dynamics reveal a tradeoff between the intolerance of fundamentalism and the likelihood of a takeover. This tradeoff is reversed if fundamentalism is falsifiable: affording non-fundamentalists the ability to signal fundamentalist traits produces a bandwagon effect. JEL Classification: D74, C73

*Arce is the Robert D. McCallum Distinguished Professor of Economics & Business, and Sandler is the Robert R. and Katheryn A. Dockson Professor of International Relations & Economics. Arce’s and Sandler’s research was funded through the McCallum and Dockson endowments, respectively. We have profited from comments by Werner Güth, Christoph Engel, and Timur Kuran on an earlier draft. Comments from the participants at the Wörlitz conference are also gratefully acknowledged. The authors assume full responsibility for the paper’s contents.

AN EVOLUTIONARY GAME APPROACH TO FUNDAMENTALISM AND CONFLICT

1 Introduction

Economists have increasingly turned their attention to the study of conflict since KENNETH

BOULDING [1962] published Conflict and Defense: A General Theory. Although four decades

have now elapsed, BOULDING’S emphasis on equilibrium, strategic interactions, and dynamics

continues to characterize modern treatments of conflicts. Conflict can stem from myriad causes

that include contests over resources, political identity, social control, or grievances. Despite the

end of the Cold War and the superpower confrontation, conflict remains prevalent today as

interstate conflict has given way to intrastate conflicts in the form of civil wars (MURDOCH AND

SANDLER [2002]) and subnational clashes among rivalry interests.

There are a number of theoretical foundations to the study of conflict. One foundation

depends on contests or tournaments in which opposing interests use their resources to vie with

one another for a prize (DIXIT [1987], HIRSHLEIFER [2001], SANDLER [2000a]). This literature is

closely akin to the theory of rent seeking, which involves an agent or collective expending

resources to obtain a return that results in no gain to society – i.e., a directly unproductive

activity. For these contests and rent-seeking activities, the conflictual outcome is affected by a

contest success function, which defines appropriative outcome based on the relative “inputs” of

fighting effort (HIRSHLEIFER [2000]). Another theoretical basis of conflict comes from a general-

equilibrium representation, in which a government must allocate resources to stay in power when

confronted by an aggrieved subpopulation, whose resources are being appropriated (GROSSMAN

[1991]). A third foundation for conflict can come from population dynamics, for which

subgroups’ traits or (dissimilar) values can lead to conflict (HIRSHLEIFER [1998], SKYRMS

[1996]). This third basis of conflict is dependent on evolutionary game theory, which predicts

2

that those displaying the “fittest” strategy choices, as determined by their resulting payoffs, will

survive, multiply, and characterize the population.

In this paper, we put forward an evolutionary game approach to analyze fundamentalism

and conflict, consistent with the coexistence of both fundamentalist and non-fundamentalist

subpopulations in the same society. The analysis relies on the Nash demand game (NASH

[1953]), played between pairings of individuals drawn from the society, and SKYRMS’ [1996]

model of evolutionary justice. In pairwise interactions, individuals must bargain over the extent

of social control, for which an equal footing gives each half of the one-unit pie up for

negotiations. One player gains a social dominance over another if his or her take exceeds .5.

The fundamentalist subpopulation is assumed to be sufficiently dogmatic to never settle for a

minority share of social control. We use simulations of the underlying evolutionary dynamics to

show that whether fundamentalist mores characterize social interactions depends upon the

distribution of demands within each subpopulation, and, surprisingly, is inversely related to the

level of fundamentalist intolerance or greediness.

The model is then extended to provide an evolutionary game underpinning to KURAN’S

[1989] novel and important notion of preference falsification, where individuals present public

preferences that may differ from their true private preferences in order to maximize their well-

being. Preference falsification is particularly appropriate for dealing with fundamentalists who

provide more favorable terms for those (i.e., fundamentalist or otherwise) who display

fundamentalist traits (e.g., dress, customs, views). The analysis is also descriptive of any regime

– e.g., communist or fascist – where signaling loyalty is rewarded with preferential treatment that

allows one to “fit in.” A rich set of population dynamics is shown to derive from either the

initial demand proportions of the constituent subgroups or the intolerance of fundamentalists to

those not signaling fundamentalist characteristics. Under some circumstances, even a relatively

3

small percentage of the general subpopulation abiding by a fundamentalist orientation may be

sufficient to lead to a fundamentalist domination over time if intolerance (i.e., greedy demands)

is sufficiently high. Furthermore, fundamentalist intolerance of non-abiders is now

complementary to this process.

Our analysis is in the spirit of recent political science papers where evolutionary game

theory is offered as a basis for understanding ethnic conflict (GOETZE AND JAMES [2001],

JOHNSON [2001], ROSS [2001], SALTER [2001]). Evolutionary game theory treats conflict as

dynamic, so that those in conflict may change over time depending on the efficacy of strategies

played. Moreover, our model accounts for rewards to those who signal in-group loyalty, a

behavior that is consistent with RUSSELL HARDIN’S [1995] notion of One for All, where group

identity can promote collective action. Unlike these earlier contributions, we develop an explicit

model to capture evolutionary dynamics. In particular, we represent a dynamic analysis where

subgroups can change in numbers over time and fundamentalists can differentiate their

treatments of others depending on group actions and identity. Finally, our study differs from

BRETON AND DALMAZZONE [2002], for which the emergence of political extremism hinges on

information control and not on evolutionary dynamics.

The remainder of the paper contains five sections. The basic SKYRMS [1996] model is

presented in Section 2 for a single homogeneous population, where conflicts result from

incompatible demands leading to zero payoffs. In Section 3, our evolutionary game depiction of

the “clash of cultures” extends the Skyrms model to heterogeneous populations consisting of

fundamentalists and a more general subpopulation. Section 4 applies replicator dynamics to

simulate the evolution of ethnopolitical conflicts under alternative population and intolerance

parameters. In Section 5, the analysis permits fundamentalists to make fair demands when

matched with others displaying fundamentalist traits or norms. This behavior not only

4

encourages preference falsification by non-fundamentalists, but also gives rise to interesting

population dynamics. Concluding remarks are drawn in Section 6.

2 The Basic Model

In social interactions, paired agents compete for superiority or control over his or her

counterpart. GIURIATO AND MOLINARI [2002] characterize this control when applied to two rival

groups – fundamentalist and the government – as the share of political power, which varies

between zero (no power) and one (complete power), over the rival group. GURR [1994] similarly

asserts that such rivalries can ultimately lead to conflict over the distribution of access to state

power, which we extend to the notion of social control. Culturally distinct people in mixed

societies are often locked in rivalries over the way that societal norms are consistent with their

distinct identity traits. A larger amount of social control means that an agent has more say over

norms, income distribution, justice, and other social divisions. Because we focus on population

dynamics among heterogeneous groups, the unit of analysis that drives these dynamics is the

division of social control among paired individuals, drawn from different cultural groups.

If two or more groups disagree about the distribution of social control, then a conflict

ensues. Our focus is on dyads, with the goal of displaying the evolution of conflict in pairwise

interactions among individuals belonging to two groups with distinct identities. Rather than being

a limiting assumption, our concentration on dyadic interactions among members of the general

and fundamentalist subpopulations focuses the analysis where the potential for conflict is the

greatest. Such dyads result in equilibrium characteristics for the competing subpopulations that

are truly the collective result of individual fitness instead of corporate or hierarchically decreed

behavior. By correlating fitness with social control, we adapt a longstanding game – the Nash

demand game – that SKYRMS [1996] employs to examine issues of social justice. In the Nash

5

demand game, two players must agree on how to divide a 1-unit good. Each player

simultaneously proposes a share for himself or herself. In terms of our context, a player’s demand

is the minimal amount of social control that he or she is willing to accept. If the proposals are

jointly feasible (their sum is less than or equal to one), then each gets what he or she demands;

otherwise, each receives zero (conflict ensues). Conceptually, this payoff structure allows for

“anti-conflicts” where both parties receive less than what is available (jointly feasible, but

inefficient demands). This feature gives players a strong incentive to increase their demands as

much as possible without losing compatibility (NASH [1953, 131]). The problem of social control

therefore becomes one of coordinating demands in an efficient manner. A priori there is no

assumption of efficiency, but evolutionary pressure will ultimately lead to efficient outcomes. The

game captures the dichotomy between mutual identity and individual self-interest because

cooperative ethnopolitical interactions occur only if each group receives a degree of social control

that meets or exceeds their demand.

SKYRMS [1996] turns the analysis of the Nash game on its head. The usual procedure is

to take the demands of the players as given – i.e., more is better – and find the equilibrium split

given these demands under varying game forms. Instead, SKYRMS posits various types of

demands related to social norms such as fairness and greediness, and analyzes which would

survive in the long-run via an evolutionary framework. This is our point of departure.

Specifically, SKYRMS indicates the following types of demands:

Modest (M): demand xM, where 0 ≤ xM < .5;

Fair (F): demand exactly half, xF = .5; and

Greedy (G): demand more than .5, 1 ≥ xG > .5.

Definition: Πi(xi,xj) defines the fitness of an individual making demand xi in a pairwise

6

encounter with another individual xj; i, j = M, F, G. In the Skyrms game, this payoff is:

(1) Πi(xi,xj) = i i jx if x x 1,

0, otherwise.

+ ≤

Suppose that there is a large population of individuals and that they are randomly matched in

a pairwise fashion to play the Nash demand game. The entries in each cell of Box 1 represent the

outcomes of matching between any combination of modest, fair, and greedy types, as dictated by

Eq. (1). Reading across the M-row of Box 1, the first entry indicates that M-types earn a fitness or

payoff of xM each in pairwise encounters amongst themselves. As previously discussed, such an

inefficient pairing is expected to lead to more competitive future demands and does not bias the

efficiency of our results. In the second entry, when paired with an F-type, the M-type’s fitness is xM

and the F-type’s fitness is .5. In the final entry of this row, an (M,G) matching yields fitness of xM

and xG for the M- and G-types, respectively. The other six sets of payoffs are computed in a similar

manner. If, for example, two F-types are paired, then each receives .5. The pairing of F- and G-

types results in conflict with each receiving 0, as is the case when two G-types are paired.

[Box 1 near here]

This game has several important properties. First, it is an example of a symmetric game,

which has the following two characteristics:

a. Each player has the same strategy set, S.

b. If Πr and Πc are the row and column player’s fitness/payoff functions, respectively, then

Πr[x,y] = Πc[y,x] for all pure strategies x, y ∈ S.

Payoff symmetry implies that an individual who makes demand x against another making

demand y earns the same fitness regardless whether he or she is the row or column player.

7

Second, the concept of a payoff as a measure of fitness indicates that the relative return of

one demand when matched with another (or itself) determines the likelihood that a particular

demand will characterize the population. The lower the relative payoff, the more likely a demand

will eventually be driven out in the evolutionary sense. Over time, the success of a particular

demand is also affected by the distribution of demands within the population. For example, when

greedy types predominantly demand .6, and fitness is as determined in Eq. (1), we need only

consider modest types who demand .4, because this is the demand that earns them the highest

possible fitness in pairwise encounters with greedy types. The reverse could also be said (xG = 1 –

xM) for the survival of greedy types in a population where there is only one predominant xM

demand. As in SKYRMS, we therefore assume that xM = 1 – xG throughout. To capture this

symbiosis in terms of evolutionary dynamics, we make the following set of definitions:

Definition: If ρi is the proportion of individuals in the population making demand xi, and

ρ = (ρ1,ρ2,....,ρN) is the (finite) distribution of all demands, N

ii 1

1,=

ρ =∑ then the expected fitness of

type ‘i’ in the population is: N

i i i j jj 1

E[x , ] (x , x ) •=

ρ = Π ρ∑ .

Definition: The population mean fitness of distribution ρ is E[ρ,ρ] = N

i ii 1

• E[x , ]=

ρ ρ∑ .

A demand has a higher fitness if it receives a better than average return. The average returns

received will be a function of the proportions of the population choosing each of the strategies, so

that we are dealing with the possible equilibria of a dynamic process (HIRSHLEIFER [1982, 15]).

Definition: The growth rate, iρ! , of demand xi behaves according to the evolutionary

replicator dynamic if:

8

(2) i i i•[E[x , ] E[ , ]]ρ = ρ ρ − ρ ρ! .

The replicator dynamic states that the growth rate of demand xi is proportional to the difference

between the expected fitness of types xi relative to the mean population fitness. If i-types

(i = F, M, G) do better than the average fitness, then they will grow within the population;

otherwise, the process of natural selection will cause them to die out. The replicator dynamic

predicts the following growth rate for each type in Box 1:

M M M M M M M F M F G G M•[E[x , ] E[ , ]] •[x • x •.5• ( ) • x • ]ρ = ρ ρ − ρ ρ = ρ − ρ + ρ ρ + ρ + ρ ρ! ;

F F F F M F M M F M F G G M•[E[x , ] E[ , ]] •[.5• ( ) • x •.5• ( ) • x • ]ρ = ρ ρ − ρ ρ = ρ ρ + ρ − ρ + ρ ρ + ρ + ρ ρ! ;

G G G G G M M M F M F G G M•[E[x , ] E[ , ]] •[x • • x •.5• ( ) • x • ]ρ = ρ ρ − ρ ρ = ρ ρ − ρ + ρ ρ + ρ + ρ ρ! .

Instead of finding all equilibrium points for this system of differential equations, we are

particularly interested in those distributions that are dynamically stable. An equilibrium is

asymptotically stable if when slightly perturbed – say, by a mutant invasion of the population –

the system tends to return back to the equilibrium point of the evolutionary dynamics. To this

end, MAYNARD SMITH AND PRICE [1973] made the following definition:

Definition: Distribution ( )1 2 N, ,...,ρ = ρ ρ ρ is evolutionary stable for a symmetric game if:

a. It is a population characteristic that ρrow = ρcolumn = ρ.

b. This distribution fends off mutant invasions that are represented by the alternative

distribution ρm, as specified by the first-order condition (F.O.C) and second-order condition

(S.O.C.):

(F.O.C.) m mE[ , ] E[ , ] ρ ρ ≥ ρ ρ ∀ ρ .

(S.O.C.) m m m mIf E[ , ] E[ , ], then E[ , ] E[ , ]ρ ρ = ρ ρ ρ ρ > ρ ρ .

9

In game-theoretic terms, ρ can be interpreted as a mixed strategy that is an evolutionary stable

strategy (ESS). The condition (a) and the F.O.C. imply that ρ is a symmetric Nash equilibrium.

The S.O.C. is an additional stability condition indicating that if ρm is an alternative best reply to

ρ, then ρ is a better reply to ρm than ρm is to itself. The S.O.C. implies that ESS is a refinement

of Nash equilibrium; indeed, it is a stricter refinement than properness.1 If ρi = 1, then we have

an ESS in pure strategies. ESS is our equilibrium concept because TAYLOR AND JONKER [1979]

establish that it is a sufficient condition for the asymptotic stability of equilibrium points for the

replicator dynamic.

Result 1 [SKYRMS, 1996]: The ESSs for the Nash demand game given in Box 1 are

( M F Gˆ ˆ ˆρ , ρ , ρ ) = (0, 1, 0) and M F G ( , , )ρ ρ ρ = (xM/xG , 0, (xG – xM)/xG).

In biological terms, the first population distribution, (0,1,0), can be interpreted as a

monomorphism, since every individual in this population exhibits the fairness trait. The second

population distribution, (xM/xG , 0, (xG – xM)/xG), can be interpreted as a polymorphism, with

(xM/xG) percent of the population making modest demand xM, and the remainder making greedy

demand xG. If the percentage of M-types exceeds xM/xG, then G-types acquire an advantage

within the population and Mρ! will decrease via the process of natural selection. In equilibrium,

neither the M-types nor the G-types earn a higher expected payoff than the other.

Rather than predicting the particular split that will occur in the Nash demand game,

SKYRMS’ analysis is novel because it identifies the types of demands than can characterize a

population. The strategies employed by individuals become the units of selection, as opposed to

the individuals who employ such strategies. This facilitates our analysis of fundamentalism at a

population level, where identity traits may define ethnopolitical conflict. For example, even 1 In contrast to properness, for n × n symmetric games where n ≥ 3, there may be no ESS (e.g., rock-paper-scissors).

10

though Skyrms’ game is played amongst a homogeneous population, the polymorphic

equilibrium distribution allows for conflict – with probability G G • 0ρ ρ > , a pairwise matching

results in conflicting demands. In the following section, we analyze demands when two

heterogeneous subpopulations interact in the Nash demand game, where one’s demands more

closely resemble the identity traits and cohesiveness of a fundamentalist subpopulation.

3 Clash of Cultures

A clash of cultures between fundamentalists and a general subpopulation is coming to characterize

parts of the globe today (HUNTINGTON [1996]). In northern Africa, this clash involves Islamic

fundamentalists and other population subgroups in Egypt, Algeria, and Sudan (SANDLER [2000b]).

This ethnic conflict may spread to Tunisia and other southern Mediterranean countries. Islamic

extremism also poses political and social instabilities for Turkey (GIURIATO AND MOLINARI

[2002]) and Saudi Arabia. In Israel, Jewish fundamentalists are in conflict with other more

moderate groups, and present a barrier to the peace process, as the 1995 assassination of Prime

Minster Yitzhak Rabin so clearly demonstrated. Fundamentalists have kept Afghanistan at war

for over two decades. Within nearby states, Islamic fundamentalists represent significant political

and social challenges in Pakistan, Uzbekistan, and Tajikistan. In India, Sikh and other extremists

represent a clash of cultures with the general subpopulation. Fundamentalists also pose threats in

the Philippines (Abu Sayyaf Islamic fundamentalists) and Indonesia (Laskar Jihad).

When a fundamentalist subpopulation interacts with a more general subpopulation, the

effect is two-fold. First, the fundamentalists are generally more cohesive; there are organizational

economies of scale associated with a singleness of purpose. Second, fundamentalists are, by

definition, less likely to compromise on societal issues. In this context, we interpret the greedy

strategy as a way of asserting sufficient influence to change the way in which culture, religion,

11

politics, language, status, and other traits determine the outcome of a transaction. Another

interpretation is that fundamentalism signals one’s unwillingness to compromise on these issues.

Our definition of fundamentalism purposely avoids specific reliance on issues such as

religion, violence, irrationality and other characterizations that can misrepresent or too narrowly

define what is a widespread phenomenon. Instead, we represent fundamentalism in terms of group

cohesiveness and an inability to compromise over issues such as morality in private life, corruption in

public state life, and deficiencies in the rule of law, all of which translate into demand for social

control.2 The fundamentalist subpopulation consists of both “zealots” and “followers.” In fact, many

economists have experienced fundamentalism of this type in their academic departments, where some

subgroup gains control over the departmental agenda and will never settle for modest demands. Such

academic fundamentalists exercise decisions on the rankings of journals, hiring, and acceptable

research topics. They often direct the seminar series and determine the prestige afforded to

colleagues’ accomplishments.

At the very least, fundamentalists do not propose minority status for themselves on the

cultural/ethnic issues that define their identity, which implies that fundamentalists eliminate the

modest/moderate strategy from their strategy set. We can use the Nash demand game to examine

whether this interpretation of fundamentalism affects the coordination of social control. Such a

comparative static is an explicit part of evolutionary game theory, where the strategies themselves are

the units of selection rather than the players. Peaceful coexistence often characterizes inter-ethnic

relations (FEARON AND LAITIN [1996]), so that the F strategy remains relevant for fundamentalists.

Fairness implies relatively equal social control irrespective of cultural/ethnic identity. If a more

general subpopulation is represented by the row strategies and the fundamentalist subpopulation is

represented by the column strategies, then the interaction between these two subpopulations is

2 We thank GEORG ELWERT for a discussion of these issues at the Wörlitz conference.

12

displayed in Box 2.

[Box 2 near here]

For this interaction, the Nash demand game is no longer symmetric, so that the replicator

dynamics and definition of ESS do not directly apply. The notion of replicator dynamics can,

however, be adapted by recognizing that, in pairwise matching between agents from distinct

subpopulations, an individual from the row subpopulation only meets individuals from the

column subpopulation. That is, an individual does not meet a colleague or mutant from his or

her own subpopulation, which implies that the S.O.C. for an ESS is vacuous, so that only the

F.O.C. applies. Hence, the asymptotic stability of an incumbent strategy of a subpopulation

requires that it must perform strictly better against the other subpopulation than does any other

(mutant) strategy from its own subpopulation. In such a situation, we must specify distinct

distributions, ρ and σ for the row and column subpopulations, respectively. The replicator

dynamics corresponding to our cross-population discussion of fitness (TAYLOR [1979]) are

defined as:3

(3) i i i i row r•[E[x , ] E[ , ]] for x S S ,ρ = ρ σ − ρ σ ∈ =!

(4) j j j j column c•[E[y , ] E[ , ]] for y S S .σ = σ ρ − σ ρ ∈ =!

Again, a simple static characterization holds for the asymptotic stability for fixed points of these

coupled differential equations:

Result 2 [SELTEN, 1980]: (xi,yj) is an ESS for an asymmetric game if and only if it is a

3 Result 2 is a direct function of SELTEN’S requirement that pairwise matchings occur as in a truly asymmetric contest; i.e., those in ρ-subpopulation (σ-subpopulation) do not meet others in the ρ-subpopulation (σ-subpopulation) in contests that determine social control. Hence, one need not consider mutants representing alternative best replies within the same subpopulation, thus implying that the F.O.C. must hold with strict inequality. By contrast, WÄRNERYD [1993] considers an evolutionary model (in an unrelated context) where matchings within and across subpopulations are possible and the equilibrium occurs in mixed strategies.

13

strict Nash equilibrium.

Strategy pair (xi,yj) is a strict Nash equilibrium when xi is the unique best reply to yj, and

vice versa. Hence, an ESS cannot occur in mixed strategies, because, by definition, any pure

strategy that is played with positive measure receives the same expected payoff. Result 2 is

stated in terms of pure strategies with foresight of this consequence.

From the perspective of our analysis of fundamentalism, SELTEN’S result states that the

equilibria in clash of cultures can only be monomorphic outcomes. This is entirely the aim of

fundamentalist attempts at social control – first, to remove any heterogeneous elements within its

own subpopulation (cohesively raising ethnic identity), and second, to impose its doctrine as the

cultural norm for interaction throughout society. Application of this result to the clash of

cultures game illustrates this point.

Result 3: The ESSs for the game in Box 2 are (F,F) and (M,G).

In contrast to the analysis of the Nash demand game among a single population, now all equilibria are

monomorphic. The monomorphism of the fundamentalist subpopulation is not surprising. What is

novel is that ESS requires the general subpopulation to be monomorphic as well, which is a direct

consequence of SELTEN’s [1980] result. Fairness in both subpopulations is a distinct possibility, but

if any group is to gain the lion’s share, it is the fundamentalist subpopulation – as identified by the

(M,G) equilibrium.

4 The Evolution of Ethnopolitical Conflict

One of the most important contributions of evolutionary game theory is that it provides a theory

of population dynamics that determines how equilibrium is reached. The initial distribution of

demands is unlikely to be monomorphic. If, indeed, the fundamentalist subpopulation rules out

14

moderate behavior – as in the clash of cultures game – the degree to which this creates conflict is

a likely predictor of whether the (F,F) or (M,G) equilibrium prevails. The replicator dynamic

allows us not only to focus on the equilibrium outcome, but also to predict the evolutionary path

over generations of pairwise matchings leading to that equilibrium. We are particularly

interested in how initial demand distributions – among the general subpopulation and/or

fundamentalists – determine which equilibrium results. For this exercise, we use the discrete

version of the replicator dynamics (THOMAS [1986]), where for the initial population distribution

(ρ0,σ0), the distribution at generation k + 1 is given by:

(5) k k k

k 1 i i ii k k k

E[x , ] expected fitness of x under distribution ρ

E[ , ] mean fitness of distribution ρ+ ρ σρ = =

ρ σ,

(6) k k kj j jk 1

j k k k

E[y , ] expected fitness of y under distribution σE[ , ] mean fitness of distribution σ

+ σ ρσ = =

σ ρ.

Eq. (5) states that the proportion of players in the non-fundamentalist subpopulation that make

demand xi in the next generation (k + 1) depends only on how non-fundamentalists do against the

fundamentalists (in generation k), rather than amongst themselves. This is the essence of SELTEN’S

[1980] result, and is reflected in the fact that the fitness of demand xi ∈ Si in the general

subpopulation is determined only through its matching with demand yj ∈ Sj from the fundamentalist

subpopulation. Such matchings occur in generation k according to distribution σk. The numerator of

(5) measures the expected fitness of xi ∈ Si against the fundamentalist subpopulation, σjk, weighted

by the proportion of the general subpopulation, ρik, that makes demand xi. The denominator

measures the average expected fitness of the general subpopulation when distributed according to ρk,

and each individual is matched with a fundamentalist according to distribution σk. If non-

fundamentalist demand xi does better (worse) against the fundamentalists than the mean fitness, this

15

type will increase (decrease) in generation k + 1. Similar intuition holds for (6) – the evolution of

fundamentalist demands depends on the success (failure) of their dealings with non-fundamentalists.

The growth and possible convergence of the demands in the fundamentalist and non-

fundamentalist subpopulations are, in part, determined by the distribution of demands in the

opposing population. Eqs. (5) and (6) reflect a coupled symbiosis – whether or not a

subpopulation converges to distribution ρ* (σ*) not only depends on the initial distribution of its

own demand ρ0 (σ0), but also on that of the coupled subpopulation, σ0 (ρ0). The asymptotic

stability of such a distribution is characterized by SELTEN’S [1980] theorem, stated in result 2.4

The implications of fundamentalism and the potential for conflict can be derived through

a simulation of the discrete replicator dynamics for the clash of cultures game. This simulation

depends on three variables: the greedy demand (xG), assumed to be the same in either

subpopulation;5 the initial distribution (ρ0) in the general subpopulation; and the initial

distribution over fundamentalist demands (σ0). The results for each triple can be summarized by

the graphical depiction of ρFk in Figures 1 and 2. According to result 3, only (F,F) and (M,G)

are asymptotically stable. It follows that if ρFk = 1, the system converges to the (F,F)

equilibrium; if, however, ρFk = 0, the system converges to (M,G).

[Four-panel Figure 1 near here]

In each of the four panels of Figures 1 and 2, the vertical axis depicts the ratio of F-types

in the general subpopulation, ρF, while the horizontal axis indicates the number of generations.

For example, in panel a of Figure 1, a greedy type demands xG = .6 and half of the general

subpopulation is initially fair (ρF0 = .5). If half of the fundamentalist subpopulation is initially

fair (σG0 = .5), the system converges to the (F,F) equilibrium, as ρF

k→1. Yet, the conventional

4 See also TAYLOR [1979]. 5 As xG is dominated for the general subpopulation in Box 2, it is played with probability zero by the general subpopulation in our simulations.

16

wisdom is that it is unlikely that the fundamentalist subpopulation will be so compromising, with

half of its members making fair demands. If, instead, we allow σG0 = .6, Figure 1a illustrates

that the system converges to the (M,G) equilibrium (ρFk→0). For a larger proportion of greedy

fundamentalists, the convergence to the (M,G) equilibrium is even faster. What the simulation

illustrates is that when the fundamentalists are not overly insistent in their demands (xG = .6),

they do not need an initially high level of cohesiveness in order for their identity traits to define

social control. The system converges to (M,G) even though initially only 60% of the

fundamentalists are greedy.

In sharp contrast, Figure 1d illustrates that if we have ρF0 = .5, but the fundamentalist

subpopulation is more obstinate, demanding xG = .9, the system converges to an (F,F)

equilibrium even if 80% of the fundamentalist subpopulation is greedy. The intuition is that,

from such a starting point, fair elements of the fundamentalist subpopulation do much better than

greedy ones against the non-fundamentalist subpopulation. In order for xG = .9 to lead to the

(M,G) outcome, at least 90% of the fundamentalist subpopulation must initially be making this

demand (σG0 = .9). Figures 1a-1d demonstrate that as fundamentalists show less tolerance

(increasing xG), greater proportions of their initial subpopulation distribution must possess this

intolerance if (M,G) is to be the equilibrium.

[Four-panel Figure 2 near here]

Figure 2 presents four panels – 2a-2d – where 80% of the general subpopulation is

initially fair. Even for a small degree of fundamentalist intolerance, xG = .6, in Figure 2a, 90%

of the initial fundamentalist subpopulation must be intolerant for the equilibrium to converge to

(M,G). As xG increases, the speed of convergence to (F,F) increases. In Figure 2d, convergence

to (F,F) occurs within eight generations, even when 90% of the fundamentalists possesses greedy

demands of xG = .9.

17

Result 4: For the clash of cultures game, the following holds:

i. Intolerant fundamentalism (increasing xG) requires initially greater cohesion (a higher σG0) if

they are to take social control. This can be seen by consulting panels a-d of Figures 1 and 2.

Higher fundamentalist demands, xG, require a more cohesive fundamentalist subpopulation

in order for fundamentalism – (M,G) – with a subservant general subpopulation to prevail.

ii. The success of fundamentalism depends on the existence of moderate behavior in the

non-fundamentalist subpopulation. This can be seen through side by side panel

comparisons of Figures 1 and 2. As ρM0 decreases (ρF

0 increases), implying that the

general subpopulation is less willing to acquiesce to fundamentalist demands, the (F,F)

outcome prevails.

iii. Dogmatic fundamentalists (xG = 1) die out quickly. This is because modest elements of

the general subpopulation would earn a fitness of zero when matched against greedy

fundamentalists. If the greedy demand is 1, then the system converges to the (F,F)

equilibrium (not illustrated).

iv. We extend FEARON AND LAITIN’S [1996] study of peaceful and cooperative ethnopolitical

interactions – based on the Prisoner’s Dilemma – to the case of the Nash demand game.

The (F,F) equilibrium occurs for a wide array of initial population distributions and greedy

demands.

5 Preference Falsification

As there are countless incidents of peaceful inter-ethnic relations (e.g., Jordan and Morocco)

despite the presence of fundamentalist groups, the xF demand remains relevant for the

fundamentalist subpopulation. One of the stated goals of fundamentalism is to transform the

general subpopulation, so that fundamentalist traits and norms determine access to state power.

18

An often-observed aspect of fundamentalism is the willingness to make fair demands for

pairwise matchings with others who observe fundamentalist behavior. Notice that we are careful

not to say that fundamentalists make fair demands only with other fundamentalists. When there

are two distinct subpopulations, what is important is the willingness of non-fundamentalists to

behave according to fundamentalist doctrine. If fundamentalism operates in this vein, then the

opportunities are ripe for preference falsification as a means to maximize payoffs and fitness. In

Afghanistan, for example, non-Taliban women wore Burqas and men grew beards as a signal of

their adherence to Taliban mores. In academic departments, non-fundamentalists may mimic

fundamentalist traits so that they are treated better. If, for example, the empiricists are the

fundamentalists, then some theorists may co-author papers with empiricists to enhance their

position.

Our use of preference falsification provides an evolutionary game foundation to the

influential work of TIMUR KURAN [1989, 1991], for which the truthful revelation of preferences

depends on threshold choices for participating in a revolution and the size of a revolutionary

collective. In our model, preference falsification or truthful expression hinges on population

dynamics driven by fitness. As such, the initial demands of non-fundamentalists, as well as the

intolerance (greed) of the fundamentalists, determine whether non-fundamentalists falsify their

preferences by signaling fundamentalist traits. Thus, the underlying “thresholds” for truthful

revelation is dependent on population dynamics and preference parameters. Shocks that change

the population proportions – e.g., US bombing of Afghanistan on 7 October 2001 – can either

augment non-fundamentalist proportions (i.e., ρF) or decrease fundamentalist proportions (i.e.,

σG), so that preference falsification decreases sufficiently, thereby ending an intolerant

fundamentalist regime.

Suppose that non-fundamentalists and fundamentalists alike have access to such a

19

strategy, which signals their willingness to adhere to fundamentalist doctrine, thereby avoiding

cross-population conflict. That is, fundamentalism affords falsifiable behavior to the general

subpopulation such that adherence to this behavior reduces cross-cultural friction. In this

scenario, the following definition proves important:

Definition: A falsifiable fundamentalist strategy, ℑ , is a conditional strategy6 that is

greedy when matched with any strategy other than itself, and fair when matched with others

exhibiting the ℑ -traits. Formally, we have the following strategy:

(7) G

Demand .5 when matched with a from the other subpopulation, and

demand x in all other subpopulation matchings.

ℑℑ =

When falsifiable behavior replaces greediness in the clash of cultures game, the results of

pairwise matchings are given in Box 3. The analyses of Boxes 1, 2, and 3 therefore represent a

natural progression from a situation where fundamentalists eliminate moderate demands in an

attempt to gain social control (Box 1 to Box 2) to one in which they allow for preference

falsification (ℑ ) in a further bid for social control (Box 2 to Box 3). The latter eliminates the

greedy demand, because it is dominated by ℑ .

[Box 3 near here]

By allowing the general subpopulation to avoid intolerance only by adhering to

fundamentalist’s terms, the fundamentalists create a model of behavior – alternative to fairness – that

is aligned with their identity traits. Fundamentalists prefer that social power sharing be done on their

terms, rather than a general principle of fairness. Iran after the 1979 revolution, which brought

Ayatollah Khomeini to power, conforms to this scenario, because individuals who signaled their

adherence to the strict Islamic doctrine were integrated into the society. Similar situations

6 See DAWKINS [1980] for an introductory discussion of conditional strategies.

20

characterize present-day Algeria, Nazi Germany under Hitler, or any regime where tolerance is solely

based on displaying certain identity traits. In contrast to the clash of cultures – where greediness is a

dominated strategy for the general subpopulation (in strategy set Sr) – falsification is not a dominated

strategy for this subpopulation. Indeed, even if preference falsification comes at some cost, ℑ is an

undominated strategy, provided that Πr(ℑ ,ℑ ) > xM – i.e., preference falsification is not too costly. In

this way, the results presented below are not tied to the requirement that Πr(ℑ ,ℑ ) = .5. We have

similar results for simulations in which falsification is costly, i.e., .5 > Πr(ℑ ,ℑ ) > xM.

The game has two ESSs – (F, F) and (ℑ ,ℑ ). At first, the ℑ strategy may appear as little

more than fairness, but an illustrative comparison of two simulations demonstrates that sharing

under fundamentalist terms differs substantially from fairness. Consider the case where the

fundamentalist subpopulation is not initially cohesive; there is a 60:40 split among ℑ - and F-types.

Further assume that the greedy demand is .6. In our first simulation, the initial general

subpopulation distribution is (ρM0, ρF

0, ρℑ0) = (.45, .05, .50). This is illustrated in panel a of Figure

3 where, in contrast to Figures 1 and 2, the evolution of all three types in the general subpopulation

are depicted for an initial fundamentalist distribution (σℑ = .6). The system then converges to the

(ℑ ,ℑ ) outcome. As expected, if more of the general subpopulation is inclined toward ℑ at the outset

(as compared to F), then (ℑ ,ℑ ) results.

[Three-panel Figure 3 near here]

The key to the effectiveness of the ℑ strategy’s impact on the general subpopulation is seen

through a second simulation, where the initial ℑ and F proportions for the non-fundamentalists are

reversed. Suppose that just 5% of the modest types in the general subpopulation are at the outset

willing to behave according to ℑ . That is, given that there are rewards for behaving according to

ℑ , we ask what happens if even a tiny proportion of the modest elements of the general

21

subpopulation opts for ℑ instead, as represented under the distribution (ρM0, ρF

0, ρℑ0) = (.45, .50,

.05). Panel b of Figure 3 illustrates that once such a perturbation occurs, preference falsification

occurs in an extreme way, ultimately resulting in the (ℑ ,ℑ ) equilibrium. From this initial ρ0, the

replicator dynamics produce a situation where by generation 13 the general subpopulation is

almost entirely modest, and 70% of the fundamentalist subpopulation will share with those

elements in the general subpopulation who adopt their cultural identity (σℑ13 = .7 – not illustrated).

Hence, the situation is not stable; (ρM13, σℑ

13) ≈ (1, .7) is not an ESS and the replicator dynamics

bear this out. The general subpopulation further evolves, completely switching to the ℑ strategy!

The convergence to (ℑ ,ℑ ) is unexpected and indicates that ℑ has a much larger basin of attraction

than F, even though each yields .5 payoffs in symmetric matches. The fundamentalist

subpopulation increases monotonically in ℑ – it is becoming more cohesive – and by generation

46 the overall distribution is (ρℑ46, σℑ

46) = (1, 1). This outcome is asymptotically stable, as it is an

ESS for the game in Box 3. Allowing for falsification therefore undermines the robustness of the

fairness outcome and facilitates the acceptance of fundamentalist terms in the general

subpopulation.

Another novel result is that our prior observation that increased greediness requires a

more cohesive fundamentalist subpopulation no longer applies when fundamentalism is

falsifiable. Panels b and c of Figure 3 reveal that, when xG is increased from .6 to .8, the intra-

state distribution rapidly converges to (ℑ ,ℑ ) even though σℑ0 is unchanged at 60% (and ρℑ

0 =

.05). This follows because the benefits of modest demands have decreased relative to falsifiable

ones. Payoffs for xM are .4 in Figure 3b and are just .2 in Figure 3c. Without a falsifiable trait,

the success of increased greediness hinges on the cohesiveness among the fundamentalist

subpopulation (an increase in σG0) (see Figures 1 and 2). For falsifiable traits, more extreme

22

fundamental demands, in sharp contrast, result in rapid convergence to the entire population

displaying fundamentalist traits. This bandwagon effect occurs even for small ρℑ0. Thus, we

have:

Result 5: When the identity traits of fundamentalism are falsifiable and conditionally

fair, then :

i. The falsifiable strategy has a larger basin of attraction than fairness.

ii. Extreme demands applied to anyone not adhering to fundamentalist identity traits will not

only increase the cohesiveness of the fundamentalist subpopulation, but will also cause

the general subpopulation to capitulate rapidly.

As noted by KURAN [1991], the breakdown of preference falsification can result in the

rapid elimination of a regime – e.g., the Milosevic regime in Bosnia, the 1989 Velvet Revolution

in Czechoslovakia, the Taliban in Afghanistan, and the communist regime in East Germany.

With less preference falsification, intolerance is unable to sustain a fundamentalist regime when

the proportion of the general subpopulation making fair demands is large, or the cohesiveness of

the hardline fundamentalists is reduced. Similarly, when members of an academic department

stop falsifying their preferences owing to the departure of a few intolerant colleagues, the overall

acceptance of alternative viewpoints may return, rapidly.

6 Concluding Remarks

This paper has put forth an evolutionary game-theoretic basis of conflict between subpopulations

making different demands for control. The underlying dynamics of our approach to conflict,

where paired individuals cannot agree on a division, is quite different from the (static) rent-

seeking conflict models so prevalent in the literature. Both the evolutionary game and the rent-

23

seeking approaches have their relative strengths and weaknesses. The former is particularly

suited to displaying population dynamics and convergence to an equilibrium where a single type

or trait is in control. Additionally, the evolutionary representation provides a dynamic

framework for KURAN’S [1989, 1991] theory of preference falsification, whereby a non-

fundamentalist subpopulation can co-exist in equilibrium with a fundamentalist one by taking on

the latter’s identity traits. In so doing, greater greed by the fundamentalists to those not

displaying their traits may bolster the fundamentalist’s hold, unlike the case with no preference

falsification. This chameleon behavior by non-fundamentalists may be consistent with rapid

regime changes in response to either the elimination of preference falsification or changing

population distributions brought about by external shocks. Although chameleon behavior can

ensure co-existence between fundamentalists and non-fundamentalists, this behavior is apt to

eliminate non-chameleons from the general subpopulation who make modest or fair demands,

owing to the large basin of attraction for preference falsification. Thus, co-existence through

signaling may come at a high price as Afghanistan sadly demonstrated to the world.

A wide variety of conflict relationships can be examined by evolutionary game theory.

Games other than the Nash demand game can form the basis for future analyses. Additionally,

elements of rent seeking can be introduced into our framework, so that relative efforts by

opposing interests can help determine fitness results among paired encounters with and without

preference falsification.

24

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Princeton, NJ.

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— [2001], The Dark Side of the Force: Economic Foundations of Conflict Theory, Cambridge

University Press: Cambridge.

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Schuster: New York.

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Westport, CT.

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18.

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Its Management”, pp. 71 – 94 in: P. James and D. Goetze (eds.), Evolutionary Theory

26

and Ethnic Conflict, Praeger: Westport, CT.

SANDLER, T. [2000a], “Economic Analysis of Conflict”, Journal of Conflict Resolution, 44, 723

– 729.

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and K. Hartley (eds.), The Economics of Regional Security: NATO, the Mediterranean,

and Southern Africa, Harwood Academic Publishers: Amsterdam.

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Nepotism”, pp. 39 – 70 in: P. James and D. Goetze (eds.), Evolutionary Theory and

Ethnic Conflict, Praeger: Westport, CT.

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of Theoretical Biology, 84, 93 – 101.

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Daniel G. Arce M. Department of Economics Rhodes College 2000 N. Parkway Memphis, TN 38112-1690 USA E-mail: arce@rhodes.edu

Todd Sandler School of International Relations University of Southern California Von Kleinsmid Center 330 Los Angeles, CA 90089-0043 USA E-mail: tsandler@usc.edu

Box 1: Skyrms’ Game (xM = 1 – xG)

M F G Modest (M) xM, xM xM, .5 xM, xG

Fair (F) .5, xM .5, .5 0, 0 Greedy (G) xG, xM 0, 0 0, 0

Box 2: Clash of cultures

F G Modest (M) xM, .5 xM, xG

Fair (F) .5, .5 0, 0 Greedy (G) 0, 0 0, 0

Box 3: Falsifiable Fundamentalism

F ℑ Modest (M) xM, .5 xM, xG

Fair (F) .5, .5 0, 0 Falsifiable (ℑ ) 0, 0 .5, .5

Figure 1

Figure 2

Figure 3

Terrorism and Game Theory

By

Todd Sandler School of International Relations University of Southern California

And

Daniel G. Arce M.

Department of Economics Rhodes College

Forthcoming

Simulation & Gaming

Vol. 34 (3) September 2003

Terrorism and game theory

Abstract

This article examines how game-theoretic analyses of terrorism have provided some policy

insights that do not follow from nonstrategic analyses. Some new game-theoretic applications

are indicated that concern terrorist targeting of businesses, officials, and the general public,

where targets can work at cross-purposes as they attempt to deflect the attack. Other novel

applications involve government choice among alternative anti-terrorism policies, and

government concessionary policy when terrorists are either hard-liners or moderates in their

viewpoint. Directions for future research are also indicated.

KEYWORDS: game theory, terrorism, transnational terrorism, deterrence, preemption,

concessionary policy, target choice, asymmetric information

Terrorism and Game Theory

Over the last two decades, a small group of analysts in economics and political science

have applied game theory to study terrorism,1 which involves the premeditated use or threat of

use of violence or force on the part of terrorists to achieve a political objective through

intimidation or fear. For example, Sandler et al. (1983) present some rational-actor models that

depict the negotiation process between terrorists and government policymakers for incidents

where hostages or property are seized and demands are issued. In their model, terrorists’

valuation of the likely concession to be granted by a government is based on a probability

distribution, conditioned on past governmental concessions. Their analysis illustrates that the

terrorists’ choices and actions are influenced by those of the government and vice versa.

Moreover, each adversary acts on its beliefs of the opponent’s anticipated actions.

Since 11 September 2001 (hereafter 9/11), there are many papers being written by

scholars who apply game theory to the study of terrorism. Game theory is an appropriate tool for

examining terrorism for a number of reasons. First, game theory captures the strategic

interactions between terrorists and a targeted government, where actions are interdependent and,

thus, cannot be analyzed as though one side is passive. Second, strategic interactions among

rational actors, who are trying to act according to how they think their counterparts will act and

react, characterize the interface among terrorists (e.g., between hard-liners and moderates) or

among alternative targets (e.g., among targeted governments, each of which is taking protective

measures). Third, in terrorist situations, each side issues threats and promises to gain a strategic

advantage. Fourth, terrorists and governments abide by the underlying rationality assumption of

game theory, where a player maximizes a goal subject to constraints. Empirical support for

terrorists’ rationality is given credence by their predictable responses to changes in their

constraints – e.g., the installation of metal detectors in January 1973 led to an immediate

2

substitution away from skyjackings into kidnappings (Enders, & Sandler, 1993, 1995; Sandler, &

Enders, 2004). Fifth, game-theoretic notions of bargaining are applicable to hostage negotiations

and terrorist campaign-induced negotiations over demands. Sixth, uncertainty and learning in a

strategic environment are relevant to all aspects of terrorism, in which the terrorists or

government or both are not completely informed.

The purpose of this keynote article is to review how game theory has been applied in the

literature on terrorism. Another purpose is to present some new applications that include

terrorists’ choice of target (i.e., business people, officials, and tourists), governments’ choice

between preemption and deterrence, and government concessionary policy when terrorists are of

two minds – hard-liners and moderates. These applications illustrate how game theory can be

fruitfully employed to enlighten policymaking.

A brief look at the literature

One of the pillars of US anti-terrorism policy is never to negotiate or capitulate to the

demands of hostage-taking terrorists (US Department of State, 2002, p. xii). This same no-

negotiation stance has been taken by other countries, such as Israel. The logic to this policy is

that if a target adheres to its stated no-negotiation policy, then would-be hostage takers would

have nothing to achieve and so would stop abducting hostages. This outcome implicitly assumes

that terrorists only gain from achieving their demands and that both sides are completely

informed so that the subgame perfect equilibrium is to pledge not to concede. Obviously,

something is incomplete about this logic, because terrorists continue to take hostages and even

the staunchest advocates of the no-negotiation policy have reneged on their pledge. For

example, the Reagan administration bartered arms for the release of Rev. Benjamin Weir, Rev.

Lawrence Jenco, and David Jacobsen during the 1985-86 “Irangate” scandal; Israel was prepared

3

to trade prisoners for the school children taken Maalot in May 1974.

Lapan and Sandler (1988) elucidate the policy’s incompleteness with a game in extensive

form where the government first chooses the level of deterrence, which, in turn, determines the

logistical failure or success of terrorists when they engage in a hostage mission. A higher level

of deterrence elevates the likelihood of logistical failure. Based on their perceived likelihoods of

logistical and negotiation success, the terrorists decide whether or not to attack. If their expected

payoffs from hostage taking are positive, then they attack. The game can end in four ways: no

attack; an attack that results in a logistical failure; a successful attack that ends with the terrorists

obtaining their demands; and a successful attack that results in no concessions. Information is

incomplete because the government does not know the payoffs associated with not capitulating

prior to hostage incidents. If a sufficiently important person is secured, then the government

may regret its no-negotiation pledge, because the expected costs of not capitulating may exceed

that of capitulating. That is, the no-negotiation policy is time inconsistent if sufficiently valuable

hostages are captured. Even when the government’s pledge not to negotiate is believed by the

terrorists, a fanatical group may still engage in a hostage mission when a positive payoff is

associated with either a logistical or negotiation failure by advertising the cause or achieving

martyrdom.

Lapan and Sandler (1988) demonstrate that the effectiveness of the no-negotiation

strategy hinges on the credibility of the government’s pledge, the absence of incomplete

information, the terrorists’ gains being solely tied to a negotiation success, and sufficient

deterrence spending to eliminate logistical success. In practice, each of these implicit

assumptions is suspect. Efforts to restrain a government’s discretionary action in hostage

scenarios – say, through a constitutional amendment or costly punishment – are required to

eliminate a government’s ability to renege on its stated policy. Lapan and Sandler (1988)

4

examine the importance of reputation costs in a multi-period model. Their analysis stands in

stark contrast to nonstrategic hostage-taking models by Islam and Shahin (1989) and Shahin and

Islam (1992), where there are no explicit strategic interactions and feedback between adversaries.

Atkinson et al. (1987) uses an extension to Nash’s bargaining game, where time involved

in negotiations is included (Cross, 1969, 1977). The duration of the incident and the bargains

consummated depend on the costs of bargaining, the impatience of the adversaries, the duration

of the incident, and the discovery of bluffs (i.e., threats not carried out). These authors utilize

real-world data from hostage-taking incidents to test the underlying model of bargaining.

Another application of game theory involves terrorists’ choice of targets for a three-

player game involving two targeted nations and a common terrorist threat (Sandler, & Lapan,

1988; Sandler, & Siqueira, 2003). Each nation independently chooses its deterrence

expenditures, which again determines the terrorists’ logistical failure probability on that nation’s

soil. The terrorists pick the venue with the highest expected payoff for their attack. Each

nation’s choice of deterrence confers benefits and costs on the other target. By transferring the

attack abroad, each nation imposes an external cost on its counterpart; however, by limiting

attacks and their severity at home, each nation provides an external benefit to foreign residents.

Moreover, an external benefit arises whenever the deterrence efforts of the nations sufficiently

degrade the terrorists’ expected benefits, so that they attack no one. The more fanatical are the

terrorists, the less likely is the no-attack scenario. Sandler and Lapan (1988) show that the Nash

equilibrium where each nation chooses its deterrence in isolation may result in too much or too

little deterrence when compared with a social optimum, depending on the pattern of external

costs and benefits.3 If, for example, attacks in either country leads to no collateral damage on

foreign residents or interests, then the countries will engage in a deterrence race as each tries to

transfer the potential attack abroad, where it has no residents.4 In a globalized society where a

5

country’s risks from a terrorist attack are equal everywhere, independent deterrence choices

imply too little deterrence as each country fails to account for the protection that its efforts confer

on foreign residents (Sandler, & Siqueira, 2003).

The game-theoretic approach reveals a couple paradoxes. Countries may work at cross-

purposes when deterring terrorist attacks. Although the United States (US) is the target of

approximately 40% of all transnational terrorist attacks, virtually all of these attacks occurred

abroad in recent years with 9/11 being a noticeable exception (Sandler, 2004). US

overdeterrence means that it experiences attacks where it has little authority to do anything about

them. Additionally, efforts to share intelligence on terrorists’ preferences and resources may

exacerbate this overdeterrence if deterrence decisions are not coordinated as nations use this

information to augment efforts to transfer the attacks abroad (Sandler, & Lapan, 1988; Enders, &

Sandler, 1995). This is a standard second-best result in economics in which there are two

relevant policy variables – share intelligence and coordinate deterrence – but joint action only

involves a single variable. This result highlights the beauty of a strategic approach. Standard

intuition suggests that pooling information should enhance welfare, but this is not the case if this

sharing worsens the deterrence race that wastes resources without necessarily increasing security

against a determined terrorist group.

Another game-theoretic representation analyzes a situation of asymmetric information

where the terrorists know their true strength, but the targeted government must guess the

terrorists’ resources based on the level of their attacks. These attacks are intended to apply

sufficient pressures, in terms of costs, to a government, so that it concedes to terrorist demands.

In a deterministic setting, the outcome of the struggle between the adversaries would be known

even before the first play of the game, because, in the absence of ties, a finite game of perfect

information has a unique subgame perfect equilibrium. If, for example, the government is aware

6

that the terrorists possess sufficient resources to force the government to surrender eventually,

then the optimal strategy is for the government to concede at the outset and suffer no attack

damage. If, moreover, a well-informed terrorist group understands that it has insufficient

resources to obtain its political demands, then it is optimal either to abandon the campaign or

expend all of its resources at the outset.

A more interesting and relevant scenario is when the government is incompletely

informed about the terrorists’ capability.5 Lapan and Sandler (1993) analyze this scenario in

which a signalling equilibrium may allow a government to limit its expected costs from attacks,

even though the likelihood of surrender may increase. In this scenario, the extent of terrorist

incidents may provide information to the government about the type of terrorist group – strong or

weak – that it confronts. Attacks therefore serve as a signal that the government can process to

adjust its posterior beliefs concerning the resources of the terrorists (also, see Overgaard, 1994).

Such updated beliefs permit the government to decide whether to capitulate or resist. The

terrorists face an interesting tradeoff – the use of large amounts of their resources at the outset

may correctly or incorrectly convince the government that they are strong, but this outlay results

in less future attacks if the government is unconvinced. A perfect Bayesian equilibrium for the

two-period signalling game is derived in which the government prefers the associated partial-

pooling equilibrium, where the government surrenders to groups whose first-period attacks

exceed a certain threshold, over the never-surrender equilibrium. The pooling equilibrium is

associated with some regret when the government misjudges the terrorists’ true strength based on

initial attacks. Intelligence is valued, because it can reduce this regret by curtailing the variance

of government priors.

Another interesting application of game theory to terrorism involves accommodations

reached between terrorists and a host government (Lee, 1988; Lee, & Sandler, 1989). In such

7

scenarios, a terrorist organization has an implicit understanding that it can operate with impunity,

provided that its attacks do not create collateral damage for the host country. This

accommodation can undo efforts of other countries to retaliate against a terrorist group by

reducing their cooperative payoffs. Thus, nations now have three options in their reaction to

terrorists and their sponsors: do nothing, retaliate against the terrorists and their sponors, or

accommodate the terrorists. The last option helps the terrorists at the expense of the cooperating

nations. Lee (1988) shows that this third option dominates the other two, thereby resulting in a

PRISONER’S DILEMMA where some nations seek such accommodations and, in so doing,

undo the accomplishments of others to curtail the terrorist threat. Once again, pursuit of self-

interest may harm others owing to strategic considerations.

Proactive versus reactive policies

Governments’ anti-terrorism policies are either proactive or reactive. Proactive policy

involves aggressively going after the terrorists and eliminating their resources, infrastructure, and

personnel, while reactive policy concerns protective measures either to divert the attack or limit

its consequences. A preemptive strike against the terrorists or their state sponsors (for example,

the Taliban in Afghanistan) is an example of a proactive policy. Because a preemptive attack, if

successful, eliminates the terrorist threat for all potential targets, there is a tendency to free ride

or rely on the efforts of others.

This is illustrated in matrix a in Figure 1 in which two players – the US and the European

Union (EU) – must decide whether or not to preempt a common terrorist threat. Suppose that

preemption by each country confers 4 in benefits on both countries at a cost of 6 to the country

doing the preemption. If, therefore, the US preempts and the EU free rides, then the EU receives

4 in benefits, while the US nets –2 (= 4 – 6) as costs of 6 are deducted from derived benefits of 4.

8

The payoffs are reversed when the US free rides, while the EU takes action. If, however, both

countries preempt, then each receives 2 in net benefits, as preemption costs are deducted from

gross benefits of 8 (= 2 × 4). The resulting game is a PRISONER’S DILEMMA where no one

takes an aggressive stance against the terrorists.

Figure 1 about here

In matrix b, a different scenario is depicted where, unlike the EU, the US gains a net

benefit from its own preemption, because it is the favorite target for transnational terrorists.

Suppose that US preemption gives it 8 in benefits while conferring just 4 in benefits to the EU as

the US counters its greater threats. Further suppose that preemption by the EU gives 4 in

benefits to both countries. Preemption is again assumed to cost 6. If the US preempts alone,

then it nets 2 (= 8 – 6), while the EU still gets a free-riding gain of 4. If, instead, the EU

preempts alone, then the US receives 4 as the free rider and the EU receives –2. When both the

US and the EU preempt, the US nets 6 [= (8 + 4) – 6] and the EU nets 2. Now, the US has a

dominant strategy to preempt and the EU has a dominant strategy to free ride, leading to the

asymmetric-dominant Nash equilibrium in the upper right-hand cell of matrix b. This game

representation may well characterize the US position after 9/11, where US action was going to

yield high payoffs to the US government. With the collapse of the twin towers of the World

Trade Center and the damage to the Pentagon, the US had to take some kind of decisive action to

maintain legitimacy.

Up to this point, the status quo of doing nothing resulted in a 0 payoff. Suppose,

however, that no action whatsoever leads to a world under siege by terrorists. In this scenario,

the absence of any preemption may imply a negative payoff, which for matrix a would result in a

CHICKEN game whenever this payoff is less than –2 (not shown in Figure 1), the payoff from

acting alone. For CHICKEN, the Nash equilibria has some country responding. A

9

COORDINATION game may also apply to preemption if both countries must combine forces to

achieve the positive payoffs of 2 (= 2 × 4 – 6). This game is displayed in matrix c in Figure 1. If

only a single country preempts, then there are no benefits, but the preemptor incurs a cost of 4 –

thus, the off-diagonal payoffs are (–4, 0) and (0, –4). The two pure-strategy Nash equilibria in

matrix c correspond either to both countries preempting or neither preempting. Thus,

preemption may be consistent with a number of different game forms depending upon symmetry,

penalties for the status quo, preemption thresholds, or other considerations. Even though

preemption confers free-rider benefits, a PRISONER’S DILEMMA may not result.

Next, consider other proactive policies and their associated game forms. In the case of

group infiltration, the nation conducting the operation often secures benefits over and above

those conferred on other potential targets. This follows because the infiltrator can exploit the

intelligence first and will target those terrorist groups that pose the greatest risks to its interests.

As a consequence, an asymmetric dominance is likely to apply, not unlikely the preemption

scenario in matrix b in Figure 1. If, however, the infiltrator receives no special advantages, then

a PRISONER’S DILEMMA is anticipated. Retaliation against a state sponsor of terrorism, such

as the US raid against Libya in April 1986 or the US-led attack against Afghanistan following

9/11, is an analogous situation to preemption with lots of potential free-rider benefits. As such,

the same game forms as those associated with preemption, are relevant. When intelligence is

collected as a proactive policy, the asymmetric-dominance scenario is appropriate, especially if

one nation is more often the target of transnational terrorist attacks. The intelligence collector

gains relative to free riders.

Reactive responses include deterrence, embassy fortification, and UN conventions. For

deterrence, each target takes protective actions to divert the attack. Any nation that spends less

on deterrence becomes the more desirable target. This scenario often leads to a deterrence race,

10

best described as a PRISONER’S DILEMMA with too much action (Sandler, 2003).6 An

analogous scenario characterizes embassy fortification, since the least-fortified embassy becomes

the target of opportunity for the terrorists. All potential targets increase fortification

expenditures, but do not necessarily eliminate the attack if the terrorists are bent on attacking

someone. For UN conventions, a PRISONER’S DILEMMA results when it comes time to

enforce the convention as each nation sits back waiting for others to act for the good of all. UN

conventions on outlawing terrorism and its modes of operation (e.g., skyjackings, attacks against

diplomatic personnel) have been shown to have no impact whatsoever in accord with the Nash

equilibrium of no enforcement, associated with the PRISONER’S DILEMMA representation of

enforcing UN conventions (Enders et al., 1990).

Table 1 about here

Table 1 summarizes the different proactive and reactive policies and their associated

game forms.

Alternative targets

To illustrate the deterrence decision, we apply the model from the literature (Sandler, &

Lapan, 1988; Sandler, & Siqueira, 2003) to a novel choice where a terrorist group can target a

business (B) or tourist (T) venue. As such, this terrorist choice of targets may involve domestic

or transnational terrorism. The terrorists are assumed to stage their attack at a single venue in

each period.7 Additionally, the terrorist group is assumed to be fanatical (i.e., gaining a net

benefit even if the mission fails), so that the group will attack one of the two venues.8 Figure 2

depicts the associated deterrence game tree where the targets go first and choose their level of

deterrence or deterrence costs – i.e., D(θB) for the business target and D(θT) for the tourist target.

By choosing their deterrence expenditure to thwart attacks, the two targets affect the terrorists’

11

perceived probability of success or failure, where θB and θT are the probabilities of logistical

failure when the business or tourist venue is attacked, respectively. Thus, 1 – θB and 1 – θT are

probabilities of logistical success for attacks at these two venues. Deterrence costs increase with

θB at an increasing rate, so that D′(θB) > 0 and D″(θB) > 0. The same is true for deterrence costs

spent to protect tourists.

Figure 2 about here

The terrorists move second where they decide whom to attack, in which their attack

probability πi against target i (= B, T) depends on their perceived probabilities of failure – i.e.,

πi(θi, θj) for i, j = B, T and i ≠ j. This probability function is assumed continuous with ∂πi/∂θi < 0

and ∂πi/∂θj > 0, so that information is not complete with respect to terrorists’ beliefs and values.

The assumed partial derivatives indicate that efforts to decrease success in venue i through

greater deterrence lowers the likelihood of attack there and transfers the attack to the other

venue, so that independent deterrence decisions may work at cross-purposes.

Because terrorists are assumed fanatical, the game can end in four outcomes: terrorist

failure or success at the business target, or terrorist failure or success at the tourist target. Within

the four bold parentheses in Figure 2, the payoffs to business, tourists, and the terrorists are listed

in descending order. Both targets confront costs that they want to minimize, while the terrorists

receive benefits that they want to maximize. Terrorists’ payoffs mi and ni (i = B, T) are not

necessarily known with certainty, so that the terrorists must make an educated choice of target

based on their anticipated gain from success and failure at each of the two potential targets.

We shall focus on the actions of the targets. The business (tourist) target must pay

deterrence costs regardless of the game’s outcomes; hence, this expense is like an insurance

premium, paid in good and bad states. In Figure 2, the payoffs are depicted so that there is no

collateral damage on tourists at a business venue. There are, however, collateral damage of a or

12

h on business interests when a tourist venue is attacked. That is, a terrorist attack on an airport is

sure to affect tourists and business people, while a terrorist attack on a specific business is

unlikely to harm tourists. Some symmetry of costs is assumed in which a direct attack on a

business or tourist location causes damage of A for a failure and H for a success, where H > A.

For collateral costs to business interests, terrorist success is more costly that failure – i.e., h > a.

Based on Figure 2, the expected costs to business from a business attack is:

l(θB) = θBA + (1 – θB)H, (1)

while the analogous costs to tourists from a tourist attack is:

l(θT) = θTA + (1 – θT)H. (2)

The collateral damage from a terrorist attack on business interests is:

v(θT) = θTa + (1 – θT)h, (3)

while the collateral damage from a business attack on tourist interests is:

v(θB) = 0. (4)

Given the assumption on A, H, a, and h, l(θi) decreases as θi increases for i = B, T, and v(θT)

decreases as θT increases, because expected damage falls as terrorist failure becomes more likely.

When acting independently, the expected costs of terrorism to business – denoted by CB – is:

CB = D(θB) + πBl(θB) + πTv(θT). (5)

Owing to the absence of collateral damage, the cost to tourists is:

CT = D(θT) + πTl(θT) + 0. (6)

A Nash equilibrium corresponds to each target choosing its respective deterrence level to

minimize these expressions while taking the other target’s deterrence as given.

To ascertain the relative efficiency of the Nash solution, we must find the social ideal and

compare it with the Nash equilibrium. This ideal is obtained when the deterrence levels are

13

chosen for the two targets to minimize the aggregate cost C:

C = D(θB) + D(θT) + πB(θB, θT)[l(θB)] + πT(θB, θT)[l(θT) + v(θT)]. (7)

For the business target, the comparison is accomplished in a couple of steps. First, we derive the

first-order condition for minimizing costs to the business target by taking the derivative of CB

with respect to θB. This condition includes marginal deterrence costs, the potential harm to

business interests as attacks are diverted to the tourist site, and the marginal benefits of diverting

attacks and limiting damage of a business attack. Second, we minimize social cost, C, with

respect to θB. Third, we evaluate these first-order conditions for social cost at the θB that satisfies

the Nash equilibrium where ∂CB/∂θB = 0,9 denoted by NθB . This evaluation leads to just,

( )N πθ 0θ

TT

B

l∂ >∂

,

since there is no collateral damage on tourists at the business site. This term represents the

external costs that the independent deterrence decision of the business target imposes on tourists

by transferring more attacks to them. This inequality accounts for the potential deterrence race

and implies that business interests independently spend too much on deterrence. Because there

are no tourists to protect at the business venue, there is no opposing external benefits coming

from this deterrence spending.

A different situation characterizes the deterrence decision of the tourist target, because

diversion of a potential attack protects business visitors to the tourist venue in two ways: (1) it

limits the damage to business interests by increasing the likelihood of terrorist failure, and (2) it

makes business interests safer at the tourist site by diverting the attack. To these external

benefits, there is also the external cost of a greater likelihood of attack at the business venue as

the attack is diverted. Thus, whether the tourists’ Nash equilibrium implies underdeterrence or

overdeterrence hinges on which of these opposing influences dominates.10 Compared with the

14

deterrence choice of the business target where there are no opposing external benefits, the

tourists will either underdeter or overdeter to a smaller extent.

There is also a collective action rationale why tourists may actually underdeter and are

less adept at deflecting attacks than a business target. Business firms or their employees at risk

need only act unilaterally to increase their protection; in contrast, tourists at risk must mount a

collective response (which is highly unlikely) or lobby the government for help. This lobbying

effort is anticipated to take a long time before there is any government response and, in the

meantime, tourists or the public at large remain vulnerable. Moreover, tourist targets are varied

and diffused, while business targets are generally more specific and easier to guard. Tourist

attacks have resulted in better protection at airports, monuments, bridges, and some public

places, but not every location can be equally protected, which results in targets of opportunity for

terrorists.

Next consider what would happen if the two targets were officials and businesses (or the

general public). Now officials are better equipped to solve the collective action problem, since

they can allocate public funds to protect themselves as has been done at US embassies and other

government buildings. Thus, it is no wonder that the smallest number of transnational terrorist

attacks are now against the military and government targets. Both the general public and

businesses face the largest number of attacks (US Department of State, 2002, p. 174). As

alternative targets divert attacks, those least able to do so become the victims.

Deterrence or preemption

As shown in the last section, many terrorism-related games involve at least three players.

Another instance concerns two targeted governments – the US and UK – that must choose

whether to focus their anti-terrorism policy on deterrence or preemption. Deterrence diverts the

15

attack by making such acts more difficult, while preemption seeks out the terrorists by

eliminating their base of operations and resources. Each player has two choices: each

government can either concentrate on deterrence or preemption, while the terrorists can either

execute a spectacular terrorist event (e.g., 9/11 or the 1998 simultaneous bombings of the US

Embassies in Nairobi, Kenya and Dar es Salaam, Tanzania) or a normal terrorist event.

For a spectacular terrorist event, preemption costs exceed deterrence costs, while, for a

regular terrorist event, deterrence costs exceed preemption costs. The US-led October 2001

attack on the Taliban and al-Qaida in Afghanistan was an effort to preempt future spectacular

events and was extremely expensive. When a government protects against a spectacular event,

intelligence can limit deterrence costs, so that only key sites are afforded increased security.

Deterrence can, however, be quite expensive for normal terrorism, since potential targets

everywhere must be guarded. Because regular events are planned by terrorists with less security

precautions than spectaculars, preemption costs are anticipated to be less costly than protecting

such a target-rich environment. To simplify the mathematics without changing the strategic

aspects of the underlying game, we normalize deterrence costs for spectaculars to 0 and let C be

preemption costs above and beyond deterrence costs for such events. Similarly, we normalize

preemption costs for regular terrorism to 0 and let c be deterrence costs above and beyond

preemption costs for such events.

The three-player deterrence-preemption game is displayed in normal form in Figure 3,

where the US chooses the row, the UK the column, and the terrorist group the matrix. Matrix a

corresponds to a spectacular, whereas matrix b corresponds to a normal terrorist event. In each

cell, the first payoff is that of the US, the second is that of the UK, and the third is that of the

terrorist group. The payoffs depend on the following “technologies” of deterrence and

preemption. To thwart a spectacular event with certainty, both the US and UK must preempt. If

16

only one country preempts and the other deters, then the event occurs with probability p in the

country doing the preempting. If, however, neither country preempts and a spectacular event

occurs, then it is logistically successful. A “best-shot” technology of preemption applies to a

normal terrorist event; i.e., preemption by either country is sufficient to make the event fail with

certainty.

Figure 3 about here

To compute the payoffs in Figure 3, we must define a couple more terms: S is the

terrorists’ payoff for a successful spectacular, and T is their payoff for a successful normal event,

where S > T. Deterrence by a single nation deflects the attack to the other target, while

deterrence by both countries makes the US the target of choice. With the US being the target of

40% of all transnational terrorist attacks, this is a reasonable assumption. In matrix a, if both

countries deter, then the spectacular is successful against US interests, so that the US loses S

(hence, the –S payoff), and the terrorist group gains S. Owing to our cost normalization, UK’s

deterrence cost is 0. If only one country deters and the other preempts, then the former nets 0

and the latter endures an expected cost of –pS – C, which equals the expected loss from the

attack and the spent preemption costs. The terrorists receive an expected payoff of pS over and

above the costs of the operation.11 In the case of mutual preemption, the spectacular is averted,

so that the countries only cover their preemption costs of C, while the terrorist group loses the

costs of their operation, L, which may include fallen comrades and wasted resources.

Next, consider the payoffs in matrix b, associated with a normal terrorist attack. Mutual

deterrence will lead to a terrorist attack on the US, whose net payoff is the damage, –T, plus the

costs of deterrence, –c. With no preemption, the attack is not stopped. The UK loses just its

costs of deterrence, which has shifted the attack to the terrorists’ preferred target – the US. The

terrorists obtain a gain of T, equal for the simplicity to the US losses. When one country

17

preempts and the other deters, the attack is foiled, so that the former nets 0 and the latter pays its

deterrence costs. The terrorists lose their logistical costs of l, where l is less than L, since more

planning and effort goes into a spectacular. Finally, if both countries preempt, then each nets 0

and the terrorists lose their logistical costs.

There are two potential pure-strategy Nash equilibria for this game. For normal events,

preemption is a dominant strategy for both countries because preemption costs are less than

deterrence costs and preemption can remove the threat. Even though only one country needs to

preempt, both have incentive to do so despite the redundancy of effort. When the payoffs in the

lower right-hand cell in matrix b and matrix a are compared for the terrorists, they prefer

planning the normal event. Thus, the lower right-hand cell is a Nash equilibrium. For a

spectacular, the two countries do not necessarily have a dominant strategy, because S is so large

compared with C, we anticipate that (1 – p)S > C unless the probability of a terrorist success is

near certainty.12 If, however, this inequality does not hold, then the pure-strategy Nash

equilibrium in matrix a is in the upper left-hand cell since S > T for the terrorists. Given a Nash

equilibrium in matrix a and b, there is also a mixed-strategy equilibrium involving a

randomization of strategies. The existence of an equilibrium in both matrices means that the

failure of the targeted governments to coordinate their preemption policy will mean that a

spectacular will succeed on occasions, despite the huge costs that such events imply. This

outcome accords with the facts, where spectaculars with hundreds of deaths occur about once

every two years (Quillen, 2002a, 2002b; US Department of State, 2002).

The outcome of this game is also descriptive of real-world policy where nations rarely

coordinate their deterrence or preemption decisions. In matrix a, this coordination failure leads

to insufficient preemption so that spectacular events occur, whereas, in matrix b, this

coordination failure results in too much preemption. If the Nash equilibrium is as indicated in

18

matrix a of Figure 3, then observation of deterrence by the terrorists encourages a spectacular

insofar as S > T and pS > –L, which holds whether the terrorists observe US or UK deterrence.

If, however, the terrorists only observe preemption by either country, then they require more

information to make the best choice (i.e., pS > –l and –L < –l).

Granting concessions and terrorist types

An unresolved issue in the literature on negotiating with terrorists is the unintended

consequences of increasing violence by conceding to the demands of the more moderate

elements within a terrorist organization. The appeasement of the moderates isolates hard-liners,

thereby leaving an adverse selection of terrorists more inclined to violence. Adverse selection

involves one side of a transaction being more informed than another, which implies asymmetric

information. In the classic example of a used car market, the uninformed buyers reduce their

offers on cars to an average price where many reliable cars are taken off the market, so that a

preponderance of “lemons” remain (Akerlof, 1970).

Figure 4 about here

Figure 4 displays a model of bargaining between a government (G) and a terrorist group

with moderate (M) and hard-line (H) members in proportion p and 1 – p, respectively. Hard-

liners make demands of H, while moderates make demands of M, where H > M. The

government moves first and makes an offer, Ω, of either M or H to the terrorist group. The

government is uncertain about the actual distribution between hard-liners and moderates; hence,

nature (N) moves first and selects the terrorist group’s composition so that the government faces

hard-liners (node GH) in proportion p and moderates (node GM) in proportion 1 – p.

Due to the government’s lack of information about terrorists, nodes GH and GM are

contained within the same information set, thereby implying that the government cannot tailor

19

one offer to moderates and another to hard-liners. Given H > M, there is an incentive for

moderates to posture as hard-liners, because they are better off receiving an offer of H from the

government, the acceptance of which yields a payoff of H – M > 0, as indicated by the third-

from-the-left payoff in Figure 4. In contrast, the acceptance on an offer of M gives the

moderates the baseline payoff of zero as their demands are met.

The government’s benefits from an agreement (prior to deducting the offer) are B when

hard-liners accept and b when moderates accept, where B > b ≥ M and H > b. Although either

terrorist type accepts an offer of H, the government experiences a cost, b – H < 0, from appearing

weak when it concedes H to moderate terrorists. If the government offers H to hard-liners, then

the terrorists accept, giving the hardliners a payoff of 0 and the government a net payoff of B –

H, which may be positive. When, alternatively, hard-liners reject an offer of M, we assume that

they resort to terrorism and violence. For simplicity, we assume that this terrorism costs hard-

liners V to commit, while it inflicts damages of V on the government – the (–V, –V) payoffs. We

assume that M – H < –V, so that hard-liners prefer a terrorist attack to accepting a moderate offer.

Rearranging this inequality makes the definition of a hard-liner more apparent: M < H – V

implies that hard-liners are willing to engage in violence at cost V to obtain demand H in lieu of

the moderate concessions. Since moderates are satisfied with M, there is no net benefit to them

or to the government if they reject such an offer, leading to the far-right (0, 0) payoffs.

What kind of offer should a government make? If it concedes a moderate offer, then

hard-liners will reject it, while moderates will accept it. Given the uncertainty over the

composition of the terrorist organization, the government’s expected payoff for a moderate offer

is:

–pV + (1 – p)(b – M). (8)

In comparison, both hard-liners and moderates will accept an offer of H. The expected payoff

20

for the government is:

p(B – H) + (1 – p) (b – H). (9)

We are concerned when a moderate offer leaves an adverse selection of hard-liner terrorists for

the government to contend with. The government makes a moderate offer only if the expected

payoff in eq. (8) is as least as great as that in eq. (9), which holds for:

(H – M)/(V + B – M) ≥ p. (10)

If the government’s belief that it is facing hard-line terrorists, p, is less than the left-side of eq.

(10), then an adverse selection results, in which moderates are placated and hard-liners resort to

violence. This outcome is contrary to the ultimate goal of the government to end violence.13 A

notable feature of eq. (10) is that the benefits to making a moderate offer, b, do not even figure

into the equilibrium condition.

The possibility of adverse selection increases with hardliners’ demands, H. Moreover,

this likelihood falls with higher costs of violence, V. As B approaches H in value, so that

government’s and hard-liners’ preferences converge, V becomes the sole determinant of the

adverse-selection equilibrium. This may explain why the Diaspora or state sponsors are essential

in perpetuating violence, even though the government and hard-liners agree on the need for a

solution. Subsidies from outside interests reduce V and lead to an adverse selection that

perpetuates hostilities.

Unanswered questions and future directions

There are many unanwered questions with respect to terrorism, for which game theory

can be fruitfully applied. In terms of noncooperative game theory, there is no true multi-period

analysis of terrorist campaigns, where the terrorist resource allocation is studied over time. The

closest analysis is that of Lapan and Sandler (1993) and Overgaard (1994), where terrorists

21

signal their alleged strength in the initial period, but only a two-period analysis is presented. A

many period investigation is required where the conflict between terrorists and the government

has an unknown (probabilistic) endpoint that is influenced by actions of the adversaries. Ideally,

information must be treated as incomplete or imperfect when investigating the temporal and

strategic aspects of terrorist campaigns.

Another area for study involves the use of differential game theory to examine how

terrorist organizations – their personnel and resources – are influenced by successful and failed

operations. By applying a differential game framework, the analyst can display the dynamics of

the strategic choices of the terrorists and the government in which the underlying constraints

capture the rate of change over time of resource supplies based on terrorists’ operations and the

government’s policy choices. The genesis and demise of terrorist groups can be analyzed based

on strategic considerations. If, for example, this demise is understood, then governments may

better plan their anti-terrorist policies. Do some policies (i.e., harsh reprisals) actually encourage

recruitment, opposite to the government’s intent? This question and others can then be

addressed.

To date, cooperative game theory has not been applied to the study of terrorism. In

contrast to governments that have not cooperated effectively, terrorists have formed elaborate

cooperative networks (Arquilla, & Ronfeldt, 2001). Terrorists share training facilities,

intelligence, operatives, innovations, and logistical methods. This cooperation is motivated by

the weakness of terrorists who must pool resources and knowledge if they are to threaten much

stronger governments. Terrorists often harbor common resentment of governments which unite

their interests. Moreover, terrorists are in repeated interactions with one another, where leaders

have no known endpoints unlike officials in democratic governments whose time horizons are

quite finite. These repeated interactions allow terrorist groups to maintain agreements through

22

trigger tit-for-tat mechanisms that punish defections. A careful cooperative game-theoretic

analysis of terrorist groups can provide some useful insights in assessing the true threat of

terrorism. Terrorists’ cooperation allows them to prod government defensive measures to

uncover the weakest link, to which they dispatch their best-shot team to create maximum

damage.

Concluding remarks

Strategic interaction between terrorists and governments, among targeted governments,

and among terrorists make game theory an appropriate tool to enlighten policymakers on the

effectiveness of anti-terrorist policies. This article takes stock of past game-theoretic

applications to the study of terrorism. The article also presents novel applications and suggests

some future applications. Since 9/11, academic interest in modeling and studying terrorism is

increasing greatly.

23

Notes

1. The relevant literature includes Lapan and Sandler (1988, 1993), Lee (1988),

Overgaard (1994), Sandler (2003), Sandler and Enders (2004), Sandler and Lapan (1988), Scott

(1991), and Selten (1988).

2. Terrorists’ high success rate and their ranking of tactics based on risk, time, and

potential confrontation with authorities also support the rationality assumption (Sandler et al.,

1983).

3. At the social optimum, the sum of the two countries deterrence spending is minimized

in order to identify the cooperative outcome.

4. As for an arms race, a PRISONER’S DILEMMA applies in a 2 × 2 representation

(Sandler, 2004).

5. Scott (1989) examines terrorism when the terrorists are uninformed about the type of

government that they confront, but Scott does not consider a signalling equilibrium.

6. This deterrence race is analogous to the problem of the open-access commons, where

mutual action in the form of exploitation of the shared resource leads to a PRISONER’S

DILEMMA and a suboptimal Nash equilibrium (Sandler, & Arce M., 2003).

7. Of course, multiple attacks can be easily addressed, but, for simplicity, we assume a

single attack per period.

8. Other scenarios are addressed in Sandler and Lapan (1988). As groups have become

more religious-based over the last two decades, the act itself gives a positive payoff to the

terrorists.

9. For more complex and different scenarios, these steps are displayed in detail in

Sandler and Siqueira (2003).

10. Overdeterrence or underdeterrence depends on the sign of the following composite

24

term:

( ) ( ) ( )N N N ,T BT T T B

T T

v v lπ ππ θ θ θθ θ

∂ ∂′ + +∂ ∂

where the first two terms are negative and the third term is positive. If the overall sum is

negative (positive), then there is underdeterrence (overdeterrence).

11. This payoff could be easily changed to pS – L with no change in the analysis.

Moreover, a cost less than L could be deducted. Our simple model in Figure 3 only allows the

government to choose between preemption and deterrence. In reality, governments preempt and

deter at the same time. To allow for this possibility, one should view the government strategies

in the model as a greater reliance on deterrence or preemption. Different payoff arrays and

alternative underlying “technologies” of deterrence and preemption can be incorporated into the

model. A rich number of interesting models and outcomes can be displayed, as noted by

Hirofumi Shimizu.

12. This inequality implies that –pS – C > –S.

13. There is, indeed, nothing in the model that restricts us from setting B equal to V.

25

References

Akerlof, G. (1970). The market for lemons: Qualitative uncertainty and the market mechanism.

Quarterly Journal of Economics, 84, (3), 488–500.

Arquilla, J., & Ronfeldt, D. (2001). Networks and netwars. Santa Monica, CA: RAND.

Atkinson, S. E., Sandler, T., & Tschirhart, J. T. (1987). Terrorism in a bargaining framework.

Journal of Law and Economics, 30, (1), 1–21.

CHICKEN. Rapaport, A., & Chaman, A. M. (1969). The game of chicken. In I. R. Buchler and

H. G. Nutini (Eds.), Game theory in the behavioral sciences (pp. 151–175). Pittsburg:

University of Pittsburg Press.

COORDINATION. Watson, J. (2002). Strategy: An introduction to game theory. New York:

W. W. Norton.

Cross, J. G. (1969). The economics of bargaining. New York: Basic Books.

Cross, J. G. (1977). Negotiations as a learning process. Journal of Conflict Resolution, 21, (4),

581–606.

Enders, W., & Sandler, T. (1993). The effectiveness of anti-terrorism policies: Vector-

autoregression-intervention analysis. American Political Science Review, 87, (4), 829–

844.

Enders, W., & Sandler, T. (1995). Terrorism: Theory and applications. In K. Hartley & T.

Sandler (Eds.), Handbook of Defense Economics, Vol. 1 (pp. 213–249). Amsterdam:

North-Holland.

Enders, W., Sandler, T., & Cauley, J. (1990). UN conventions, technology and retaliation in the

fight against terrorism: An economic evaluation. Terrorism and Political Violence, 2,

(1), 83–105.

Islam, M. Q., & Shahin, W. N. (1989). Economic methodology applied to hostage-taking in

26

light of the Iran-Contra affair. Southern Economic Journal, 55, (4), 1019–1024.

Lapan, H. E., & Sandler, T. (1988). To bargain or not to bargain: That is the question.

American Economic Review, 78, (2), 16–20.

Lapan, H. E., & Sandler, T. (1993). Terrorism and signalling. European Journal of Political

Economy, 9, (3), 383–397.

Lee, D. R. (1988). Free riding and paid riding in the fight against terrorism. American

Economic Review, 78, (2), 22–26.

Lee, D. R., & Sandler, T. (1989). On the optimal retaliation against terrorists: The paid-rider

option. Public Choice, 61, (2), 141–152.

Overgaard, P. B. (1994). Terrorist attacks as a signal of resources. Journal of Conflict

Resolution, 38, (3), 452–478.

PRISONER’S DILEMMA. Tucker, A. (1950). A two person dilemma. In E. Rasmussen (Ed.),

Readings in games and economics (pp. 7–8). Malden, MA: Blackwell, 2001.

Quillen, C. (2002a). A historical analysis of mass casualty bombers. Studies in Conflict &

Terrorism, 25, (5), 279–292.

Quillen, C. (2002b). Mass causalty bombings chronology. Studies in Conflict & Terrorism, 25,

(5), 293–302.

Sandler, T. (1992). Collective action: Theory and applications. Ann Arbor: University of

Michigan Press.

Sandler, T. (1993). Collective action and transnational terrorism. World Economy, 26, (4),

forthcoming.

Sandler, T., & Arce M., D. G. (2003). Pure public goods versus commons: Benefit-cost duality.

Land Economics, 79, (3), forthcoming.

Sandler, T., & Enders, W. (2004). An economic perspective on transnational terrorism.

27

European Journal of Political Economy, 20, (1), forthcoming.

Sandler, T., & Lapan, H. E. (1988). The calculus of dissent: An analysis of terrorists’ choice of

targets. Synthèse, 76, (2), 245–261.

Sandler, T., & Siqueira, K. (2002). Global terrorism: Deterrence versus preemption.

Unpublished manuscript, University of Southern California.

Sandler, T., Tschirhart, J. T., & Cauley, J. (1983). A theoretical analysis of transnational

terrorism. American Political Science Review, 77, (4), 36–54.

Scott, J. L. (1991). Reputation building in hostage incidents. Defence Economics, 2, (2), 209–

218.

Selten, R. (1988). A simple game model of kidnappings. In R. Selten (Ed.), Models of strategic

rationality (pp. 77–93). Boston: Kluwer Academic Press.

Shahin, W. N., & Islam, M. Q. (1992). Combating political hostage-taking: An alternative

approach. Defence Economics, 3, (4), 321–327.

United States Department of State (2002). Patterns of global terrorism. Washington, DC: US

Department of State.

28

Todd Sandler is the Robert R. and Katheryn A. Dockson Professor of International Relations &

Economics, University of Southern California. He has used game theory in the study of

terrorism since 1983. In 2003, he is a co-recipient of the National Academy of Sciences’ Estes

award for excellence in science for his research on terrorism. Daniel G. Arce M. is the Robert

D. McCallum Distinguished Professor of Economics & Business, Rhodes College. He has

applied game theory in economics and international relations to a wide variety of problems. His

teaching and research interests involve many aspects of game theory.

ADDRESS: TS: School of International Relations, University of Southern California, Von

Kleinsmid Center 330, Los Angeles, CA 90089-0043, USA; telephone +1 213-

740-9695; fax +1 213-742-0281; e-mail: tsandler@usc.edu.

DGAM: Department of Economics, Rhodes College, 2000 North Parkway,

Memphis, TN, 38112-1690, USA; telephone +1 901-843-3121; fax +1 901-843-

3736; e-mail: arce@rhodes.edu.

EU Preempt Do not preempt

Preempt

2, 2

–2, 4

US

Do not preempt

4, –2 Nash

0, 0

Matrix a: PRISONER’S DILEMMA

EU Preempt Do not preempt

Preempt

6, 2

Nash 2, 4

US

Do not preempt

4, –2

0, 0

Matrix b: Asymmetric-Dominance Equilibrium

EU Preempt Do not preempt

Preempt

Nash 2, 2

–4, 0

US

Do not preempt

0, –4 Nash

0, 0

Matrix c: COORDINATION

FIGURE 1. Three alternative game forms for preemption

!"#$%&'

UK UK

Deterrence Preemption Deterrence Preemption

Deterrence

–S, 0, S

0, –pS – C, pS

Deterrence

–T – c, –c, T

–c, 0, –l

US Preemption

Nash –pS – C, 0, pS

–C, –C, –L

US

Preemption

0, –c, –l

Nash 0, 0, –l

Matrix a: Spectacular Event Matrix b: Normal Event

FIGURE 3. Two-country choice of deterrence versus preemption

(

) *

) *

+,

-

-".

".

!"#/% 0-

1

2

Policies Alternative game forms Proactive policies Preemption Group infiltration Retaliation Intelligence

! PRISONER’S DILEMMA, CHICKEN, COORDINATION,

Asymmetric-Dominance Equilibrium ! Asymmetric-Dominance Equilibrium, PRISONER’S

DILEMMA ! PRISONER’S DILEMMA, CHICKEN, COORDINATION,

Asymmetric-Dominance Equilibrium ! Asymmetric-Dominance Equilibrium

Reactive policies Deterrence Embassy fortification UN conventions

! PRISONER’S DILEMMA (deterrence race) with action ! PRISONER’S DILEMMA with action ! PRISONER’S DILEMMA in terms of enforcement

TABLE 1. Policy choices and underlying games

© Blackwell Publishing Ltd 2003, 9600 Garsington Road, Oxford, OX4 2DQ, UKand 350 Main Street, Malden, MA 02148, USA

779

Blackwell Publishing LtdOxford, UKTWECThe World Economy0378-5920© 2003 Blackwell Publishing Ltd (a Blackwell Publishing Company)June 20032661000Original ArticleCOLLECTIVE ACTION AND TRANSNATIONAL TERRORISMTODD SANDLER

Collective Action and

Transnational Terrorism

Todd Sandler

This paper applies modern tools of economic analysis to examine the nature of transnational terrorism and associated collective action concerns that arise in the aftermath of September 11. Throughout the paper, the strategic interaction between rational terrorists and targeted governments are underscored. Networked terrorists draw on their collective strengths to exploit a maximum advantage over targetedgovernments’ inadequate and uncoordinated responses. A wide range of issues are explored including governments’ deterrence races, undersupplied pre-emption, and suicidal attacks. Myriad substitutions by terrorists limit government anti-terrorism policy effectiveness. A host of policy responses are evaluated in light of economic analysis and past econometric evidence.

1. INTRODUCTION

O

N a clear, crisp morning, US peace and security was forever shattered byfour hijackings on 11 September, 2001 (henceforth, 9/11) that resulted in

the collapse of the World Trade Centre (WTC) towers, the destruction of asection of the Pentagon, and the passenger-induced plane crash on a rural Penn-sylvania field. Within a mere 90 minutes, the potential threat of terrorism and thevulnerabilities of America became understood by a traumatised public. In today’stechnology-based society, an everyday object could be transformed into a wea-pon of mass destruction (WMD). Apparently, al-Qaida terrorists surpassed theirwildest dreams of robbing Americans of their serenity and security. Their hein-ous attack captured headlines for months and will continue to do so for yearsto come on 9/11 anniversaries or as the perpetrators are brought to justice. Bybroadcasting much of the disaster live, including the toppling of the north andsouth WTC towers, the media unwittingly assisted in magnifying the potentialrisks that modern-day terrorism poses. This heightened state of anxiety probablyinduced the anthrax terrorist to act so as to capitalise on the insecurity andhysteria that had already gripped the nation. That is, the mailing of anthrax letterswas a complementary incident for the 9/11 hijackings, thereby allowing the twoincidents to have a greater influence than either would have had on its own.Although those responsible for the two sets of events surely differed, the timingof the anthrax letters was not coincidental.

The events of 9/11 marked the largest ever terror attack on US soil – oranywhere – and resulted in the deaths of just under 3,000 people. The secondlargest terrorist attack on US soil had been the bombing of the Alfred P. MurrahBuilding in Oklahoma City on 19 April, 1995, where 168 people died, while thethird largest attack had been the bombing of Wall Street on 16 September, 1920,

TODD SANDLER is the Robert R. and Katheryn A. Dockson Professor of International Relationsand Economics at the University of Southern California, School of International Relations. Thispaper was presented as a Leverhulme Globalisation Lecture at the University of Nottingham.

780 TODD SANDLER

© Blackwell Publishing Ltd 2003

where 34 people died and 200 were injured.

1

The Wall Street time bomb, left ina horse-drawn carriage, had been technologically unsophisticated, similar to theMurrah building bomb and the 26 February, 1993, bomb at the north tower of theWTC. The 1993 WTC bombing resulted in a 100

×

100 foot crater in the under-ground parking garage (US Department of State, 1994); a slightly different place-ment of this bomb could have imploded the building with greater loss of life than9/11. Based on these last two US incidents, we see that terrorism has been a threatfor some time, while mass-casualty terrorism has been tried well before 9/11.

Terrorists bent on mass destruction only have to be ‘fortunate’ once, whilesociety must be fortunate daily to avoid such catastrophes.

2

Another asymmetrybetween terrorists and the targeted society involves resources: society must pro-tect everywhere to be secure, so that homeland security is very expensive, whileterrorists can concentrate their best effort at a single vulnerable point, so thatterrorism is a cost-effective activity. This is well-illustrated by the 1993 bomb offertiliser, diesel fuel, and icing sugar at the WTC. Even though this bomb costjust $400, it caused $550 million in damages (Hoffman, 1998). Yet another asym-metry involves information, in which the terrorists know their own capabilities,unlike the targeted government, which is not fully informed about the terrorists’resources.

Terrorism is the premeditated use, or threat of use, of extra-normal violenceor brutality to gain a political objective through intimidation or fear of a targetedaudience. To qualify as terrorism, an act must be politically motivated; that is,the act must attempt to influence government policy at home or abroad. Incidentsthat are solely motivated for profit and do not directly or indirectly support apolitical objective are not considered to be terrorism. The political motives ofterrorism are varied and may include Marxism, nihilism, religious freedom,racism, separatism, anti-capitalism, anti-US dominance, or other goals. Since the1979 November takeover of the US Embassy in Tehran, some terrorism hasbeen motivated by the establishment of an Islamic state.

3

To create an atmosphereof fear where everyone feels vulnerable, terrorists

simulate randomness

whenchoosing targets. As the authorities focus on a likely venue, the terrorists oftenstrike elsewhere at less-watched targets. Frequently, terrorists direct their vio-lence against a large audience, not directly involved with the political decisionthat they seek to influence. On 9/11, the plane that crashed into the Pentagon and

1

On mass casualty bombings since 1946, see Quillen (2002a and 2002b). For Quillen, a bombcauses mass casualties if more than 24 people die.

2

This asymmetry paraphrases what the IRA terrorists said in a letter after they learned that their12 October, 1984, bombing of the Grand Hotel in Brighton had narrowly missed killing PrimeMinister Margaret Thatcher. Their letter said, ‘Today, we were unlucky. But remember we haveonly to be lucky once. You will have to be lucky always’ (Mickolus et al., 1989, vol. 2, p. 115).

3

The takeover of the US Embassy in Tehran is a watershed event, which marks the rise ofreligious terrorism in recent decades (Hoffman, 1998; and Enders and Sandler, 2000).

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the one that was intended for the US Capitol marked departures from this pat-tern by targeting decision makers. Extra-normal violence is employed not only tograb headlines but also to elevate anxiety levels, so that the general populationoverreacts to these low probability but high-cost events. As the public becomesdesensitised to the violence, terrorists have escalated the lethality of their attacks.

Terrorism falls into two essential categories: domestic and transnational.Domestic terrorism is home grown and has consequences for only the host coun-try, its institutions, people, property, and policies. In a domestic terrorist incident,the perpetrators and targets are from the host country. Through its victims, tar-gets, institutions, supporters, or terrorists,

transnational terrorism

involves morethan one country. If an incident begins in one country but terminates in another,then it is transnational terrorism, which would be the case for a hijacking of aplane in country A that is made to fly to country B. The toppling of the WTCtowers was transnational, because victims came from many different countries,the mission was planned abroad, and the terrorists were foreigners. An incidentmay be transnational if its implications transcend the host nation’s borders.Transnational terrorist incidents represent

transboundary externalities

, insofaras actions conducted by terrorists or authorities in one country may imposeuncompensated costs or benefits on people or property of another country. In aglobalised world of augmented cross-border flows, there is a blurring of thedistinction between domestic and transnational terrorism.

When terrorist events have significant transnational consequences, numerouscollective action concerns arise. Targeted countries may either work at cross-purposes or fail to cooperate to address the terrorist threat. For example, deter-rence efforts by two or more countries to deflect an attack from the same terroristnetwork may create a deterrence race as each country overspends. In someinstances, the deflection may result in a country’s people or property being hitabroad, where the country has little say over terrorism-thwarting efforts. Theabsence of cooperation may involve a country single-handedly mounting apre-emption on the terrorists and their bases. The purely public benefits, derivedfrom the annihilation of a common terrorist threat, lead to free riding, especiallywhen a powerful country is anticipated by other targeted countries to act. Asimilar retaliator’s dilemma characterises actions to punish a state-sponsor ofterrorism. Ironically, terrorists’ ability to form global networks not only solvestheir collective action problem but exacerbates the collective action problem forthe target countries.

4

The purpose of this paper is to investigate the nature of transnational terrorismand some of the collective action issues that it poses in the aftermath of 9/11. Inparticular, rationality is investigated from alternative viewpoints that includethe terrorist group’s leaders, suicide bombers, and the targeted government.

4

On terrorist networks, see Arquilla and Ronfeldt (2001).

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Additional difficulties, associated with the deterrence and pre-emption dilemmasof targeted governments, are discussed. These governments’ cooperative failuresare shown to play into the hands of networked terrorists, who utilise their collec-tive strengths to augment these governments’ inadequate and non-cooperative re-sponses. Other collective action failures on the part of governments that involveintelligence and duplication of efforts are investigated. Another purpose is toidentify what works and what does not against terrorism. Finally, the costs ofterrorism are addressed for a globalising society.

2. A LOOK AT THE PAST

Table 1 provides a perspective on the nature of transnational terrorist incidentsfrom data published by the US Department of State (1988–2002) or else madeavailable by the Office of the Ambassador at Large for Counterterrorism, USDepartment of State. The coverage is the 1968–2001 period, which representsthe era of transnational terrorism, which really began following the Arab-Israeliconflict in 1967 and the subsequent Israeli occupation of captured territory. Thecolumns in Table 1 indicate the year, the number of transnational terrorist events,deaths from these events, wounded from these events, and attacks on US interests.

A number of essential insights can be drawn from these numbers. First, withthe exception of 2001, transnational terrorism on average results in relatively fewdeaths, especially when compared with the annual 40,000 people killed on justUS highways. In fact, the deaths on 9/11 are approximately equal to all trans-national terrorist-related deaths recorded during the 1988–2000 period. Second,transnational terrorism follows a cyclical pattern with much of the 1990s beinga relatively calm era.

5

Third, attacks on US interests account for a high propor-tion of events, even though relatively few transnational terrorist incidents tookplace on US soil. In 1998 and 2000, there were no such events, while, in 1999,there was just one such event (US Department of State, 1999–2001). This isespecially noteworthy from a transnational externality perspective and under-scores that US success in deflecting attacks abroad has

not

secured the safetyof US interests. Fourth, some years may represent outliers in terms of deaths,wounded, or attacks on US interests. For example, a single noteworthy event –known in the terrorism literature as a ‘spectacular’ – may account for a spike inthe number of dead or injured. Obviously, 9/11 is such an event regarding deaths.In 1998, the simultaneous bombings of the US Embassies in Nairobi, Kenya andDar-es-Salaam, Tanzania, accounted for 291 deaths and almost 5,000 injuries(US Department of State, 1999). The presence of outliers means that statistical

5

The cyclical nature of transnational terrorism is established with rigorous statistical analysis inEnders and Sandler (1995 and 1999), and Im et al. (1987).

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analysis must take them into account. Fifth, except for the casualty figures, trans-national terrorism in 2001 does not appear to be different from other years. Thislack of difference would be confirmed by examining other measures not dis-played in Table 1 – for example, terrorist modes of attacks, venue for attacks, orworldwide distribution of attacks. Terrorist modes of attacks include bombings,kidnappings, assassinations, skyjackings, threats, and other kinds of events.

TABLE 1Transnational Terrorism: Events 1968–2001

Year Number of Events Deaths Wounded Attacks on US Interests

2001 348 3,572 612a 2192000 426 405 791 2001999 395 233 706 1691998 274 741 5,952 1111997 304 221 693 1231996 296 314 2,652 731995 440 163 6,291 901994 322 314 663 661993 431 109 1,393 881992 363 93 636 1421991 565 102 233 3081990 437 200 675 1971989 375 193 397 1931988 605 407 1,131 1851987 665 612 2,272 1491986 612 604 1,717 2041985 635 825 1,217 1701984 565 312 967 1331983 497 637 1,267 1991982 487 128 755 2081981 489 168 804 1591980 499 507 1,062 1691979 434 697 542 1571978 530 435 629 2151977 419 230 404 1581976 457 409 806 1641975 382 266 516 1391974 394 311 879 1511973 345 121 199 1521972 558 151 390 1771971 264 36 225 1901970 309 127 209 2021969 193 56 190 1101968 125 34 207 57

Note:a Data on the number of wounded in the WTC attack is not available and, thus, is not part of this figure.

Source: US Department of State, Patterns of Global Terrorism (1988–2002) and tables provided to ToddSandler in 1988 by the US Department of State, Office of the Ambassador at Large for Counterterrorism.

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Recent analyses show that the underlying motive behind transnational terror-ism has become less driven by Marxist left-wing beliefs and more directed byreligious fundamentalism.

6

Of course, a mixture of motives still justify trans-national terrorism, but the dominant drivers have changed. With this shift to morereligious-based terrorism has come a greater willingness on the part of terroriststo cause casualties. For example, religious groups that declare a Jihad or holywar against another nation consider its people, not just its officials, as the enemyand, thus, legitimate targets. Moreover, religious terrorist groups act out of adesire to satisfy their own goals (for example, ascent to heaven) rather than towin favour with an external constituency. Violence may be viewed as a purifyingact, justified for its own sake, so that claims of responsibility or a list of demandsare not issued. Even though the number of transnational terrorist events is gen-erally lower in the post-Cold War era, the greater violence prediction is borneout by statistical analyses – the likelihood of death or injury for each event isnow 17 percentage points greater per incident (Enders and Sandler, 2000).

3. SUICIDE ATTACKS

In recent times, the importance of suicide attacks has increased; 9/11 illus-trates the carnage that a suicidal mission can wreak. The presence of suicidalpilots allowed the planes to be guided into the WTC towers and the Pentagon. Abomb placed on board these same flights is unlikely to have caused the samedeath toll and destruction on the ground. In addition, Hamas’ use of suicidebombers against Israeli targets has increased greatly during 2002, thereby aug-menting public awareness of such attacks. Suicidal missions are, of course, notnew and can be traced back to Japanese kamikaze pilots during World War II.Kamikaze planes were loaded with explosives to create maximum damage toenemy targets such as ships.

One must ponder a rationality argument for suicide bombers. Alternativeexplanations have, however, been offered to justify suicide missions. Wintrobe(2001) characterises suicidal terrorists as rational individuals, who engage in anextreme trade-off between their autonomy and group solidarity. Wintrobe’ssimplistic analysis hinges on an individual’s desperate search for group accep-tance and cohesion as driving a suicidal terrorist into a

corner

solution, wheregroup solidarity is more valuable than one’s very existence.

7

Wintrobe, however,

6

On the changing motives of terrorists, see Hoffman (1997 and 1998), Enders and Sandler (2000)and Wilkinson (2001 and 2002).

7

Wintrobe’s (2001) argument bears some similarity to Hardin’s (1995)

One for All

theory toexplain the logic of group conflict, where the collective action problem can be overcome throughgroup identity that bolsters individuals’ self-interest when engaging in extreme behaviour againstmembers of a hated opponent group. Self-sacrifice is not a necessary outcome in Hardin’s theory.

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rejects that rewards in heaven can motivate a rational self-sacrifice in a suicidemission.

To show that self-sacrifice is rational, one must demonstrate that the utilityassociated with the suicidal mission is at least as large as the utility of the statusquo. If the utility of the status quo is sufficiently low owing to an absence ofeconomic opportunities or to a sense of injustice, or if the utility of the suicideact is sufficiently high owing to group approval or other rewards, then a terroristmay rationally choose the corner trade-off of self-sacrifice.

There is no reason to dismiss heavenly rewards as one, but not the only, factorthat can tip the utility comparison in favour of a suicide mission. Compensationpaid by Iraq to the family of Palestinian suicide bombers can also tip the balance,especially when the status quo offers grim economic realities. If heavenlyrewards, martyrdom, or family compensation are relevant, then an intertemporalutility comparison is necessary in which the decision maker places value onpostmortem utility. Everyday acts of purchasing life insurance or church attend-ance suggest the relevancy of postmortem utility in individuals’ decision calcu-lus. The suicide mission can also be motivated by deceit, where the terrorist isnot told the true nature of the mission. There is some evidence that the twoterrorists, who drove a yellow Mercedes truck full with explosives into the USMarine barracks at Beirut International Airport on 23 October, 1983, were notinformed about the suicidal nature of their mission (Mickolus et al., 1989, vol. 1).After setting the bomb to detonate, the bombers jumped from the cab of thetruck and tried to run to safety, but did not get very far. In some instances, theterrorists may be forced to take the action because of threats made to their family.Thus, many considerations can induce a terrorist to make the ultimate trade-off,ending at a corner solution.

While poverty can play a role in limiting the operative’s status-quo utility,there is no reason why poverty must be a factor if group identity or heaven’srewards are large. In a recent study of Hezbollah martyrs, an inverse relationshipbetween poverty and participation in suicidal missions was found; this is contraryto what the media say (Krueger and Maleckova, 2002). Hezbollah suicidal ter-rorists did not tend to be poor nor poorly educated in the sample. The study didnot, however, include the employment opportunities of these suicidal terrorists.

8

Education is a necessary, but not a sufficient, condition for obtaining a good job.Nevertheless, this study suggests that the size of the expected utility from carry-ing out the suicidal mission may have to be large, insofar as the utility of thestatus quo is not necessarily small.

Important participants in suicidal missions who have been left out of theanalysis to date are the terrorist leaders and strategists – for example, Osama bin

8

In the case of Israeli Jewish settlers, individuals who attacked Palestinians in the West Bank weregenerally from high-paying jobs. These settlers were not on suicide missions.

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Laden and Ramzi Binalshibh – who dispatch terrorists to their death. It is note-worthy that the higher echelon of al-Qaida, Hamas, and Hezbollah do notsacrifice themselves. Their calculus is impeccable – they preserve their organisa-tion by employing low-cost resources in the form of dispensable young men (andsometimes women) to create maximum anxiety in a targeted audience. Theinverse relationship between poverty measures and participation in suicide mis-sion is probably due to these leaders choosing people to carry out the missionwho possess the requisite intelligence for logistical success. Moreover, the attain-ment of a level of education is a signal of a person’s determination to carrythrough on commitments. Suicidal missions can create particularly high anxietyin a targeted society, because a determined suicide bomber can not only mimicthe identity of the target audience (for example, dress like a devout Jew), but canalso create maximum damage by detonating the bomb at the most opportunemoment. Such missions underscore both the determination of the terrorists andthe vulnerability of the targeted audience.

A final participant is the targeted government, charged with protecting thelives of its citizens. Suicide missions present a real dilemma to these govern-ments. In general, deterrence policies work best if they can create price changesassociated with terrorist operations that induce terrorists to substitute from moreharmful activities into less harmful ones. The presence of a corner solutionfor the terrorist operative and also for the terrorist leader implies that policieswhich reduce suicidal missions’ probabilities of success have no influence what-soever on these agents’ choices (Enders and Sandler, 2003). This then impliesthat the government must either apprehend or kill suicidal terrorists for attacksto stop.

4. COOPERATION FAILURES AND THEIR COSTS

Unlike the governments that they target, terrorists have progressed in solvingtheir collective action problem. From the early 1970s, terrorist groups engagedin transnational acts have been tied either explicitly or implicitly to networksconsisting of left-wing terrorist groups united in their goal to overthrow demo-cratic governments (Alexander and Pluchinsky, 1992), Palestinian groups unitedin their aim to establish a homeland or to destroy Israel, and fundamentalistterrorist groups united in their goal to create nations founded on fundamentalistprinciples (Hoffman, 1998; and US Department of State, 2001). Terrorist net-works cooperate on many levels, including training, financial support, logisticalhelp, intelligence, weapon acquisition, pooling resources, and the exchange ofoperatives – for example, operatives were exchanged in the 21 December, 1975,attack on the Organisation of Petroleum Exporting Countries ministerial meetingin Vienna, and in the 27 June, 1976, hijacking of Air France flight 139 (Alexander

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and Pluchinsky, 1992).

9

The al-Qaida network operates in upwards of 60 coun-tries and stages their attacks worldwide. This network includes such groups asAbu Sayyaf (the Philippines), Egypt’s Islamic Group, Harakat ul-Mujahidin(Pakistan), Islamic Movement of Uzbekistan, Al-Jihan (Egypt), and bin Laden’sown group (US Department of State, 2001). Even left-wing groups and Palestin-ian groups have been known to train together and to have other ties (Hoffman,1998; and Wilkinson, 1986 and 2001), so that separate networks have explicitlinks to one another. These networks’ common hatred of the United States andIsrael means that heightened attacks by groups in one part of the world can sparkincreased attacks in other parts of the world. This implicit coordination shows upas distinct cycles of peaks and troughs in transnational terrorist activities.

10

The ability of terrorists to cooperate heightens the inefficiencies associatedwith governments’ inability to cooperate, except episodically – for example, inbuilding the coalition to defeat the Taliban and to attack al-Qaida camps andbases in Afghanistan. This inability of governments to cooperate is first illus-trated for deterrence and pre-emption.

a. The Deterrence Race

In the top panel of Figure 1, a symmetric deterrence game is displayed for twocountries –

A

and

B

– that are confronted by a common terrorist threat. Supposethat increased deterrence gives a private, country-specific gain of 6 to the deter-ring country at a

cost

of 4 to

both

countries. For the deterring country, cost arisesfrom deterrence expense and the increased likelihood of experiencing damagesabroad if the attack is deflected there. For the non-deterring country, the coststems from the damages that it can suffer from attacks diverted to its soil. If thereis a host-country disadvantage from damages, then this damage can exceed thatof the other country. For simplicity, the damage and deterrence expense of thedeterring country is equated to the damage cost of the non-deterring country –hence, the common cost of 4.

Based on country-specific gains of 6 and the public cost of 4 stemming fromeach country’s deterrence, the payoffs listed in panel

a

arise, where country

A

’spayoff is on the left and country

B

’s payoff is on the right in each cell. If, forexample, each country increases its deterrence, then each receives

−

2 (= 6

−

2

×

4); if, however, only one country augments its deterrence, then the deterringcountry nets 2 (= 6

−

4) and the other country suffers the spillover cost of

−

4.The deterrence game has a dominant strategy since

−

2 >

−

4 and 2 > 0, so that

9

These specific incidents are described in Mickolus (1980) under their specific dates. The hijack-ing of Air France flight 139 is famous because of the eventual storming of the plane at the Entebbeairport in Uganda by Israeli special forces.

10

See the statistical results in Enders and Sandler (1999).

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the payoffs associated with increased deterrence are larger than the correspond-ing payoffs associated with the status quo for each of two countries.

11

Eachcountry plays its dominant strategy and augments deterrence, thereby ending upat the Nash equilibrium of mutual action where payoffs are less desirable thanmutual inaction. The former is a Nash equilibrium, because neither countrywould

unilaterally

want to change its strategy and return to the status quo. Thedeterrence scenario in Figure 1 is a Prisoners’ Dilemma, analogous to an armsrace, where countries spend more but do not necessarily become more secure.With fanatical terrorists who will not be deterred from attacking some country,deterrence will not necessarily improve security, especially in a globalised worldwhere a country’s citizens can be attacked at home or abroad. Thus far, thedeterrence analysis suggests

over-deterrence

in which each country does notaccount for the external cost that their efforts to deflect the attack generate foranother country. For this scenario, the greater the number of countries, thegreater the extent of over-deterrence.

11

This analysis of deterrence is analogous to models presented in much greater detail in Sandlerand Lapan (1988) and Sandler and Siqueira (2002).

FIGURE 1Deterrence and Pre-emption Games

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Under-deterrence may characterise the deterrence game for an alternative setof payoffs. Suppose that a country’s people or property is most vulnerable abroadowing to secure borders at home. Further suppose that the host country experi-ences little collateral damage from an attack on its soil. In this case (not dis-played in Figure 1), there will be under-deterrence, because the host country willnot account for the external benefit that its deterrence confers on foreign visitors,targeted by host-country terrorists.

12

In the general case, the deterrence scenario has both external cost and externalbenefit. External cost arises as deterrence deflects an attack abroad, while exter-nal benefit stems from either the protection afforded to foreigners or the elimina-tion of an attack altogether. Thus, a wide range of strategic scenarios and resultsare possible depending on whether external cost or benefit is stronger.

b. Pre-emption Game

In the bottom panel of Figure 1, a canonical

pre-emption game

is displayed,in which each of two targeted countries must decide whether or not to launch apre-emptive attack against a common terrorist or state-sponsor threat. The pre-emptive strike is intended to weaken the terrorists or their sponsors, so that theypose a less significant challenge. For comparison purposes, payoffs analogous tothe symmetric deterrence game in Figure 1 are chosen. If a sole country pre-empts, then it confers a public benefit of 4 on itself and the other country at acost of 6 to just itself. In the off-diagonal cells in the bottom matrix, the countrydoing the pre-emption nets

−

2 (= 4

−

6), while the free rider receives 4. Whenneither country pre-empts, each receives 0, whereas mutual pre-emption gives 8(= 2

×

4) in benefit at a cost of 6 for a net payoff of 2, as listed, for bothcountries. The dominant strategy is not to pre-empt, since 0 >

−

2 and 4 > 2.Mutual inaction results in the Nash equilibrium of this Prisoners’ Dilemma game.

Even though in their most basic form, the deterrence and pre-emption games leadto Prisoners’ Dilemma, there are essential collective action differences in thesetwo collective action problems. First, the Nash equilibrium for the deterrence gamerequires mutual action, while the Nash equilibrium for the pre-emption gamerequires mutual inaction. Second, the matrix games are negative transposes of oneanother, in which the Nash payoffs are more damaging for the deterrence game.

13

Third, whereas the deterrence game has both over-deterrence and under-deterrence

12

This scenario characterises the Greek authority’s inability to deter 17 November terrorist attacksagainst US, NATO, and other foreign targets in Greece. In the summer of 2002, an accidentalexplosion – and not clever police work – led to the first arrests of 17 November members. Since1973, 17 November carried out 146 attacks and murdered 22 people prior to these arrests (Wilkin-son, 2001, p. 54).

13

The deterrence game is analogous to the commons problem, while the pre-emption game isanalogous to the pure public good problem (Sandler and Arce, 2002).

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scenarios, owing to the presence of external cost and benefit as the game isgeneralised, the pre-emption game involves too little pre-emption owing to thepresence of just external benefits. Fourth, deterrence efforts may be complemen-tary, while pre-emption efforts are always substitutable unless a threshold levelof action is required. Thus, increased deterrence by one country should augmentthese efforts by the other country, whereas pre-emption actions by one countryshould limit these efforts by the other country.

c. A Maximal Externality

The deterrence and pre-emption dilemmas have plagued international effortsat a coordinated response for the last 35 years from the start of the modern eraof transnational terrorism. The deterrence and pre-emption dilemmas are but twomanifestations of the unwillingness of nations collectively to confront the terroristthreat. Similar dilemmas involve retaliation against a state-sponsor of terrorismor the pooling of intelligence. The application of game theory to the study of terrorismshows that there may be a rational basis – for example, the playing of a dominantstrategy – for these collective action failures. Nevertheless, one must wonderwhy terrorists solve their collective action dilemma, but governments do not.

Governments place great weight on the importance of their autonomy overnational security. Only during times of great threat (such as after 9/11) or war donations eschew their autonomy and form tight alliances to present a united frontagainst an adversary. In contrast, the terrorists are always at grave risks from amore powerful opponent, so that they have little choice but to pool their limitedresources and rely upon one another. In addition, the terrorists are relatively unitedin their hatred of a few countries – the United States, Israel, and the United Kingdom.Countries perceive their risks differently – that is, some are worried about beingthe target of an attack and others are not – and possess economic interests that maybe at odds with addressing the terrorist threat. If, for example, country

A

has lucra-tive contracts with a country that helps sponsor terrorism, then country

A

will notsupport hostile actions against this alleged state-sponsor. Moreover, terrorists takea long-term view of their struggle and consider their interactions with other groupsas continual; in contrast, governments take a short-term view (limited by the elec-tion period) of the terrorist threat and do not necessarily consider their interactionwith other governments as continual. As a consequence, the terrorists view the under-lying game as infinitely repeated, while the governments do not, so that cooperationbecomes a potential solution for the terrorists but not for the government.

14

By forming a global network and exploiting targeted countries’ uncoordinatedresponses, terrorists not only limit the effectiveness of these countries’ efforts tocounter terrorism, but are also able to maximise the externalities (and, hence,

14

On such repeated games and cooperative solutions, see Sandler (1992, Ch. 3).

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inefficiency) that governments impose on one another. Uncoordinated responseson the part of governments mean that there is a weakest-link vulnerability for theterrorists to exploit. For example, by not maintaining airport security to anagreed-upon global standard, some airports present an easier target than others.Terrorists will probe airport security until these weakest links are uncovered andthen direct attacks there. Such terrorist actions are no different from those of avirus that seeks out and attacks a more vulnerable host. In a globalised worldwhere a country’s citizens can be targeted anywhere, the consequences of terror-ist cooperation coupled with government non-cooperation is that targets’ truelevel of protection is very small. The external cost imposed by the most inade-quate prophylaxis is exacerbated further, because the terrorist network dispatchesits

best-shot

response in the form of its best placed and trained squad. Hence,terrorist targets experience the maximal external cost possible, while the terroristsgain the maximal external benefit. This nightmarish outcome continues today.

This combination of collective action success and failure on the part of terror-ists and governments, respectively, highlights the unusual challenge that trans-national terrorism really poses to the world. Today, a country cannot rely on itsown efforts to ensure its citizens’ safety. As Table 1 illustrates, the United Statesexperiences the largest share of transnational attacks even though few occur athome. So what is the solution? The answer is easier said than accomplished.Unlike the terrorists, nations must also form a global network to face off againstthe terrorist networks. Short of terrorists using WMD, governmental networks onpar with those of the terrorist will not be formed; instead, there will be partialcooperation – for example, sharing of select intelligence.

Ironically, partial cooperation can worsen the inefficiency as compared tonon-cooperation. Suppose that countries are deciding whether or not to coordi-nate efforts on deterrence and intelligence. Further suppose that countries decideto share intelligence but not deterrence efforts, which is a common outcome.Among other things, the intelligence provides information as to the terrorists’preferred target – that is, which country it wants to attack. Knowledge of terrorists’preferences assists the would-be targets to better deflect the attack, so that aneven greater level of over-deterrence results.

15

This ‘second-best’ outcome is notuncommon in economics when only one of two choice variables is controlled.

5. ANOTHER COLLECTIVE ACTION FAILURE

To date, nations have relied on their own commando forces to address hostageexigencies at home or abroad involving their citizens. Thus, the United States hasDelta Force, while virtually every EU country maintains its own force. This

15

This outcome is shown mathematically in Enders and Sandler (1995) and Sandler and Lapan (1988).

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failure to pool resources means that economies of scale are not exploited, so thatthe average cost of these squads is much higher than they need be. Moreover,since each country’s force is dispatched less often when compared with a multi-country force, learning economies, which shift down the average cost per deploy-ment, are not captured. The infrequent use of these commandos means that theydo not acquire the experience to hone their skills in real deployments. Of course,the presence of parallel forces indicates that efforts are duplicated, which is anadditional waste of resources. Because a squad may have to be dispatched somedistance away to address a hostage mission abroad (for example, Delta Force wassent to the Mediterranean during the

Archille Lauro

ship hijacking), a countrymust either maintain a network of bases worldwide or else risk the news mediaalerting the hostage takers of the commandos’ travel progress (as CNN did dur-ing the

Archille Lauro

incident). A multi-country squad can establish such aglobal network at a more reasonable per country expense than associated with asingle country’s effort. Once again, nations cherish their autonomy and balk atsuch cooperative approaches. Countries do not want to obtain other countries’ per-mission to deploy such forces during a crisis. Consequently, anti-terrorist effortsremain expensive and generally independent among nations.

6. IS THE WORLD DIFFERENT AFTER 9/11?

Following the events of 9/11, the world better understands the threat thattransnational terrorism poses. Before 9/11, only 14 transnational terrorist inci-dents involved more than 100 deaths and none had over 500 deaths (Hoffman,2002, p. 304). Although the events of 9/11 have dramatically changed our livesin terms of our risk assessment of terrorism and governments’ efforts to ensureour safety, terrorists’ activities have not altered much because of 9/11. That theauthorities had dismissed the use of a commercial airliner as a murderous bombis rather incomprehensible given some earlier events. On 5 September, 1986,hijackers took over Pan American flight 73, a Boeing 747, at the Karachi airportwith the aim of crashing it into an Israeli city (Mickolus et al., 1989, vol. 2, pp. 452–7).This plan was never executed, because commandos stormed the plane in Karachiwhile it was still on the tarmac. The true intentions of the terrorists were revealedduring the 1988 trial of those captured. Another unmistakable omen was the24 December, 1994, hijacking of an Air France passenger plane in Algiers by ArmedIslamic Group (GIA) terrorists, dressed in Air Algerie uniforms. Their missionwas to crash the Algiers-Paris flight into a crowded area of Paris with great lossof life. In a stopover in Marseille, a French anti-terrorist commando squad stormedthe plane and killed the four hijackers before they could wreak death and destruc-tion from the sky (Oklahoma City National Memorial Institute for the Preventionof Terrorism, 2002, website at http://db.mipt.org). Another portentous event was

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the capture of Ramzi Youssef, the mastermind of the 1993 bombing of the WTCand an al-Qaida associate, in the Philippines in 1996. At the time of his capture,he had plans to use a dozen commercial airliners to destroy a variety of targetsincluding the Central Intelligence Agency (CIA) headquarters in Virginia.

These forerunners to 9/11 indicate that the threat of catastrophic incidents withmassive casualties has been around since 1986. As such, 9/11 marked the daywhen the terrorists were very lucky and their target very unlucky. Although 9/11was a watershed event of transnational terror, given its horrible consequences, itis better viewed as a reality check than the start of a new type of terrorism.Annual death tolls will remain like those of Table 1 with deaths well below 1,000on average in any given year. There has been little change in the pattern of globalterrorism since 9/11, except that the total number of events are somewhatsmaller, but not greatly so, owing to the disruption in al-Qaida operations inAfghanistan. Given the massive casualties of 9/11, authorities are quite worriedabout terrorist use of WMD in the form of chemical, biological, radiological, ornuclear (CBRN) attacks. Nevertheless, many terrorist experts believe that greatervigilance should be directed toward conventional methods rather than CBRNattacks (Hoffman, 2002; and Wilkinson, 2002).

Global efforts to thwart terrorism have only changed marginally. The globalresponse is still US-led, which is not surprising because US interests remainthe favourite target of international terrorists. As such, the United States gains themost country-specific benefits from their anti-terrorism ‘war.’ With US actions inAfghanistan, the Philippines, and Iraq, US interests will continue to attract the lion’sshare of transnational terrorist attacks. Unlike other countries, the United Stateshas the power-projection capabilities to move massive forces to troublespotsquickly; as such, the United States affords free-rider opportunities for others.

Although the US-led retaliation against the Taliban on 7 October, 2001, forharbouring Osama bin Laden involved other nations as allies, the current fightagainst terrorist networks is mostly nation driven. Nations still refuse to extraditeterrorists and to integrate their anti-terrorism efforts, except in terms of the shar-ing of intelligence. Concern for national autonomy still dominates against effortsto mount a united front against terrorists. Even international actions to freezeterrorist assets have not progressed much after some initial headway immediatelyfollowing 9/11. International cooperation remains a collective action failureexcept for a few bright spots – for example, the capture in 2003 of an al-Qaidacell in Spain and US-UK cooperation.

7. WHAT WORKS AND WHAT DOES NOT AGAINST TERRORISM?

One possible recommendation as to what works is to eliminate the causesof terrorism under the presupposition that, with no grievances or perceived

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injustices, there will be no terrorism. There are some obvious difficulties withthis quick fix. If terrorists can extort any political change that they desire byeither threatening or performing violent acts, then democratically elected govern-ments would lose their intended purpose, because the voters’ choices can becircumvented by well-armed minorities. Obviously, the legitimacy of a liberaldemocracy, whose mandate rests on the protection of lives and property, wouldbe greatly weakened. Part of these property rights is the ability of duly-electedofficials to pursue policies that reflect the wishes of the electorate. If governmentsseek to correct any claimed injustice, then an aggrieved minority can inducesizeable redistributions of wealth to them by threatening terrorism unless suchinequities are redressed. Such extortion-based redistributions undermine propertyprotection. Once terrorists discover a causal link between alleged grievances andgovernment actions, there will be no stemming the growth of terrorism as atactic. Moreover, social discontent is a dynamic factor that is constantly chang-ing; efforts to rectify one social wrong do not eliminate new injustices tomorrow.In fact, tomorrow’s injustice may stem from addressing yesterday’s injustice.

a. Barriers and Fortifications

Given the absence of a simple panacea for transnational terrorism, potentialtargets have relied on technological barriers to thwart a particular type of attack.The installation of metal detectors to screen airline passengers is, perhaps, thebest instance of such barriers. These metal detectors were installed in US airportsbeginning 5 January, 1973. Shortly thereafter, these devices were placed in air-ports worldwide to monitor passengers and their carry-on luggage on domesticand international flights. Prior to January 1973, skyjackings worldwide averagedover 16 per quarter or 64 per year. Shortly after metal detectors were installed,there was an immediate and permanent drop of almost eleven skyjackings perquarter (Enders et al., 1990a). This is a rather dramatic impact that was long-lasting. A similar effectiveness was experienced following the fortification of USembassies and missions in October 1976: prior to the fortification, there wereabout eight attacks per quarter against US diplomatic targets; after the fortifica-tion, there were just over three attacks per quarter against US diplomatic targets(Enders et al., 1990b, Table 2).

But this is not the whole story. When one mode of attack is made moredifficult or expensive to conduct, terrorists have substituted other relatively cheaperevents. If, for example, skyjackings are more difficult due to metal detectors, thenother hostage-taking events are now relatively cheaper. Similarly, recent effortsto secure commercial airliners from terrorists’ attempts to use them as massivebombs will induce terrorists to look to the use of cargo planes to accomplish suchmissions. If the effectiveness of an anti-terrorism policy is to be analysed prop-erly, then its influence on other related modes of attack must be investigated.

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When the impact of metal detectors is examined more closely, these detectorsare seen to decrease skyjackings and threats, but to increase other kinds ofhostage incidents and assassinations, not protected by the detectors. For example,Enders and Sandler (1993, Table 4) show that the installation of metal detectorsin 1973 is associated with 14 fewer skyjackings per quarter, and almost 12additional hostage incidents per quarter (not involving planes) and 7 more assas-sinations per quarter. Enhanced embassy security, while effective at reducingembassy attacks, had the unintended consequence of increasing assassinations ofdiplomatic and military personnel when they left secured compounds. This sub-stitution is toward events that are more costly to society than those being pro-tected. This outcome suggests that piecemeal policy, in which a single attackmode is considered when designing anti-terrorism action, is inadequate. Terroristsubstitution among attack modes must be anticipated. Policies that decreaseterrorist resources are particularly effective, because they should result in anacross-the-board decrease in attacks.

Even when barriers and fortifications work and do not cause more costlysubstitutions, the authorities must be ever-vigilant to outguess the next terroristinnovation. There is, thus, a dynamic concern with such barriers and fortification,which are static inhibitors that invite the terrorists to invent novel circumven-tions. Hence, plastic guns replaced metal ones and bottles of inflammable liquidsreplaced hand grenades, because these innovations can pass undetected throughmetal detectors. Not only have the authorities failed to second guess the terror-ists, but the authorities have been slow to respond to innovations. Media accountsof innovations allow terrorists to rapidly adopt the breakthroughs of others, mak-ing such innovations pure public goods.

b. What Kinds of Substitutions Are There?

Thus far, substitutions among attack modes have been stressed. Another typeof substitution is across countries. As discussed earlier, more secured bordersdeflect attacks elsewhere. Terrorist attacks aimed at foreign direct investmentinfluence the flow of capital and cause investors to transfer their capital to coun-tries, where terrorist risks are smaller (Enders and Sandler, 1996). Thus, sub-stitutions may characterise different agents associated with the terrorism problem.If, analogously, terrorist attacks put tourists at risk, then tourism may be negat-ively impacted (Enders et al., 1992), as in the case of the hijacking on TWAflight 847 on 14 June, 1985. This flight departed Athens enroute for Rome with145 passengers and 8 crew before it was first diverted to Beirut. This protractedhijacking was not resolved until 30 June 1985, with the release of the remaining39 hostages (Mickolus et al., 1989, vol. 2, pp. 221–5). Greek tourism sufferedgreatly as tourists chose alternative holiday venues, because this hijacking andothers exposed security weaknesses at the Athens airport.

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An intertemporal substitution may involve terrorists’ timing of incidents. Forexample, a retaliatory raid by a targeted government may unleash a wave ofterrorist incidents against the retaliator(s) as terrorists move events planned forthe future into the present to protest the raid (Enders and Sandler, 1993). Laterterrorism may temporarily decline as terrorists replace expended resources. Con-sequently, the news media may mistakenly view the temporary lull as a positiveresult from the raid. These and other substitutions (for example, terrorists chang-ing their target of opportunity from business people to tourists, as the formeracquire bodyguards) highlight the interdependency of decisions of terrorists andauthorities. If the analysis or policy is too focused, then important consequencesand trade-offs will be missed.

c. Evaluation of Other Policies: Domestic Laws, International Conventions, and Retaliation

When dealing with domestic crime, nations have instituted laws with stiffpunishments in the hopes of deterring crime by making would-be criminalsweigh the consequences of their contemplated actions. If the society has thepolice force to bring criminals to justice and courts to impose harsh sentences,then offences may be reduced. Similar reasoning may persuade governments torely on domestic laws and international conventions to curb transnational terror-ism. Unfortunately, the anti-terrorism effectiveness of such laws and conventionsare very disappointing, as shown by past empirical investigations. For example,the so-called Reagan get-tough laws with terrorism (Public Law (PL) 98-473 andPL 98-553 signed by President Reagan in October 1984) were shown to haveno statistical effect whatsoever against US-directed terrorist acts (Enders et al.,1990a and 1990b).

PL 98-473 requires up to life imprisonment for individuals taking US hostageseither within or outside of the United States. This law also raised penalties fordestroying aircraft or placing a bomb aboard an aircraft. PL 98-553 authorisesthe US Attorney General to pay rewards for information leading to the apprehen-sion or conviction, inside or outside the United States, of terrorists who targetedUS interests (Pearl, 1987, p. 141; and Mickolus et al., 1989, vol. 2). These lawsfailed to deter terrorism for a number of reasons. First, because most terrorist actsagainst US people or property occur abroad, the United States must rely onforeign governments to extradite criminals, which for capital offences is highlyunlikely. Second, by staging their events abroad, terrorists greatly discount theability to be brought to justice. US successes in capturing terrorists abroad havebeen sufficiently few in number prior to 9/11 that there has been little influenceon terrorists’ anticipated probabilities of being brought to US justice. Third,fundamentalist terrorists, who are prepared to make the supreme sacrifice, areundeterred by policy-induced marginal changes in risks.

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Over the years, nations have formed international conventions and resolutionsto thwart terrorist acts. Two early instances include the 1971 Montreal Conven-tion on the Suppression of Unlawful Acts against the Safety of Civil Aviation(Sabotage) and the 1977 UN General Assembly Resolution 3218 on the Safetyof International Civil Aviation.16 Although well-intended, neither of thesetreaties appeared to have much effect on aviation’s safety from terrorism. Othersignificant anti-terrorism treaties include the following: the UN Convention onthe Prevention and Punishment of Crimes against Internationally ProtectedPersons, Including Diplomatic Agents (adopted by the United Nations on14 December, 1973), the UN Security Council Resolution against Taking Hostages(adopted by a 15-0 vote on 18 December, 1985), the UN General AssemblyResolution 2551 on the Forcible Diversion of Civil Aircraft in Flight (adoptedon 12 December, 1969), the Hague Convention on the Suppression of UnlawfulSeizure of Aircraft (adopted on 16 December, 1970), and the UN GeneralAssembly Resolution 2645 on Aerial Hijacking (adopted on 25 November,1970). Conventions are more binding than resolutions, since resolutions aremerely agreements in principle and do not imply any real commitment on thepart of the adopters. Conventions, in contrast, require that the nations rely ontheir own judicial system to implement and enforce the agreement. But in neithercase is there a central enforcement agency that can force the nations to comply.Without such an enforcement mechanism, signatories will do what is convenientfrom their viewpoints – a Prisoners’ Dilemma is apt to underlie the pattern ofpayoffs, not unlike the pre-emption or deterrence games.

When the average number of attacks is examined both before and after theadoption of these conventions and resolutions, there is no statistically significantreduction in the post-treaty number of attacks for the relevant attack modes(crimes against protected persons or skyjackings) (Enders et al., 1990a). This isconvincing evidence that these UN conventions and resolutions really had noimpact. To acquire the requisite support from the world community, these anti-terrorism treaties were drafted so as to permit too many loopholes and too muchautonomy on the part of the signatories. A more effective treaty-making processinvolved neighbouring nations agreeing to control a common terrorism problemthat presented significant and localised effects. Thus, Spain and France havemade progress in concerted efforts to control Basque terrorism.

Prior to the US ‘war on terrorism,’ retaliatory raids had very little long-runimpact on terrorism. One study examines the impact that Israeli retaliatory raidshad following significant terrorist incidents (Brophy-Baermann and Conybeare,1994). Retaliations investigated included the raid on Palestine Liberation Organ-isation (PLO) bases in Syria following the Black September massacre of Israeliathletes during the 1972 Olympic Games; the attack on Palestinian guerrilla

16 See Alexander et al. (1979) for the text of the treaties on the suppression of terrorist acts.

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bases in Lebanon following a March 1978 Haifa bus hijacking; and the bombingof Palestinian bases in Lebanon following a June 1982 assassination attemptagainst the Israeli ambassador in London. This study finds that such raids onlytemporarily suppressed terrorism: within three quarters, terrorism had returned toits old mean values. Another study shows that the US raid on Libya in 1986 hadthe unanticipated consequences of actually raising the level of terrorism in theimmediate aftermath as terrorists lashed out against the United States and theUnited Kingdom (Enders and Sandler, 1993). Within a matter of months, terror-ism was back to its old level.

The long-run effectiveness of the US-led retaliation against al-Qaida will notbe known for years to come. Nevertheless, some conclusions seem self-evident.Given the sustained level of attack against al-Qaida and the unprecedented (butstill modest) international cooperation, US-led actions to suppress internationalterrorism will be longer lived than in the past. The al-Qaida network has not onlylost significant assets (for example, training camps, safe and inaccessible havens,and key strategists), but it has also had linkages within the network disrupted.Grievances against America will surely worsen, because of US actions, so thatattacks have been returning as the network reconfigures itself. It is, however,anyone’s guess as to the future effectiveness of a reconfigured al-Qaida com-pared with its capabilities prior to 7 October, 2001.

d. No-negotiation Strategy

One of the four pillars of US anti-terrorism policy is never negotiate andcapitulate to hostage-taking terrorist demands. The logic behind this policy is thatif a nation adheres to this stated no-negotiation policy, then would-be hostagetakers would have little to gain. For the policy to work, the nation must preserveits reputation (Lapan and Sandler, 1988). Virtually every nation that confrontsterrorism has, at times, violated its pledge never to negotiate with hostage takers.The Reagan administration’s barter of arms for the release of Rev. BenjaminWeir, Rev. Lawrence Jenco and David Jacobsen during 1985–6 is a violation ofthis pledge that resulted in the ‘Irangate’ scandal (Mickolus et al., 1989, vol. 2).Even Israel, the staunchest supporter of the no-negotiation strategy, has madenotable exceptions in the case of the school children taken hostage at Maalot inMay 1974, and during the hijacking of TWA flight 847.17 The effectiveness ofthe conventional policy never to negotiate with terrorists hinges on a number ofcrucial implicit assumptions. First, the government’s pledge is completely cred-ible to would-be hostage takers. Second, there is no uncertainty concerning pay-offs. Third, the terrorists’ gains from hostage taking only derive from ransoms

17 These events are described in Mickolus (1980, pp. 453–4) and Mickolus et al. (1989, vol. 2,pp. 219–25).

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received. Fourth, the government’s expenditures on deterrence are sufficient todeter all attacks. Each of these assumptions is tenuous in practice.

If the terrorist group realises a net gain from a negotiation failure, as it mayif it values media exposure or martyrdom, then the government’s proclamationsand its level of deterrence cannot necessarily forestall an attack, so that hostagesare abducted. Once hostages are taken, the government must weigh the expectedcosts of not capitulating against those of capitulating. Conceivably, the govern-ment may view the cost of not capitulating as too high for the right hostage, evenwhen accounting for lost reputation. In such situations, the government renegeson its pledge. If would-be hostage takers believe that they can impose costssufficient for a targeted government to renege on its stated policy, then they willabduct hostages, because the credibility of the government’s pledge depends onan uncertain outcome. Each time a government caves in, the terrorists will updateor raise their beliefs about future capitulations. That is, learning based on pastactions allows terrorists (and the governments) to update their beliefs in an inter-active fashion. When a government reneges and negotiates, it emboldens terror-ists to take additional hostages. In so doing, a capitulating government imposesa public bad on future domestic governments and on governments worldwide.Constitutional constraints or congressional hearings, which impose huge costs onthese officeholders who capitulate, may be only means of raising the cost ofcapitulation sufficiently to make a precommitment never to negotiate a policywithout regrets, once hostages are captured. Such actions would severely restrictdiscretionary action for the good of the world community.

8. WHAT ARE THE ECONOMIC COSTS OF TERRORISM?

Given the annual number of people murdered by international terrorism, theassociated security spending may appear excessive. President Bush’s proposedbudget for 2003 earmarks $37.7 billion to homeland security, which representsan $18.2 billion increase over 2002 (www.whitehouse.gov). This expendituredoes not include the tens of billions spent to bring down the Taliban in Afghan-istan and smash al-Qaida’s operations there. One must wonder how many of the40,000 lives lost each year on US highways would be saved if some of thismoney went to making US highways safer. If lives lost are the only considera-tion, then clearly margins have not been equated and more lives can be saved bya reallocation of spending. There is, however, the all-important political benefitfrom the security outlay that the government appears in control. When this secu-rity perception is achieved, there is the psychological benefit derived by a trau-matised public from feeling safer. This security benefit is difficult to evaluate,but is certainly very high. The perception of security is arguably more importantthan the reality for such a political benefit.

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Homeland security is expensive, because terrorists force governments toprotect myriad targets, insofar as an attack can take place almost anywhere. High-profile targets – bridges, monuments, government buildings, and public places –receive the most security. Deterrence expenditure is an insurance payment thatmust be paid regardless of the outcome – that is, it is not refunded when noterrorist attack ensues. Unfortunately, the enhanced security may not be all thateffective despite great efforts, because the terrorists will merely look for a less-watched alternative target. If the attack is diverted to where both the symbolicvalue and lives lost are more limited, then there is a return on the deterrenceinvestment. Of course, the alternative of doing nothing would just mean that theterrorists would succeed with the most damaging attack as they did on 9/11.

After 9/11, the stock markets took a precipitous drop owing to the initialshock, associated uncertainty, and dire consequences to select industries. Manypeople viewed this tremendous loss in equity values as a new cost to terrorism.Prior to 9/11, the economic cost from terrorism was documented in two areas:reduced foreign direct investment for small countries and reduced tourism.18 Theattacks on 9/11 suggest that equity cost may be great. While there is no questionthat some industries (for example, the airline and travel industries) sufferedgreatly, the interesting thing about 9/11 is that the drop in equity prices wastemporary, with most stocks rebounding rather quickly in the ensuing months.A single act of terrorism, or even a sustained campaign, cannot really destroyconfidence in an intricate and diversified economy as that of the United States orthe global community. A massive attack can, however, temporarily shakeconfidence and cause stock prices to drop. An instructive exercise is to comparethe impact on stock values of corporate fraud, as characterised by Enron andWorld.com, with the impact on these values of 9/11. With corporate fraud, equityprices have remained depressed for months and months, because corporate fraudstrikes at the very confidence needed to hold equity shares.

9. CONCLUDING REMARKS

Modern-day transnational terrorism taxes the ingenuity of governments world-wide. Countries can limit their exposure at home by relying on barriers, fortifica-tion, and intelligence; but this protection comes at a great cost and will nevermake a society invulnerable. Given the pervasive transnational externalities asso-ciated with today’s terrorism, the real global challenge relates to the need forgreater international cooperation among governments that are loath to sacrificeautonomy. Cooperation is required in terms of deterrence, pre-emption, intelli-gence, and punishment of terrorists. Because these decisions are interdependent,

18 These losses are documented in Enders and Sandler (1996) and Enders et al. (1992), respectively.

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partial or piecemeal cooperation may achieve little. Not all of the associatedexternalities are negative, so that governments may engage in too much of someterrorism-thwarting activities and too little of others. Consequently, global actionand inaction may be problematic at times. As long as governments place moreweight on their autonomy than on their effectiveness in confronting this commonexigency, terrorists will succeed in maximising their effectiveness while limitingthe effectiveness of the targeted governments. The entire dilemma has been madeworse, because terrorists have successfully addressed their collective action prob-lem through the formation of networks, while governments have not.

No matter the ultimate fate of al-Qaida, transnational terrorism will remain athreat. In the 1980s, the Abu Nidal Organisation was the most feared group, butnow it poses a much diminished threat, especially with the death of Abu Nidalin Iraq during 2002. Dangerous groups will come and go, but terrorism will stay.More worrying, terrorists will continue to innovate and devise ghastly plots thatwill some day exceed the horrors of 9/11. Over the years, the escalation of theterrorist spectacular in terms of carnage reflects the need of the terrorists toshock, in order to capture headlines that publicise their cause. In addition, terror-ists will continue to exploit technological innovations, such as the Internet, totheir advantage. But the authorities can also exploit these technologies to theterrorist disadvantage by, for example, tracking their messages and disruptingtheir websites. Globalisation, and the increase in cross-border flows that it entails,will not only make it more difficult to protect against terrorism, but it will alsocreate more vulnerable ‘choke’ points that terrorists can exploit to adversely affectinternational commerce.

REFERENCES

Alexander, Y. and D. Pluchinsky (1992), Europe’s Red Terrorists: The Fighting CommunistOrganizations (Frank Cass, London).

Alexander, Y., M. A. Browne and A. S. Nanes (1979), Control of Terrorism: International Docu-ments (Crane Russak: New York).

Arquilla, J. and D. Ronfeldt (2001), Networks and Netwars: The Future of Terror, Crime, andMilitancy (RAND: Santa Monica, CA).

Brophy-Baermann, B. and J. A. C. Conybeare (1994), ‘Retaliating against Terrorism: RationalExpectations and the Optimality of Rules versus Discretion’, American Journal of PoliticalScience, 38, 1, 196–210.

Enders, W. and T. Sandler (1993), ‘The Effectiveness of Antiterrorism Policies: A Vector-Autoregression-Intervention Analysis’, American Political Science Review, 87, 4, 829–44.

Enders, W. and T. Sandler (1995), ‘Terrorism: Theory and Applications’, in K. Hartley andT. Sandler (eds.), Handbook of Defense Economics, Vol. I (North-Holland, Amsterdam),213–49.

Enders, W. and T. Sandler (1996), ‘Terrorism and Foreign Direct Investment in Spain and Greece’,KYKLOS, 49, 3, 331–52.

Enders, W. and T. Sandler (1999), ‘Transnational Terrorism in the Post-Cold War Era’, Inter-national Studies Quarterly, 43, 1, 145–61.

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Enders, W. and T. Sandler (2000), ‘Is Transnational Terrorism Becoming More Threatening? ATime-Series Investigation’, Journal of Conflict Resolution, 44, 3, 307–32.

Enders, W. and T. Sandler (2003), ‘What Do We Know about the Substitution Effect in Trans-national Terrorism?’, in A. Silke and G. Ilardi (eds.), Researching Terrorism: Trends, Achieve-ments, Failures (Frank Cass, Ilford, UK, forthcoming).

Enders, W., T. Sandler and J. Cauley (1990a), ‘UN Conventions, Technology and Retaliation inthe Fight against Terrorism: An Econometric Evaluation,’ Terrorism and Political Violence, 2,1, 83–105.

Enders, W., T. Sandler and J. Cauley (1990b), ‘Assessing the Impact of Terrorist-ThwartingPolicies: An Intervention Time Series Approach’, Defence Economics, 2, 1, 1–18.

Enders, W., T. Sandler and G. F. Parise (1992), ‘An Econometric Analysis of the Impact ofTerrorism on Tourism’, KYKLOS, 45, 4, 531–54.

Hardin, R. (1995), One for All: The Logic of Group Conflict (Princeton University Press, Princeton,NJ).

Hoffman, B. (1997), ‘The Confluence of International and Domestic Trends in Terrorism’, Terror-ism and Political Violence, 9, 2, 1–15.

Hoffman, B. (1998), Inside Terrorism (Columbia University Press, New York).Hoffman, B. (2002), ‘Rethinking Terrorism and Counterterrorism Since 9/11’, Studies in Conflict

& Terrorism, 25, 5, 303–16.Im, E. I., J. Cauley and T. Sandler (1987), ‘Cycles and Substitutions in Terrorist Activities: A

Spectral Approach’, KYKLOS, 40, 2, 238–55.Krueger, A. B. and J. Maleckova (2002), ‘Education, Poverty, Political Violence and Terrorism:

Is There a Causal Connection?’, NBER Working Paper 9074 (National Bureau of EconomicResearch).

Lapan, H. E. and T. Sandler (1988), ‘To Bargain or Not to Bargain: That Is the Question’, Amer-ican Economic Review, 78, 2, 16–20.

Mickolus, E. F. (1980), Transnational Terrorism: A Chronology of Events 1968–1979 (GreenwoodPress, Westport, CT).

Mickolus, E. F., T. Sandler and J. M. Murdock (1989), International Terrorism in the 1980s: AChronology of Events, 2 vols. (Iowa State University Press, Ames, IA).

Oklahoma City National Memorial Institute for the Prevention of Terrorism (2002), websitehttp://db.mipt.org

Pearl, M. A. (1987), ‘Terrorism – Historical Perspective on US Congressional Action’, Terrorism,10, 2, 139–43.

Quillen, C. (2002a), ‘A Historical Analysis of Mass Casualty Bombers’, Studies in Conflict &Terrorism, 25, 2, 279–92.

Quillen, C. (2002b), ‘Mass Casualty Bombings Chronology’, Studies in Conflict & Terrorism, 25,5, 293–302.

Sandler, T. (1992), Collective Action: Theory and Applications (University of Michigan Press, AnnArbor, MI).

Sandler, T. and D. G. Arce (2003), ‘Pure Public Goods versus Commons: Benefit-Cost Duality’,Land Economics, 79, 3 (forthcoming).

Sandler, T. and H. E. Lapan (1988), ‘The Calculus of Dissent: An Analysis of Terrorists’ Choiceof Targets’, Synthese, 76, 2, 245–61.

Sandler, T. and K. Siqueira (2002), ‘Global Terrorism: Deterrence Versus Preemption Games’,Unpublished Manuscript (University of Southern California, Los Angeles, CA).

United States Department of State (various years), Patterns of Global Terrorism (Washington, DC,US Department of State).

Wilkinson, P. (1986), Terrorism and the Liberal State (rev. ed., Macmillan, London).Wilkinson, P. (2001), Terrorism Versus Democracy: The Liberal State Response (Frank Cass,

London).Wilkinson, P. (2002), ‘Editorial’, Terrorism and Political Violence, 13, 4, vii–x.Wintrobe, R. (2001), ‘Can Suicide Bombers Be Rational?’, Unpublished Manuscript (University of

Western Ontario, London, Ontario).

TOO MUCH OF A GOOD THING? THE PROACTIVE RESPONSE DILEMMA

by

Peter Rosendorff and Todd Sandler School of International Relations University of Southern California

Von Kleinsmid Center 330 Los Angeles, CA 90089-0043

Office Phone: 213-740-9695 Office Fax: 213-742-0281 Home Fax: 323-256-7900

bpeter@usc.edu

tsandler@usc.edu

Final Revision: June 2004

AUTHORS’ NOTE: Rosendorff is the Director of the Center for International Studies and Associate Professor of International Relations and Economics. Sandler is the Robert R. and Katheryn A. Dockson Professor of International Relations and Economics. Both authors are also members of the Department of Economics. Both acknowledge research support from the Center for International Studies, University of Southern California. The authors have profited from comments provided by an anonymous referee, Barry O’Neill, Geoffrey Heal, and Bruce Russett on an earlier draft.

TOO MUCH OF A GOOD THING? THE PROACTIVE RESPONSE DILEMMA

Abstract

This paper presents a two-player proactive response game: the targeted government first

chooses its measures to weaken the terrorists, and the terrorists then choose the type of event –

normal or spectacular – whose outcome is dependent on proactive responses and nature. Unlike

previous analyses, proactive policy has a downside by increasing grievances and, consequently,

terrorist recruitment. If the government responds too harshly, its actions can empower the

terrorists by providing a larger constituency. Aggressive antiterrorist actions, encouraged by a

high perceived loss from terrorism and low marginal proactive costs, may result in spectacular

events with dire consequences. If spectaculars are transferred abroad to soft targets, then

proactive operations may be excessive from a global viewpoint as external costs are ignored.

The analysis explains why some target nations engage in a modest level of offense, while a

prime target chooses a large level.

Keywords: proactive measures; terrorist recruitment; externalities; noncooperative games;

international cooperation; terrorist spectaculars.

TOO MUCH OF A GOOD THING? THE PROACTIVE RESPONSE DILEMMA

Since 9/11, there is an enhanced interest in applying theoretical and statistical modeling

to examine terrorism (see, e.g., Azam forthcoming; Blomberg, Hess, and Weerapana 2004;

Bueno de Mesquita 2004; Heal and Kunreuther 2004; Li and Schaub 2004; Sandler and Enders

2004). Models are also being applied to investigate the effectiveness of alternative

counterterrorism policies (Arce and Sandler 2004; Enders and Sandler 1993, 1995; Sandler and

Arce 2003). Countermeasures to the threat of terrorism fall into two categories: defensive and

proactive measures. Defensive policies include hardening targets, installing technological

barriers, securing borders, deploying sky marshals, and issuing identity cards. Often such

actions deflect the intended attack to a softer target, thereby creating collateral damage. In

contrast, proactive actions involve direct strikes against a terrorist group or its assets, retaliation

against a state sponsor (e.g., a country providing a safe haven), gathering intelligence,

assassinating terrorists, or infiltrating a terrorist group. These proactive policies are intended to

weaken a terrorist group or compromise its security for the purpose of limiting and ultimately

ending the group’s operations.

Proactive tactics against a terrorist group – for example, the US-led attack in Afghanistan

against the Taliban and al-Qaida or Israel’s assassination of Hamas terrorists (Sheikh Ahmed

Yassin and Abdel Aziz Rantisi) in 2004 – are characterized in the literature as a pure public

good, because a weakened terrorist group poses less of a threat to all potential targets (Sandler

2003; Sandler and Siqueira 2003; Sandler, Tschirhart, and Cauley 1983). For international

terrorism, such benefits are received by all targeted countries and do not diminish when shared

by more at-risk countries. As a transnational pure public good, a proactive response is

anticipated to be undersupplied because the provider does not include the marginal benefits

conferred on other likely targets when deciding its provision level.

2

At the international level, a proactive response is anticipated to be taken by the prime

target of terrorist attacks, insofar as this nation derives greater benefits from such actions (Arce

and Sandler 2004). Given that 40% of transnational terrorist attacks are against US people or

property,1 the United States has understandably provided the most proactive measures against the

al-Qaida network after 9/11. During fiscal year 2004, the United States allocated almost $53

billion to combating terrorism with defensive measures accounting for $23.9 billion (US General

Accounting Office 2004). Much of the rest went to proactive efforts of the Department of

Defense and other US departments and agencies.2

Proactive operations that bomb alleged terrorist assets, hold suspects without charging

them, assassinate suspected terrorists, curb civil freedoms, or impose retribution on alleged

sponsors may have a downside by creating more grievances in reaction to heavy-handed tactics

or unintended collateral damage. Such operations can lose government support and thereby

empower terrorists through more favorable world opinion and a larger constituency.

Consequently, proactive measures may promote recruitment to the terrorist network, thus

offsetting some of the favorable effects. At the transnational level, recruitment represents a

public bad that may impact countries differently depending on their relationship with the

proactive country. This recruitment depends not only on the terrorist success in an event, where

success encourages recruitment, but also on the nature of the event – i.e., a normal event with a

modest impact or a spectacular event with a high death toll or a symbolic nature. Spectaculars

grab headlines and remain in the public’s consciousness long after the event. The term

“spectaculars” is used officially and in the literature to describe influential terrorist attacks. Such

events further recruitment to the terrorist group.

The purpose of this paper is to analyze a government’s proactive decision when it may

not only harm the terrorist group by limiting its ability, but also help the group attract recruits

3

and legitimacy. This tradeoff epitomizes the liberal democratic dilemma in responding to a

terrorist threat – a government that responds by too little appears unable to protect its citizens

and loses popular support, while a government that responds by too much appears tyrannical and

encourages opposition (Wilkinson 2001). Major proactive campaigns may actually promote

large-scale or newsworthy spectaculars if the recruitment consequence of repressive actions is

sufficiently strong; thus, too much reliance on offensive actions may result in a disastrous

outcome. Because such spectaculars can occur anywhere owing to the globalization of terrorism,

the collateral damage from excessive measures may take place half a world away from the nation

whose actions incited the grievance and recruitment. As such, proactive operations are best

understood as generating both public benefits and costs. A secondary, but related, purpose is to

contrast the US approach following 9/11 with that of the European Union (EU). The former tries

to eliminate the terrorist risk through a “war on terror,” while the latter manages the risk with

greater reliance on defensive actions.

BASIC GAME SET UP

The underlying game is played by two players: a target government (E) and a terrorist

group (T). In Figure 1, the game is displayed with the corresponding payoffs at the game’s four

possible outcomes. The target government moves first and chooses a proactive level, [ )1, ,θ ∈ ∞

followed by the terrorists who choose the type of attack – spectacular (s) or normal (n). Nature

then determines the outcome based in part on the proactive response. The cost of proactive

measures is ( )P θ , where the marginal cost is positive. For simplicity, ( )P θ is assumed to

equal , where 0.p pθ > Spectaculars are major newsworthy terrorist events with either a high

death toll or a watershed character (e.g., the 1972 Munich Olympic attack on the Israeli athletes),

4

while normal events are all other terrorist incidents. Even though just six people died, the 1993

bombing of the World Trade Center was a spectacular event, because over 1000 people were

injured, it caused over $500 million in damages, it struck a major landmark, and its remains in

the news over a decade later. The downing of an airliner or an armed massacre at an

international airport (e.g., the armed attack at Vienna’s Schwechat and Rome’s Fiumicino

Airports on 27 December 1985) are also spectaculars with lasting impacts. Although

spectaculars yield a higher payoff to the terrorists than a normal event, spectaculars have a

smaller success probability, ( ) ,sπ θ than a normal event, whose success probability is ( ).nπ θ

In particular, we assume that 1nπ θ= and ( )1 ,s rπ θ= where 1r > so

.n sπ π> (1)

At the four endpoints in the game tree of Figure 1, the payoffs of the government and the

terrorists are displayed with the government’s payoffs listed above those of the terrorists. If a

spectacular is successful, then the government loses both S and the cost of its proactive response.

The cost of a proactive measure is analogous to an insurance premium, paid in all states of the

world; thus, ( )P θ is part of the government’s loss in all four outcomes. For successful

spectaculars, the terrorists gain S plus a recruitment benefit of ssc θ , positively dependent on the

proactive effort. The marginal recruitment benefit from a successful spectacular is ssc .

Although the terrorists gain what the government loses, the game is not zero-sum because of the

second term in the two payoffs. If, however, the spectacular fails, the government just loses its

proactive expense, while the terrorists lose L but may gain recruitment benefits of fsc θ with

0fsc ≥ and ss fsc c> , since success generates more recruits than failure. In the 5 September 1972

Munich Olympics attack, the Black September terrorists failed when the West German police

5

opened fire in a rescue attempt at Fürstenfeldbruck airbase prior to the terrorists boarding a

Lufthansa Boeing 727 to take them and the hostages to Cairo. Despite Black September’s failure

to achieve any of its demands or to escape the scene, the Munich incident resulted in “thousands

of Palestinians” rushing to join the terrorist organization in the weeks that followed (Hoffman

1998, 71).

We now turn to the two sets of payoffs at the bottom right of the game tree,

corresponding to a normal event’s success and failure. For success, the government loses N and

its proactive costs, where S > N because a normal event has a smaller associated loss than a

spectacular event. The terrorists gain N plus a recruitment benefit of snc θ . The marginal

recruitment gain associated with a successful normal incident is less than that associated with a

successful spectacular – i.e., .sn ssc c< Obviously, our parameters are chosen to keep the analysis

simple while capturing the essential aspects of the underlying situation. The model is

sufficiently general to allow for ,sn fsc c! so that recruitment for failed spectaculars may exceed

or fall short of successful normal events. Finally, the payoffs for a failed normal event is ( )P θ−

and 0 for the government and terrorists, respectively. The 0 merely indicates that we have

normalized this payoff for simplification so the other payoffs to the terrorists are above this

value.

BASELINE MODEL: NO RECRUITMENT

To highlight the influence of recruitment on the analysis, we first present the case where

there is no recruitment, which comes the closest to the literature, except that we consider the

terrorists’ choice between spectaculars and normal events.3 Thus, we assume that

0ss sn fsc c c= = = in Figure 1. To solve for the subgame perfect equilibrium to the game, we

6

apply backward induction by first solving for the terrorists’ choice of events and then

conditioning the government’s choice on that of the terrorists. This procedure identifies the

subgame perfect equilibrium to this two-player game. The terrorists choose between a

spectacular and a normal event according to:

( ) ( ); ; ,T TEU s EU nθ θ! (2)

where TEU is the terrorists’ expected utility, which equals

( )1 1.S L L N

rθ θ+ − ! (3)

This last inequality follows from the no-recruitment payoffs and the relevant success

probabilities. The terrorists engage in a spectacular if and only if

,S L rN

rLθ θ+ −= ≥! (4)

and execute a normal event otherwise, where θ! denotes the critical level of proactive response

that induces a spectacular. Since 1θ ≥ , a necessary condition for the terrorists to choose a

spectacular in the subgame perfect equilibrium is that ,S N r> which follows from equation

(4).4

If the gain, S, from a spectacular rises, then 1 0;S rLθ∂ ∂ = >! thus, θ! is more apt to

exceed ,θ thereby making spectaculars more likely. When either the terrorists’ losses from a

failed spectacular rises or the relative likelihood of a spectacular’s success falls (as r rises), θ!

falls in value and a spectacular is less likely.5 These comparative static results agree with

intuition.

To complete the search for a subgame perfect equilibrium, we now turn to the

government’s choice of proactive measures, conditioned on the terrorists’ choice of events. The

government chooses θ to

7

( ) ( ) ( ) ( ) max 1s sS P Pθ θ π θ θ π θ θ≤ − − + − − !

( ) ( ) ( ) ( ) max 1 ,n nN P Pθ θ π θ θ π θ θ> − − + − − !

which can be rewritten as

( )max p S rθ θ θ θ≤ − − !

( )max .p Nθ θ θ θ> − − !

The Kuhn-Tucker conditions6 associated with the top problem in equation (6) results in a

subgame perfect equilibrium, in which the terrorists choose a spectacular and the government

chooses a proactive response where

.s

S S L rN

rp rLθ θ + −= ≤ =! (7)

The bottom portion of equation (6) involves a subgame perfect equilibrium where the terrorists

choose a normal event and the government chooses a proactive level,7

.n

N S L rN

p rLθ θ + −= > =! (8)

If, therefore, the government wants to limit spectaculars, then it must choose a sufficiently large

proactive response since s nθ θ> , which follows from .S N r>

This is readily displayed in Figure 2 where payoffs are measured on the y-axis and the

proactive level on the x-axis. The ( );TEU n θ curve is a rectangular hyperbola with asymptotes

at the two axes. When 1θ = , this expected value equals N [see the right-hand side of equation

(3)]. Similarly, the ( );TEU s θ curve is a rectangular hyperbola but with a horizontal asymptote

at −L . The critical value of θ! corresponds to the intersection of the terrorists’ expected utility

curves. In Figure 2, the subgame perfect equilibrium where the government chooses a proactive

level of N p and the terrorists engage in a normal event is displayed by the vertical line,

max

max (6)

(5)

8

where ( );TEU n θ exceeds ( );TEU s θ . If, however, the government’s proactive level of

S rpθ = exceeds 1 but is less than or equal to ,θ! then ( );TEU s θ exceeds or equals

( );TEU n θ and proactive operations are insufficient to prevent spectaculars. Without

recruitment, we find that sufficient governmental offense eliminates spectaculars by weakening

the terrorists so they must engage in more modest operations. In the absence of empowerment

and recruitment, there cannot be too much of a good thing because proactive campaigns do not

incite greater terrorism. If the government just wants to eliminate spectaculars, then it equates θ

to θ! to save on proactive costs. The reason that this is not necessarily the subgame perfect

equilibrium is that the government also limits its expected losses through its proactive response;

hence, its optimal choice of θ may lie well to the right of θ! as proactive costs are traded off

against reduced losses from fewer attacks. The likelihood of spectaculars are low when θ lies

near to .θ!

PROACTIVE CHOICES WITH RECRUITMENT

Now we return to the game tree and allow the terrorists’ payoffs at three of the outcomes

to include marginal recruitment benefits ( )0, 0, and 0ss fs snc c c> > > from a spectacular

success, a spectacular failure, and a normal success. A spectacular success leads to the greatest

recruitment, while the productivity for recruitment in the other two cases depends on the relative

values of fsc and snc . For all three cases, the heavy-handedness of the government, as measured

by the size of ,θ induces recruitment so proactive measures now have a downside.

Once again, we use backward induction to find the subgame perfect equilibrium for this

game. Terrorists now choose a spectacular when

9

( ) ( )1 1,ss fs fs snS L c c L c N c

rθ θ θ θ

θ θ+ + − − + ≥ + (9)

because ( ) ( ); ; ,T TEU s EU nθ θ≥ and engage in a normal event otherwise. Equation (9) can be

rewritten as:

( ) ( ) ( )2 ,fs ss fs snrc c c rL S L r N cθ θ θ+ − − + + ≥ + (10)

which gives two critical values θ and θ where equation (10) is satisfied as an equality. In

Figure 3, the parabola with a y-intercept at S + L and a minimum at ( ) 2fs ss fsc rL c rc+ −

corresponds to the left-hand relationship in equation (10), while the solid straight upward-sloping

line with y-intercept at rN corresponds to the right-hand relationship in equation (10). The lower

( )θ and upper ( )θ bounds of θ distinguish the type of event chosen by the terrorists. For

modest proactive levels of ( ), ,θ θ θ∈ the terrorists choose a normal event, while for θ θ≤ or

,θ θ≥ the terrorists engage in spectaculars. To the left of θ , the terrorists execute spectaculars

because proactive operations are too small to weaken them. Proactive measures are, however,

sufficiently large to the right of θ to recruit members and give the terrorists enough resources to

accomplish spectaculars.

In light of the anticipated choices of the terrorists, the target government must choose a

proactive response to

( ) ( ) ( ) ( ) ,max 1s sS P Pθ θ θ θ π θ θ π θ θ≤ ≥ − − + − −

( ) ( ) ( ) ( ) ( ) ,max 1 .n nN P Pθ θ θ π θ θ π θ θ∈ − − + − −

Recruitment has not altered the government objective from that of equation (6), but it has altered

the regions that determine the type of event. The subgame perfect equilibria to the game with

recruitment can be completely specified for all values of the exogenous parameters as follows:

(11)

max

10

If ( )θθθ ,∈n , then nθθ = and the terrorists choose a normal event; if ( )θθθ ,∉n and θθ ≤s or

θθ ≥s , then sθθ = and the terrorists choose a spectacular; and if ( )θθθ ,∈s and θθ <n , then

θθ = and the terrorists are indifferent between a normal and a spectacular.

One subgame perfect equilibrium has the government choosing N pθ = between θ

and θ and the terrorists responding with a normal event. When the marginal costs, p, of

proactive measures are low, a rational government may choose a proactive level above ,θ

hoping to make the likelihood of a successful spectacular small. Unfortunately, rational

terrorists would choose a spectacular event owing to anticipated recruitment benefits. For

S rpθ = between 1 and θ , the terrorists again engage in spectaculars, because they have a

relatively high success probability. The government must anticipate the terrorists’ derived

payoffs especially from recruitment in order not to respond to such a degree that the terrorists are

pushed to execute spectaculars with potentially disastrous outcomes. In terms of a proactive

campaign, there can be too much of a good thing when it creates grievances and swells terrorists’

ranks. There can also be too little proactive measures when recruitment is not significant so that

the pure publicness of such actions is the main consideration. Hence, governments must choose

an offensive that is neither excessive nor insufficient if spectaculars are to be avoided.

SOME COMPARATIVE STATICS

Suppose that the relative difficulty of spectaculars increases so nπ exceeds sπ by a larger

amount. This is captured by an increase in r, which has two effects in Figure 3. First, it shifts up

the straight line by increasing its intercepts while making it steeper – see dashed line

( )snr N c θ+! where r r>! . By itself, this change widens the range of normal events as seen in the

11

diagram by the θ range where the dashed line lies above the parabola. Second, the change in r

influences the parabola as follows:

( ) ( )2

2 .fs ss fs

fs

rc c c rL S Lc L

r

θ θθ θ

∂ + − − + + = −∂

(12)

If the net payoff to the terrorists from a failed spectacular is negative (i.e., fsL c θ> ), then the

parabola shifts down (not shown) and this reinforces the increase in the range of normal events

as r increases. When, instead, recruitment benefits are sufficiently large with failure, the

parabola shifts up (not shown) and the net effect on the range of normal events depends on

whether the shift up of the straight line exceeds that of the parabola. We again see that

recruitment influences can go against conventional wisdom, because enhanced riskiness of

spectaculars may not necessarily curtail spectaculars. The 1972 Munich Olympics attack

sparked other attempted spectaculars, despite the improvement in commando forces – e.g., the

German Grenzschutzgruppe Neun (GSG-9) – that raised r.8

Next consider an increase in fsc or the marginal recruitment effect during a failed

spectacular. Taking a partial derivative of the parabola with respect to fsc gives 2 0,rθ θ− >

since 1rθ > . Thus, an increase in this recruitment benefit reduces the range of normal events,

thereby augmenting the range of spectaculars. If fsc is sufficiently raised, the parabola then lies

everywhere above the straight line and only spectaculars result. In a real sense, martyrdom is a

means of raising fsc by promoting a belief that even death in attacks (successful or otherwise)

has sufficient reward for the cause by attracting other zealots to engage in large-scale events with

deadly consequences. Pape (2003) indicates that suicide missions kill on average 13 people,

while a nonsuicide mission kill on average less than 1 person.

An increase in the marginal recruitment effect, ssc , of successful spectaculars shifts up

12

the parabola by θ and, in so doing, decreases the range of normal events. In contrast, an

enhanced marginal recruitment effect, snc , of successful normal events steepens the ( )snr N c θ+

straight line without altering its vertical intercept. The comparative static change equals 0,rθ >

so that the range of normal events widens. Obviously, these two marginal recruitment influences

have opposing predictions on the range of normal events. If both ssc and snc increase by the

same amount, the latter influence dominates since rθ θ> so that normal events become more

prevalent. This outcome arises from the lower success probability associated with spectaculars.

An increase in S – the payoff from spectaculars in the absence of recruitment gains –

raises the vertical intercept of the parabola and augments the range of spectaculars. This agrees

with the earlier result regarding S when there is no recruitment; thus, the spectacular region

expands with gains to a spectacular’s success, regardless of recruitment.

The final comparative static change concerns an increase in L or the terrorists’ loss from

failed spectaculars. Taking a partial derivative of the parabola with respect to L, we get:

( ) ( )2

1 0,fs ss fsrc c c rL S L

rL

θ θθ

∂ + − − + + = − + <∂

(13)

since 1.rθ > In Figure 3, an increase in L augments the vertical intercept of the parabola, but

shifts the parabola down and to the right so the normal range expands.

FURTHER IMPLICATIONS

Target countries have different abilities to counter terrorism, which affect their marginal

proactive costs (p). To put things in perspective, we assume that one country – say, the United

States (US) – has a lower p than another target – say, the EU – but are identical in terms of other

parameters. This cost difference may stem from the US having better technology or intelligence

13

to counter terrorism. Ceteris paribus, a low p encourages a larger proactive response. This

scenario is depicted in Figure 4 for the parabola and straight line whose intersection delineates

normal events for ( ),θ θ θ∈ from spectaculars outside these bounds. In Figure 4, the small p for

the US encourages sufficient proactive measures to trigger a spectacular owing to terrorist-

perceived recruitment gains. In contrast, the EU’s high p limits its proactive operations and

results in a normal event.

If the United States places a high value on terrorism-related losses (S) from a spectacular,

or the terrorists value comparable US losses over those from other countries, then this also raises

the level of US proactive measures by raising S, thus increasing the likelihood of spectaculars

against US interests. Targets such as the World Trade Center (WTC) had a high S value owing

to the potential loss of life, its symbol of US dominance in globalization, and its potential

financial consequences. Given the failed attempt in 1993 to bring down the north tower of the

WTC, the S value was particularly high.

In fact, the scenario depicted in Figure 4 appears to capture US and EU reactions

following 9/11. Because US losses from 9/11 far exceeded those of any other country, the Bush

administration and the American public clearly put very high values on future losses –

understandably, S increased in relation to that of countries less harmed by 9/11. This

characterization of US perceptions is consistent with survey findings reported by Davis and

Silver (2004) in which Americans felt sufficiently threatened after 9/11 to sacrifice some civil

liberties for greater security. US superiority in military power and intelligence compared with

other target countries also made for a relatively low p. Past and current US efforts to secure its

borders and guard against terrorist attacks lowered p relative to other countries, which increased

US proactive response and promoted further spectaculars – e.g., the attempted shoe bombing by

14

Richard Reid of American Airlines flight 63 on 22 December 2001, en route to Miami from

Paris.9 A sizable portion of proactive spending gets included in a country’s military budget.

Unlike most European countries, the US defense budget grew greatly following 9/11. A recent

study of the composition of terrorist events indicates that the proportion of deadly bombings has

increased greatly since 9/11 and the subsequent US-led war on terror (Enders and Sandler 2004).

This suggests that a greater reliance on proactive operations may be encouraging deadlier

attacks.

There is an interesting transnational externality associated with our analysis. Insofar as

terrorists stage their attacks where targets are softer, US proactive measures are apt to result in

spectaculars against US interests being staged abroad where defensive measures are inferior to

post-9/11 measures in the United States. Thus, the US war on terror has implications for

countries not part of this effort, because greatly elevated US proactive measures can deflect

spectaculars to these countries. Examples include the simultaneous bombings of two Bali

nightclubs killing foreigners including Americans on 12 October 2002, and the simultaneous

truck bombings of a residential complex in Riyadh, Saudi Arabia, housing foreigners including

Americans on 12 May 2003. Typically, proactive measures are viewed as being undersupplied

owing to their purely public good representation (see, e.g., Sandler and Siqueira 2003), where

only external benefits are derived by other countries. The analysis here indicates that such

actions can also create external costs as spectaculars are encouraged and shifted abroad. If

proactive policy implies both external benefits and external costs, then its supply can be too

little, excessive, or just right. When external benefits dominate, a proactive response is

undersupplied; when, however, external costs dominate, a proactive response is oversupplied. In

the unlikely event that external benefits exactly match external costs, proactive policy is optimal

despite the provider acting independently.

15

There is one consideration that may curtail excessive proactive measures by a nation with

a low p and high S. Even though the attacks may be shifted abroad, the terrorists still target

some of the offensive country’s assets. If the latter incorporates these costs on its interest abroad

in its calculus, then it will curtail its proactive response somewhat. Any internalization of these

external costs will, however, be incomplete, because the host country’s losses are unlikely to

influence the proactive country’s decision. For example, on 20 November 2003, two massive

suicide truck bombs exploded at the British Consulate and the British HSBC bank headquarters

in Istanbul, Turkey. Although the bombs were against British interest, all but three of the 30 or

so dead were Turkish Muslims.10 As attacks are transferred abroad, host countries sustain

collateral damage, ignored by the proactive country when deciding its counterterrorism policy.

CONCLUDING REMARKS

If proactive measures are cheap or if the perceived costs of future attacks are high, the

subgame perfect equilibrium may involve a targeted government engaging in relatively large

amounts of proactive operations that induce terrorists to resort to occasional spectaculars to tap

into recruitment benefits. Unquestionably, the experience of 9/11 raised S for the United States,

whose marginal proactive costs are relatively low compared with other countries. Since 9/11, the

relatively large US proactive campaign is consistent with the model presented and may be

excessive from a global standpoint as transference externalities imposed on other countries are

not taken into account when the United States decides its proactive options. As a consequence,

there may indeed be too much proactive operations with unintended fall-out.

Although this paper has focused on a two-player game between the terrorists and a

targeted state, an n-player game underlies proactive decisions where players consist of the 1n−

possible target nations and the terrorist network. In choosing their proactive measures, the

16

targeted states fail to adjust for the externalities that they impose on one another, which then

allows the terrorists to exploit vulnerabilities from states’ uncoordinated actions. If resources are

to be allocated efficiently to counterterrorism, nations must act in unison. The international

community is far from accepting this basic insight.

17

Footnotes

1. This percentage is computed from Sandler (2003, Table 1), whose data comes from the

Department of State.

2. Spending on terrorist-related intelligence is not available.

3. This analysis differs from Sandler and Arce (2003), which only allowed for a discrete

choice of preemption but permitted a three-player interaction involving two targeted

governments and a terrorist group.

4. By equation (4), we have 1S L rN

rL

+ − ≥ or ,S L

rN L

+≤+

from which S N r> follows

because S S L

N N L

+>+

when S N> and 0L > as assumed.

5. These comparative static results depend on:

2

0rN S

L rL

θ∂ −= <∂

! and

( )( )2 0.

L S L

r rL

θ − +∂ = <∂

!

The first inequality follows from .S N r>

6. The Lagrangian is ( ) ,S

pr

θ λ θ θθ

− − + −

!

where λ is a nonnegative Lagrangian multiplier. The first-order Kuhn-Tucker conditions

satisfy:

( )2 0p S rθ λ− + − = and 0,θ >

and

( ) 0θ θ− ≥! and 0.λ ≥

7. The Lagrangian is ( )Npθ λ θ θ

θ − − + −

! and the relevant Kuhn-Tucker conditions

18

give equation (8) since 0λ = and 0.θ >

8. The GSG-9 pulled off a daring rescue mission of hijacked Lufthansa flight 181, while

it was on the ground in Mogadishu, Somalia, on 18 October 1977. The rescue mission freed the

hostages with just minor injures to four hostages (Mickolus 1980, 734-40). Stun grenades were

used to gain a jump on the terrorists. Clearly, r had risen after Munich.

9. In Figure 4, a reduced p shifts S rpθ = to the right.

10. The blast at the Consulate killed the UK Consul General Roger Short, 58.

19

REFERENCES

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Bueno de Mesquita, Ethan. 2004. Conciliation, commitment, and counter-terrorism: A formal

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terrorism. European Journal of Political Economy 20 (2):463-78.

Davis, Darren W., and Brian D. Silver. 2004. Civil liberties vs. security: Public opinion in the

context of the terrorist attacks on America. American Journal of Political Science 48

(1):38-46.

Enders, Walter, and Todd Sandler. 1993. Effectiveness of anti-terrorism policies: Vector-

autoregression-intervention analysis. American Political Science Review 87 (4):829-44.

______. 1995. Terrorism: Theory and applications. In Handbook of defense economics,

Vol 1, edited by Keith Hartley and Todd Sandler, 213-49. Amsterdam: North-Holland.

______. 2004. After 9/11: Is it all different now? Unpublished manuscript, School of

International Relations, University of Southern California, Los Angeles, CA.

Heal, Geoffrey, and Howard Kunreuther. 2004. IDS models of airline security. Unpublished

manuscript, Graduate School of Business, Columbia University, New York, NY.

Hoffman, Bruce. 1998. Inside terrorism. New York: Columbia University Press.

Li, Quan, and Drew Schaub. 2004. Economic globalization and transnational terrorism.

Journal of Conflict Resolution 48 (2):230-58.

20

Mickolus, Edward F. 1980. Transnational terrorism: A chronology of events, 1968-1979.

Westport, CT: Greenwood Press.

Pape, Robert A. 2003. The strategic logic of suicide terrorism. American Political Science

Review 97 (3):343-61.

Sandler, Todd. 2003. Collective action and transnational terrorism. World Economy 26 (6):779-

802.

Sandler, Todd, and Daniel G. Arce M. 2003. Terrorism and game theory. Simulations &

Gaming 34 (3):319-37.

Sandler, Todd, and Walter Enders. 2004. An economic perspective on transnational terrorism.

European Journal of Political Economy 20 (2):301-16.

Sandler, Todd, and Kevin Siqueira. 2003. Global terrorism: Deterrence versus preemption.

Unpublished manuscript, School of International Relations, University of Southern

California, Los Angeles, CA.

Sandler, Todd, John Tschirhart, and Jon Cauley. 1983. A theoretical analysis of transnational

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United States General Accounting Office. 2004. Combating terrorism: Evaluation of selected

characteristics in national strategies related to terrorism. GAO-04-408T. Washington,

DC: US General Accounting Office.

Wilkinson, Paul. 2001. Terrorism versus democracy: The liberal state response. London:

Frank Cass.

! !

""

AFTER 9/11: IS IT ALL DIFFERENT NOW?

by

Walter Enders Department of Economics, Finance, and Legal Studies

University of Alabama Tuscaloosa, AL 35487 wenders@cba.ua.edu

205-348-8972 205-348-0590 (fax)

and

Todd Sandler

School of International Relations University of Southern California

Von Kleinsmid Center 330 Los Angeles, CA 90089-0043

tsandler@usc.edu 213-740-9695

213-742-0281 (fax)

Final Revision: September 2004

Keywords: after 9/11; terrorism; time series; intervention analysis; war on terror; forecasts; Bai-Perron test. Contact author: Todd Sandler AUTHORS’ NOTE: Walter Enders is the Bidgood Chair of Economics and Finance at the University of Alabama. Todd Sandler is the Robert R. and Katheryn A. Dockson Professor of International Relations and Economics at the University of Southern California. Sandler acknowledges research support from the Center for International Studies, University of Southern California. The replication data set is available at http://www.yale.edu/unsy/jcr/jcrdata.htm. We have profited from comments of anonymous referees.

AFTER 9/11: IS IT ALL DIFFERENT NOW?

Abstract Using time-series procedures, we investigate whether transnational terrorism changed following

9/11 and the subsequent US-led “war on terror.” Perhaps surprising, little has changed in the

time series of overall incidents and most of its component series. When 9/11 is prejudged as a

break date, we find that logistically complex hostage-taking events have fallen as a proportion of

all events, while logistically simple, but deadly, bombings have increased as a proportion of

deadly incidents. These results hold when we apply the Bai-Perron procedure where structural

breaks are data identified. This procedure locates earlier breaks in the mid-1970s and 1990s.

Reasonable out-of-sample forecasts are possible if structural breaks are incorporated fairly

rapidly into the model.

AFTER 9/11: IS IT ALL DIFFERENT NOW?

Thousands of dangerous killers, schooled in the methods of murder, often supported by outlaw regimes, are now spread throughout the world like ticking time bombs, set to go off without warning… In a single instant, we realized that this will be a decisive decade…(Bush 2002).

President Bush’s “State of the Union” remarks strongly suggest that everything changed

on 11 September 2001 (henceforth, 9/11) with the world now confronting a far-flung network of

terrorists, bent on heinous attacks. While there is no question that perceptions changed and

deep-seated fears arose that fateful day, there has been no data-based analysis on how

transnational terrorism (i.e., terrorism with international implications or genesis) differs, if at all,

since 9/11. The perception on the street and the reporting in the news media is that terrorism is

now different. But is transnational terrorism really different after 9/11 and, if so, how is it

different?

The four simultaneous hijackings on 9/11 represent watershed terrorist events in a

number of ways. First, the carnage associated with 9/11 was unprecedented: the number of

people killed was as great as all deaths from transnational terrorism for 1988-2000 (Sandler

2003). Prior to 9/11, no terrorist incident, domestic or transnational, resulted in more than 500

casualties (Quillen 2002a, 2002b; Hoffman 2002). Second, 9/11 demonstrated that terrorists did

not require a weapon of mass destruction (WMD) to cause mass casualties and over $90 billion

in losses. Third, 9/11 underscored the brutality that some fundamentalist terrorists will

undertake. Terrorist experts had warned prior to 9/11 that religious-based terrorists viewed

nonbelievers as legitimate targets and sought maximum carnage (Hoffman 1997). Fourth, 9/11

created a greater vigilance on the part of industrial countries that have greatly augmented their

expenditure on homeland security. Since 2002, the budget supporting the activities of the US

Department of Homeland Security (DHS) grew by over 60% to $36.2 billion for fiscal year 2004

2

(DHS 2003). An even greater expenditure goes to fighting the “war on terror” beginning with

the invasion of the Taliban and al-Qaida in Afghanistan on 7 October 2001. Other spending

involves augmenting intelligence capabilities and underwriting efforts to enhance international

cooperation, including the freezing of terrorist assets.

Using linear time-series methods on quarterly data of transnational terrorist incidents

from 1970 through the second quarter of 2003 (i.e., 2003:2), this paper shows how transnational

terrorism has changed following 9/11 and the subsequent war on terror. In particular, we apply

formal tests for structural breaks in a number of time series including incidents involving

casualties, hostages, and bombings as well as proportion series made from these basic series. We

first look for structural breaks at 9/11 and then apply the Bai and Perron (1998, 2003) procedure

to identify breaks at unknown dates based on the data. When compared, the alternative methods

provide consistent evaluations of the impact of 9/11 on the pattern of transnational terrorism.

We use the identified break to obtain one-step-ahead and multi-step-ahead forecasts.

The analysis demonstrates that the basic time series – e.g., the all-incident series,

bombings, and incidents with casualties – displayed no changes after 9/11. Incidents remained at

their low pre-9/11 levels. What changed was the composition of events with terrorists relying on

deadly bombings to a greater extent than ever before and engaging in a very low proportion of

complex hostage-taking missions.

BACKGROUND

Terrorism is the premeditated use or threat of use of violence by individuals or

subnational groups to obtain a political or social objective through intimidation of a large

audience beyond that of the immediate victims. Although definitions of terrorism have varied,

violence and political motives are always key ingredients.1 By making attacks appear to be

3

random, terrorists intimidate a larger audience and enhance its anxiety. The targeted society

must then expend large outlays to protect a wide range of vulnerabilities. Terrorists rely on

numerous modes of attack that include hostage taking, bombings, suicide attacks, assassinations,

armed attacks, and threats. Terrorism can be divided into two categories: domestic and

transnational. Domestic terrorism begins and ends in the host country: the perpetrators and

targets are homegrown. Moreover, domestic incidents have ramifications for only the host

country. When, however, a terrorist incident in one country involves victims, targets,

institutions, or citizens of another country, terrorism assumes a transnational character. The

hijackings on 9/11 are transnational terrorist events for a number of reasons: the incidents were

planned abroad; the terrorists came from outside of the United States; support came from abroad;

victims were from over 80 countries; and the incidents had economic and security implications

worldwide. The near-simultaneous bombings of the US embassies in Nairobi, Kenya, and Dar es

Salaam, Tanzania, on 7 August 1998 as well as the two suicide car bombings aimed at British

targets in Istanbul on 20 November 2003 are transnational terrorist incidents.

We are interested in examining transnational terrorism before and after 9/11, because this

form of terrorism poses the greatest threat to developed countries. Since the late 1980s, most

industrial countries have relatively little domestic terrorism (Hoffman 1998; Wilkinson 2001).

The al-Qaida network with its affiliate terrorist groups in some 60 nations engages in

transnational terrorism. Changes in visa procedures, airport security, target fortification, and

other counterterrorism measures indicate that transnational terrorism represents the greater

concern to the authorities. By augmenting international flows of all kinds, globalization has

given potential terrorists greater cover and ability to cause larger economic repercussions from

their attacks. Because 9/11 was a transnational event, the impact of 9/11, if any, is anticipated to

be on transnational terrorism.

4

Once economists turned their attention to analyzing terrorism, they have emphasized that

terrorists are rational actors who maximize some goal subject to resource constraints (Landes

1978; Sandler, Tschirhart, and Cauley 1983). These constraints are influenced by governments’

counterterrorism policies that can change the expected price associated with different terrorists’

actions. Terrorists have been shown to respond rapidly to changes in relative risks stemming

from government actions: terrorists switched intended targets away from recently fortified

venues to relatively softer targets (Enders and Sandler 1993; Sandler and Enders 2004). Thus,

efforts following 9/11 to curb hijackings and attacks on embassies through increased security and

better intelligence should induce terrorists to use other modes of attack so that hostage-taking

events (e.g., skyjackings, and barricade and hostage-taking missions) should decrease both in

number and as a proportion of total terrorist events following post-9/11 measures.

Another important factor in anticipating a potential change in the pattern of transnational

terrorism involves the changing motives of terrorists since the November 1979 takeover of the

US embassy in Tehran and the Soviet invasion of Afghanistan in the same time period (Hoffman

1998). From the late 1960s until the latter 1980s, transnational terrorism has been primarily

motivated by nationalism, separatism, Marxist ideology, and nihilism (Wilkinson 2001). These

terrorists were interested in maintaining a constituency and, hence, tried to limit casualties. By

the 1990s, a driving force of transnational terrorism was religious-based fundamentalist groups

that are less constrained by social norms and view violence against all nonbelievers including

women and children as a sacramental duty (White 2003). The affiliates of the al-Qaida network

abide by this desire to cause casualties. Since the start of 1980, religious-based groups grew

from 2 of 64 active terrorist groups to about half of 58 active groups in 1995 (Hoffman 1997, 3).

Enders and Sandler (2000) demonstrated that events with casualties rose from 1979:4 onwards as

fundamentalist-based terrorism grew.

5

Another crucial consideration in understanding the potential pattern of transnational

terrorism following 9/11 involves the US-led war on terror, which has targeted al-Qaida and its

allied groups. Recent reports estimated that about two-thirds of al-Qaida leaders have been

either killed or captured; such attrition would severely limit the amount of command and control

that al-Qaida’s highest echelon can exercise over its far-flung cells (Gerges and Isham 2003).

These same reports indicated that al-Qaida has had 3,400 suspects arrested worldwide since 9/11

and has lost many operatives during the Afghanistan War in 2001. Additionally, significant

financial assets ($135 million since 9/11) of the network have been frozen (The Economist

2003), which also compromises al-Qaida’s capabilities. These manpower, leadership, and

financial losses are anticipated to limit the network’s ability to engage in logistically complex

modes of attacks such as hostage taking. As a consequence, the al-Qaida network will turn to

logistically simple, but deadly, bombings. Such bombings can also be more attractive than

assassinations, which can be logistically complex and yield just a single victim. Given events

following 9/11 and the preferences of many of today’s terrorist groups for carnage, we anticipate

fewer hostage-taking events and assassinations and a greater reliance on deadly bombings. Such

expected changes in the composition of the overall series of transnational terrorism would be

more evident by analyzing the proportion of hostage-taking attacks or the proportion of deadly

attacks due to bombings.

Other structural breaks are anticipated prior to 9/11. The modern era of transnational

terrorism began in 1968 following the Arab-Israeli conflict and Israel’s subsequent occupation of

captured territory. In frustration, the Palestinians resorted to international terrorism to publicize

their cause to the global community and gain recognition by the Israelis (Hoffman 1998). The

level of transnational terrorism hit a new plateau in the early to mid-1970s as Palestinian

frustration achieved new heights and their terrorist methods were copied by non-Palestinian

6

groups. For example, left-wing nihilist groups sprung up throughout Western Europe (Alexander

and Pluchinsky 1992) and ethno-nationalist movements worldwide employed transnational

terrorism to further their cause.

Another potential structural break is anticipated in the early 1990s following the end of

the Cold War when many of the left-wing terrorist groups in Europe (e.g., in France, Germany,

Spain, Portugal, and the United Kingdom) either ended their operations or were brought to

justice (Alexander and Pluchinsky 1992; Chalk 1996). This terrorism decline was also due to a

reduced interest in Marxism following the collapse of so many communist regimes. At the same

time, there was less state sponsorship of leftist terrorists by East Europeans and Middle Eastern

countries (Chalk 1996; Clutterbuck 1994). These factors in combination should lead to structural

downturns in terrorism in the early 1990s following the Gulf War, which generated some

terrorist backlash. Although terrorism is expected to decrease in the early 1990s, this time frame

also marked the rising influence of fundamentalist terrorism, so that a greater degree of

casualties is expected to characterize the anticipated reduced level of terrorism.

DATA

Data on transnational terrorist incidents were drawn from International Terrorism:

Attributes of Terrorist Events (ITERATE), a data set that records the incident date, location, type

(e.g., bombing or hostage event), number of people killed, and number of people wounded.

ITERATE relies on the world’s news print and electronic media for its information with a large

reliance on the Foreign Broadcast Information Service (FBIS) Daily Reports, which surveyed a

couple hundred of the world’s newspapers and related sources. By splicing together earlier

ITERATE data sets, ITERATE 5’s “common” file contains 40 or so key variables common to all

transnational terrorist incidents from 1968:1 to 2003:2 (Mickolus et al. 2004). Coding

7

consistency for ITERATE events data was achieved by applying identical criteria and

maintaining continuity among coders through the use of overlapping coders and monitors.

ITERATE excludes terrorist incidents associated with declared wars or major military

interventions and guerrilla attacks on military targets of an occupying force. Even though

ITERATE records events on a daily basis, we used quarterly, rather than monthly or weekly, data

to avoid periods with zero or near-zero observations which would violate the underlying

normality assumptions of the time-series techniques applied.

We extracted eight primary time series to do our structural analysis. The ALL series

includes quarterly totals of all types of transnational terrorist incidents; the most important

component of this quarterly series is BOMBINGS, accounting for over half of all annual terrorist

attacks on average. BOMBINGS combines seven types of events: explosive bombings, letter

bombings, incendiary bombings, missile attacks, car bombings, suicide car bombings, and mortar

and grenade attacks. The HOSTAGE series includes quarterly totals of kidnappings,

skyjackings, nonaerial hijackings, and barricade and hostage-taking missions, whereas

assassinations (denoted by ASSNS) consist of politically motivated murders. Two additional

primary series are: (i) a quarterly DEATH series recording the number of terrorist incidents

where one or more individuals (including terrorists) died; and (ii) a more-inclusive

CASUALTIES series recording the quarterly total number of incidents where one or more

individuals were injured or died. We further broke down the bombing series by identifying the

quarterly number of bombings with one or more deaths (i.e., BOMB_K) and the number of

bombings with one or more casualties (i.e., BOMB_CAS).

To analyze the composition of terrorist incidents, we constructed a number of proportion

series. By dividing the quarterly entries of the HOSTAGE series by the number of overall

terrorist incidents, we obtained the quarterly share of hostage events denoted by P_HOSTAGE.

8

Similar divisions for ASSNS and BOMBINGS gave P_ASSNS and P_BOMBINGS. We also

divided the quarterly totals of events with casualties or deaths by the quarterly totals of all events

to construct the proportion of terrorist events with casualties and the proportion with deaths

indicated by P_CASUALTIES and P_DEATHS. These two proportion series can show whether

a typical incident is more threatening during the 1990s when the overall incident totals are down.

If, for example, these incident proportions shift up in the 1990s, then victims in an incident are

more likely to be injured or killed. Finally, we divided the quarterly total of deadly bombings

and bombings with casualties by the quarterly total of deaths and casualties, respectively, to give

the proportion of deadly incidents due to bombings (i.e., P_DEATHS_B) and the proportion of

incidents with casualties due to bombings (i.e., P_CAS_B). These two constructed time series

indicate whether a greater share of injurious terrorist events is now due to bombings.

TESTING FOR STRUCTURAL BREAKS AT 9/11

To determine whether the various incident series behave differently after 9/11, we first

estimated each series as an autoregressive process. Consider the AR(p) model:2

1

0 1 1 10

,p

t t i t i ti

y a y yρ β ε−

− + − −=

∆ = + + ∆ +∑ (1)

where ty is the number of incidents of a particular type occurring in time period t. For each

series, the lag length was selected by estimating equation (1) beginning with p = 6. If the t-

statistic for βp was not statistically different from zero at the 5% significance level, we reduced

the p by one and repeated the entire procedure. Once the lag length was determined, we tested

for a unit root using a Dickey-Fuller test. If we reject the null hypothesis that ρ = 0, it is then

possible to estimate the series and perform hypothesis tests using standard asymptotic

distribution theory. We performed the tests without including time as a regressor, because there

9

is no evidence of a deterministic trend in any of the incident series. The presence of a unit root

may signify the presence of a structural break; i.e., Dickey-Fuller tests can have low power to

reject the null of a unit root in the presence of a structural break (Perron 1989).

PRIMARY SERIES

The results of the estimations for the eight primary incident series are shown in the top

half of Table 1. For the ALL series, the lag length is such that p = 3 (so that we used two lagged

changed for the augmented Dickey-Fuller test) and the estimated value of ρ is −0.31. Since the

t-statistic for the null hypothesis that ρ = 0 is −3.20, we can reject the presence of a unit root at

the 2.5% significance level. The critical values at the 2.5%, 5%, and 10% significance levels are

−3.17, −2.89, and −2.58, respectively. Diagnostic checks indicated that the model is adequate in

that the Ljung-Box Q-statistics using 4 and 8 lags of the residuals have prob-values of 0.95 and

0.77, respectively. An examination of the top half of the table shows that only the ASSNS

(denoting assassinations) and CASUALTIES series are candidates to have unit roots. For

CASUALTIES, we could reject the null hypothesis of a unit root at the 10%, but not 5%,

significance level. The prob-value for the ASSNS series is just over 10%.

In an attempt to resolve the ambiguity regarding the CAUSALTIES and ASSNS series,

we used Perron’s (1989) test for a unit root in the presence of a structural break. Because 9/11 is

very close to the end of the data, it is not surprising that the prob-values for this test are nearly

identical to those of the Dickey-Fuller test. Insofar as the two tests can have low power in the

presence of a structural break near the end of the data set, we do not difference the

CAUSALTIES and ASSNS series. The results using the first differences of these two series are

virtually identical to those reported in Table 1.

To test for a structural break at 9/11, we modified equation (1) by estimating an equation

10

of the form:

0 1 21

,p

t i t i Pt Lt ti

y a a y D Dα α ε−=

= + + + +∑ (2)

where PtD and LtD are dummy variables representing 9/11. In equation (2), PtD is a dummy

variable such that PtD = 1 if t = 2001:3 and PtD = 0 otherwise. This type of pulse variable is

appropriate if the 9/11 attacks induced a temporary change in the ty series. The magnitude of

1α indicates the initial effect of 9/11 on ty and the rate of decay is determined by the

characteristic roots of equation (2). To allow for the possibility that 9/11 had a permanent effect

on the level of ty , the second dummy variable in equation (2) is such that LtD = 0 for t <

2001:3 and DLt = 1 for t ≥ 2001:3. The impact effect of 9/11 on ty is given by 2α , while the

long-run effect is given by 2α /(1 − Σ ai)

For each type of incident series, the fourth column of Table 1 reports 1α , the fifth column

reports 2α , and the sixth column reports the prob-value of the F-test for the joint hypothesis that

1 2 0α α= = . For the ALL series, neither dummy variable is significant at conventional levels

and the joint test does not allow us to reject the null hypothesis that both dummy variables have

zero coefficients. An examination of Table 1 reveals some striking similarities for all of the

series reported. None of the pulse dummy variables are significant at conventional levels for the

eight primary incident series. All of the t-statistics are below 0.6 in absolute value. In fact, only

the HOSTAGE series exhibits any effects as a result of 9/11. The t-statistic for the 2α

coefficient of DL for the HOSTAGE series is −2.35, and the magnitude of the coefficient is

−6.05. This reflects the fact that the number of HOSTAGE incidents fell from a pre-9/11 mean

of almost eleven incidents per quarter to slightly more than 3. However, even this finding is

11

problematic because a careful inspection of the HOSTAGE series (reported later as Figure 1)

shows that the sharp drop in hostage incidents actually occurred in 1999.

We performed a number of other break tests to determine if they identify 9/11 as a break.

For example, a Chow test for a structural break was conducted by comparing the residual sum of

squares for the pre-9/11 period to that for the entire period; but it did not reveal the presence of a

break for any of the eight primary series. The CUSUM test also showed no evidence of

structural change in any of the series occurring in the neighborhood of 2001:3.

PROPORTION TIME SERIES

We found somewhat different patterns when we looked at the seven proportion series.

The results are reported in the bottom half of Table 1. There are several key results:

1. At the 10% significance level, we reject the null hypothesis of a unit root for all series

except the P_DEATHS and the P_CASUALTIES series. As mentioned earlier, the unit-root test

has low power in the presence of a structural break, so the failure to reject the null hypothesis of

a unit root may be evidence in favor of a structural break. When we performed unit-root tests on

the P_DEATHS and P_CASUALTIES series using only the data through 2001:2, the associated

t-statistics for the null hypothesis that ρ = 0 are −4.27 and −4.85, respectively, leading to a

rejection of a unit root.

2. The pulse dummy variable is statistically significant for the P_DEATHS and

P_CASUALTIES series. For these two series, the t-statistics for the null hypothesis that 1α = 0

are 6.31 and 4.81, respectively. On impact, the proportion of incidents with deaths rose by 54

percentage points and the proportion of incidents with casualties rose by 48 percentage points.

The level dummy variables are, however, not significant at conventional levels. Hence, the

jumps in the P_DEATHS and P_CASUALTIES are not permanent.

12

3. The level dummy variable is highly significant for the proportion of hostage incidents

(P_HOSTAGE) and the proportion of deadly incidents due to bombings (P_DEATHS_B). The

intercept for the P_HOSTAGE series decreased by 8 percentage points and that for

P_DEATHS_B rose by 25 percentage points. These changes are estimated to be permanent.

The P_HOSTAGE series falls precisely at 9/11. There is some evidence ( )1.74t = − that the

proportion of assassinations (P_ASSNS) decreased by 16 percentage points after 9/11.

Generally, we did not uncover evidence that there were changes in the primary terrorist

series following 9/11. We did, however, uncover evidence that the composition of the terrorist

time series changed. This apparent switch from logistically complex hostage events to less

complex bombings is consistent with our predictions based on post-9/11 pressures on the al-

Qaida leadership and enhanced security given to airports, embassies, and high-profile targets.

The reliance on deadly bombings also agrees with our priors concerning the changing nature of

terrorism.

MULTIPLE STRUCTURAL BREAKS

One criticism of these results is that there might be more than one structural break; e.g.,

Enders and Sandler (2000) reported significant changes in terrorism associated with the increase

in religious fundamentalism. Ignoring the effects of early breaks might cloud the effects of 9/11;

hence, one research strategy is to reestimate equation (2) by including dummy variables for all

such breaks. This strategy is problematic because there is a danger of ex post fitting if break

points are selected as a result of an observed change in the variable of interest. Moreover, a

number of events may roughly coincide with the selected break points. In addition, the efficacy

of the estimates cannot rely on the usual asymptotic properties of an autoregression, because an

increase in sample size does nothing to increase the number of points lying between two break

13

points. Just as it is difficult to know what dummy variables to include, it can be difficult to know

what factors to exclude. If important events influencing terrorism are excluded from the

estimating equation, there is still a specification problem.

An alternative methodology is to use a purely data-driven procedure to select the break

dates. Bai and Perron (1998, 2003) developed a procedure that can estimate a model with an

unknown number of structural breaks that occur at unspecified dates. For our purposes, the key

feature of the Bai-Perron procedure is that the number of breaks and their timing are estimated

along with the autoregressive coefficients. Bai and Perron (1998, 2003) also showed how to

form confidence intervals for the break dates. This is particularly important because there is

evidence that key changes in some of the incident series actually began prior to 9/11; we want to

ascertain whether the changes are due to 9/11 or to forces already in progress.

The form of the Bai-Perron specification that we considered is:

1

,p

t j i t i ti

y a yα ε−=

= + +∑ (3)

where j = 1, … , m + 1 and m is the number of breaks. Equation (3) allows for m breaks that

manifest themselves by shifts in the intercept of the autoregressive process. Our notation is such

that there are m + 1 intercept terms denoted by jα . The first break occurs at t1 so that the

duration of the first regime is from t = 1 until t = 1t and the duration of the second regime is from

1t + 1 to 2t . Because the m-th break occurs at ,mt t= the last regime begins at mt + 1 and lasts

until the end of the data set. In applied work, the maximum number of breaks needs to be

specified. We allowed for a maximum number of 5 breaks. The procedure also required that we

specified the minimum regime size (i.e., the minimum number of observations between breaks).

Because our data runs through the second quarter of 2003, we used a minimum break size of 6 to

permit a break occurring as late as the first quarter of 2002. In principal, we could allow all

14

coefficients (including the autoregressive coefficients) to change; but this would necessitate

estimating a separate AR(p) model for each regime. Since the data include only a small number

of post-9/11 observations, this procedure is not possible here. Instead, we adopted what Bai and

Perron call the “partial change” model; this specification allowed us to estimate only one new

coefficient (i.e., the intercept) for each regime.

For each series, Table 2 reports the number of breaks (m), the point estimate of each

break date, the lower and upper bounds of a 95% confidence interval around the break dates

(Lower and Upper, respectively), the sample mean in the first regime (Initial Mean), and the

short-run (SR) and long-run (LR) changes due to the break(s). The short-run effect of break j is

measured by 1j jα α+ − , whereas the long-run effect is measured by (1j jα α+ − )/( 1 − Σ ia ).

The results for the various incident series reinforce the results regarding 9/11, reported in

Section 3. For example, a single structural break, not at 9/11, is found for the ALL series. The

most likely estimate of this break is 1994:3; a 95% confidence interval for the break date spans

the period 1993:4 through 1996:4. This confidence interval is not symmetric around 1994:3,

because the break is unlikely to have occurred much earlier than this date. In the first regime

(i.e., until 1994:3), the initial mean number of incidents per quarter is 106.62. After this break,

we estimated a short-run decline of 46.46 incidents and a long-run decline of 62.63 incidents.

The crucial point is that a 95% confidence interval for the break date does not include 9/11. This

structural break is consistent with our priors about the influence of reduced state sponsorship and

the demise of many terrorist groups in the late 1980s and early 1990s. Given that bombings

constitute half of the ALL series, a similar structural break characterizes BOMBINGS at 1994:1

in Table 2.

The HOSTAGE series experiences a single break after 2000:3 (i.e., the new regime

begins in 2000:4). The 95% confidence interval does include 2001:3; hence, the decline in the

15

mean number of HOSTAGE incidents from 13.79 to about 3.85 (13.79 − 9.94 = 3.85) may be

attributable to 9/11. There is no evidence of a break in the ASSNS series. Although the time

series for casualties due to bombings and incidents with deaths, each displays two structural

breaks, none of the 95% confidence intervals of these breaks include 9/11. For BOMB_CAS, the

two breaks took place at 1992:3 and 1994:3 as incidents dropped in number but became more

lethal on average as fundamentalist-based terrorism grew in importance. For the DEATHS

series, the structural break at 1975:3 coincides with the growing importance of transnational

terrorism in the early to middle 1970s. In contrast, the structural break for the DEATHS series at

1996:2 came as the number of transnational terrorist events decreased greatly.

In the bottom portion of Table 2, the structural breaks for six proportion series are listed.

These proportion series display a larger number of structural breaks compared with the primary

series. Notably, three of the proportion series – P_HOSTAGE, P_DEATHS_B, and P_DEATHS

– have structural breaks whose confidence intervals include 9/11. In particular, we estimated

four breaks in the P_HOSTAGE series with break dates of 1994:1, 1996:2, 2000:1, and 2001:3.

The confidence interval for this last regime, spanning 2001:1 through 2002:1, is associated with

a short-run decline of 37.6 percentage points. Clearly, terrorists have reduced their reliance on

hostage events since 9/11.

The proportion of incidents with deaths (P_DEATHS) is estimated to have 5 breaks. The

point estimate of the fifth break is 2001:2, so that beginning in 2001:3 the short-run increase in

the proportion of death incidents is 17.8 percentage points. Because the confidence interval for

the fifth break is entirely contained within that for the fourth break, there may have been an

ongoing increase in the proportion of deadly incidents that included the incidents on 9/11.

Nevertheless, the estimates are consistent with the rise in P_DEATHS being primarily due to

more deadly bombs. As shown in the Table 2, there is a short-run jump in P_DEATHS_B of 20

16

percentage points that is estimated to occur at 2001:2. Moreover, we find no evidence of breaks

associated with 9/11 in the proportion series associated with assassination and casualty incidents.

Table 2 is also consistent with our priors about transnational terrorism becoming more of

a threat in the early to mid 1970s – i.e., the 1975:3 structural break for DEATHS, P_ASSNS, and

P_DEATHS, and the 1974:1 structural break for P_DEATHS_B. Moreover, the structural

breaks for B_DEATHS_B and P_DEATHS during the early to mid 1990s are consistent with our

priors that the period following the Gulf War had deadlier events on average than earlier periods.

Clearly, transnational terrorism changed in character at three times: in the mid-1970s; in the

1990s; and in and around 9/11.

FORECASTING BEYOND 9/11

We now use the previously identified structural breaks to forecast the various incident

series. Based on equation (3), the k-step ahead forecast of t ky + follows from:

1

,p

t t k t j i t t k ii

E y E a E yα+ + −=

= +∑ (4)

where t t kE y + is the expectation of t ky + conditional on the information set at t. Since a break

may occur between period t and period t + k, the appropriate value of αj is unknown at t. We

assumed that a break date becomes known in the period containing the break. Although the

structural break at 9/11 could not be forecasted in period 2001:2, forecasts beginning in 2001:3

can use the fact that a break occurred. Of course, the magnitude of the break is unknown, so its

size must be estimated. As is standard practice, to obtaint t kE y + , we estimated equation (3) with

data through period t and then used the estimated coefficient to form equation (4). If a break in

the intercept occurs in period t + 1 to t + k, the forecasts will be poor, since they do not

17

incorporate the appropriatejα .3

The break in the HOSTAGE series prior to 9/11 (indicated by a vertical line) is shown in

the top portion of Figure 1, where the HOSTAGE series fluctuates around the pre-break mean of

13.79 incidents per quarter until 2000:3. Thereafter there is a sharp drop in the series, so that the

new long-run mean is about 3.85. The lower portion of Figure 1 shows the 1-step-ahead

(unbroken line) and 8-step-ahead forecast errors, ,t k t t ky E y+ +− for t = 1999:2 through 2003:2.

The two forecast errors are reasonably similar until 2000:4, and the series of 1-step-ahead errors

does not exhibit any unusual behavior at the breakpoint. Clearly, the 1-step-ahead forecasts

quickly capture the influence of a structural break so the forecast errors remain small; however,

the 8-step-ahead forecasts perform poorly beginning with the breakpoint. The forecasts

1998:4 2000:4E y through 2000:3 2002:3E y are all quite negative. Because the long-term forecasts do not

include any information concerning the change in the intercept beginning in 2000:4, they all

perform poorly. These long-term forecasts reinforce the point that the HOSTAGE series began

to decline prior to 9/11. Moreover, the forecasts of the post-9/11 values that use the 2000:3

break date appear adequate.

The actual time series (1970:1 – 2003:2) and the forecast results for the DEATH series

are shown in Figure 2. Although the breaks are not as pronounced as those in Figure 1, the Bai-

Perron break date of 1996:2 seems quite reasonable. The lower forecast portion of the figure

reinforces the point that 1996:2 is a critical point in the data. The 8-step-ahead forecasts sharply

depart from the 1-step-ahead forecasts at 1996:2. In the top portion of Figure 2, there appears to

be a steady increase in the number of DEATH incidents following 9/11. However, the negative

finding concerning a break at 9/11 suggests that such an increase is not atypical. Moreover, the

1-step-ahead and 8-step-ahead forecasts are similar for the post-9/11 period, which is consistent

18

with 9/11 not being a structural break for the DEATH series.

The upper portion of Figure 3 shows the P_HOSTAGE series. The increases in the series

in 1994:1, 1996:2, and 2000:1 as well as the drop in 2001:3 are quite pronounced. The

appropriateness of the breakpoints is also shown in the lower portion of the figure, because the

long-term forecasts diverge from the 1-step-ahead forecasts at these break dates. For example,

the 8-step-ahead forecasts beginning from 2001:2 are all too high relative to the actual values of

P_HOSTAGE and to the 1-step-ahead forecasts. Thus, a little hindsight to recognize structural

breaks shortly after they occur can greatly assist the accuracy of forecasts.

CONCLUDING REMARKS

Over two years have passed since 9/11. In reaction to these attacks, targeted

governments have bolstered security at airports, embassies, and other high-profile targets. The

US-led offensive against al-Qaida and its network has taken a toll on al-Qaida’s leadership and

finances. As a consequence, post-9/11 policies should have hampered al-Qaida’s ability to direct

operations. We have applied time-series methods to uncover what, if anything, is now different

since 9/11. Surprisingly, little has changed to the series of all transnational terrorist incidents or

its major component of all bombing incidents. Moreover, the DEATHS and CASUALTIES

series have not changed following 9/11. The main influence of 9/11 has been on the composition

of the ALL series. In particular, hostage-taking incidents have fallen after 9/11 as terrorists, bent

on carnage, have substituted into deadly bombings. As a consequence, the proportion of deadly

incidents due to bombings has increased as the proportion of hostage-taking and assassination

attacks have decreased. Given official antiterrorist measures after 9/11, these changes are

understandable as terrorists substitute from hard to soft targets in the wake of security changes.

Additionally, stress on al-Qaida leadership may be responsible for a substitution from logistically

19

complex attacks (e.g., hostage taking and assassinations) to logistically simpler bombings. The

lack of a reversal to this composition effect in recent quarters suggests that a replacement to al-

Qaida is not yet on the scene.4

When we do not prejudge structural breaks and apply the Bai-Perron method to identify

these jumps, a number of interesting results follow. First, the Bai-Perron findings regarding 9/11

are entirely consistent with our results when 9/11 is prejudged as a structural break. Second,

structural breaks characterize two earlier periods: (i) the early to mid 1970s when transnational

terrorism became more deadly; and (ii) the 1990s when there was a reduction in transnational

terrorism as state sponsorship fell. Third, the 1990s is also seen on average to have more deadly

events. The movement to greater casualties, underscored by 9/11, was foreshadowed by the

proportion series associated with deaths and casualties well before 9/11. Finally, we show that

reasonable forecasts are possible if structural breaks are incorporated fairly rapidly in the

underlying forecast model. Our results suggest that the war on terror has had effects – some

good (e.g., the absence of an increase in incidents and fewer hostage incidents) and some bad

(e.g., a greater reliance on deadly bombings).

Because our work relies on univariate time-series methods, it can be extended in

interesting ways. A number of key series can be estimated as a vector autoregression (VAR).

Unlike a typical VAR, the intervention dummy variables DL and DP can be allowed to affect

each of the series simultaneously. In this way, the impulse responses of all of the series until

9/11 can be obtained jointly. Moreover, cross-equation restrictions can be used to obtain the

overall importance of 9/11. A second limitation of our univariate methodology is that it does not

permit us to attribute changes in the levels of the series to any precise set of economic or political

variables. The fact that many series appear to break in the early 1990s points to a decline in state

sponsorship and the demise of several left-wing groups. Without explicit incorporation of some

20

explanatory variables in our estimating equations, the causes of the breaks remain suggestive. A

worthwhile extension is to incorporate such variables. When more data points past 9/11 become

available, we can use a VAR approach, modeled after Enders and Sandler (1993), to investigate

the influence of counterterrorism actions imposed after 9/11 (Arce and Sandler 2005[this issue]).

21

Footnotes

1. Standard definitions of terrorism exclude state terror used by governments to control their

citizens through intimidation. Available data sets exclude state terror.

2. The incident series cannot go below zero and the proportion series cannot go below zero

or above unity. Most of the series do not have zero or near-zero values; the quarterly mean value

of almost all of the series are about two standard deviations from zero. Exceptions are the

ASSNS and BOMB_K series, each of which has a few zero values. Thus, the coefficient

estimates and standard errors are appropriate for all but two series. As a check, we reran Table 1

using the variables in logs for all but the ASSNS and BOMB_K series. We found no substantive

changes in the results for any series. Currently, the Bai-Perron methodology, used below, has

not been extended to include a negative binomial (or Poisson) structure to address any zero

problem for the ASSNS and BOMB_K series.

3. We remind the reader that the multi-step-ahead forecast errors are serially correlated.

4. We must remind the reader that our findings are based on data through 2003:2. Events –

e.g., the insurgency in Iraq and the kidnapping of foreigners – can change patterns in the future.

22

REFERENCES

Alexander, Yonah, and Dennis Pluchinsky. 1992. Europe’s red terrorists: The fighting

communist organizations. London: Frank Cass.

Arce M., Daniel G., and Todd Sandler. 2005. Counterterrorism: A game-theoretic analysis.

Journal of Conflict Resolution 49 (2): this issue.

Bai, Jushan, and Pierre Perron. 1998. Estimating and testing linear models with multiple

structural changes. Econometrica 66 (1):47-78.

_____. 2003. Computation and analysis of multiple structural change models. Journal of

Applied Econometrics 18 (1):1-22.

Bush, George W. 2002. State of the union. Website at

http://www.whitehouse.gov/news/releases/2002/01/20020129-11.html, accessed 2

January 2004.

Chalk, Peter. 1996. Western European terrorism and counter-terrorism. Houndsmills, UK:

Macmillan.

Clutterbuck, Richard. 1994. Terrorism in an unstable world. New York: Routledge.

Department of Homeland Security. 2003. Budget in Brief. Website at

http://www.dhs.gov/interweb/assetlibrary/FY_2004_Budget_IN_BRIEF.pdf, accessed 20

November 2003.

The Economist. 2003. Al-Qaeda operations are rather cheap. The Economist 369 (8344):45.

Enders, Walter, and Todd Sandler. 1993. The effectiveness of anti-terrorism policies:

Vector-autoregression-intervention analysis. American Political Science Review 87

(4):829-44.

_____. 2000. Is transnational terrorism becoming more threatening? A time-series

investigation. Journal of Conflict Resolution 44 (3):307-32.

23

Gerges, Fawaz A., and Christopher Isham. (2003). Sign of weakness? Do overseas terror

strikes suggest Al Qaeda inability to hit US? ABC News, November 22, 2003.

Hoffman, Bruce. 1997. The confluence of international and domestic trends in terrorism.

Terrorism and Political Violence 9 (1):1-15.

_____. 1998. Inside terrorism. New York: Columbia University Press.

_____. 2002. Rethinking terrorism and counterterrorism since 9/11. Studies in

Conflict & Terrorism 25 (5):303-16.

Landes, William M. 1978. An economic study of aircraft hijackings, 1961-1976. Journal

of Law and Economics 21 (1):1-31.

Mickolus, Edward F., Todd Sandler, Jean M. Murdock, and Peter Flemming. 2004.

International terrorism: Attributes of terrorist events, 1968-2003 (ITERATE 5). Dunn

Loring, VA: Vinyard Software.

Perron, Pierre. 1989. The great crash, the oil price shock, and the unit root hypothesis.

Econometrica 57 (6):1361-1401.

Quillen, Chris. 2002a. A historical analysis of mass casualty bombers. Studies in Conflict

& Terrorism. 25 (5):279-92.

_____. 2002b. Mass casualty bombings chronology. Studies in Conflict & Terrorism. 25 (5):

293-302.

Sandler, Todd. 2003. Collective action and transnational terrorism. World Economy 26 (6):

779-802.

Sandler, Todd, and Walter Enders. 2004. An economic perspective on transnational

terrorism. European Journal of Political Economy. 20 (2):301-16.

Sandler, Todd, John T. Tschirhart, and Jon Cauley. 1983. A theoretical analysis of

transnational terrorism. American Political Science Review 77 (1):36-54.

24

White, Jonathan R. 2003. Terrorism: 2002 update, 4th Ed. Belmont, CA:

Wadsworth/Thomson Learning.

Wilkinson, Paul. 2001. Terrorism versus democracy: The liberal state response. London:

Frank Cass.

Table 1: AR Estimation Using 9/11 as a Structural Break Series Lags ρ α1 α2 F Q(4) Q(8) ALL 3 −0.31 −22.26 −15.31 0.47 0.95 0.77 (−3.20) (−0.54) (−0.89) HOSTAGE 2 −0.55 −1.03 −6.05 0.04 1.00 0.98 (−5.38) (−0.16) (−2.35) ASSNS 3 −0.18 −1.99 −0.71 0.77 0.65 0.14 (−2.56) (−0.44) (−0.41) BOMBINGS 3 −0.37 −13.80 −9.55 0.52 0.87 0.39 (−3.64) (−0.48) (−0.84) BOMB_K 2 −0.54 −0.75 0.51 0.95 0.71 0.33 (−5.40) (−0.16) (0.30) BOMB_CAS 6 −0.32 −3.88 0.13 0.87 0.99 0.99 (−3.09) (−0.50) (0.05) DEATHS 2 −0.31 1.80 −0.63 0.95 0.74 0.74 (−3.97) (0.28) (−0.26) CASUALTIES 3 −0.22 −4.83 −1.46 0.87 0.96 0.60 (−2.84) (−0.48) (0.37) P_HOSTAGE 4 −0.28 0.14 −0.08 0.05 0.99 0.87 (−2.77) (1.37) (−2.36) P_ASSNS 3 −0.38 −0.22 −0.16 0.06 0.89 0.46 (−3.74) (−0.93) (−1.74) P_BOMBINGS 3 −0.31 −0.02 0.04 0.62 0.90 0.91 (−3.26) (−0.12) (−0.96) P_DEATHS_B 2 −1.08 −0.26 0.25 0.01 0.82 0.85 (−8.48) (−1.25) (3.32) P_CAS_B 2 −0.99 −0.10 0.07 0.48 0.21 0.18 (−8.30) (−0.57) (1.21) P_DEATHS 4 −0.24 0.54 0.03 0.00 0.84 0.32 (−2.47) (6.31) (0.72) P_CASUALTIES 4 −0.25 0.48 0.04 0.00 1.00 0.96 (−2.36) (4.81) (0.96) Note: t-statistics are in parentheses

Table 2: Estimates of Multiple Structural Breaks Seriesa Break Date Lower Upper Initial Mean SRb Effect LRc Effect ALL 1994:3 1993:4 1996:4 106.62 −46.46 −62.63 HOSTAGE 2000:3 2000:1 2002:3 13.79 −6.69 −9.94 BOMBINGS 1994:1 1993:3 1996:1 61.50 −33.92 −40.43 BOMB_CAS 1992:3 1989:4 1993:3 15.79 11.20 17.17 1994:3 1994:1 1996:1 15.64 23.97 DEATHS 1975:3 1973:2 1976:2 8.89 7.17 11.01 1996:2 1994:2 1998:4 −5.81 −8.91 P_HOSTAGE 1994:1 1991:3 1994:4 0.131 0.102 0.071 1996:2 1994:1 1998:1 0.115 0.079 2000:1 1998:4 2000:4 0.207 0.143 2001:3 2001:1 2002:1 −0.376 −0.259 P_ASSNS 1975:3 1974:1 1975:4 0.039 0.070 0.078 1990:1 1984:4 1993:2 −0.37 −0.041 P_BOMBINGS 1977:4 1973:3 1980:1 0.679 −0.097 −0.180 P_DEATHS_B 1974:1 1972:2 1974:3 0.039 0.050 0.036 1993:2 1992:1 1993:3 0.112 0.079 1997:3 1992:3 2000:2 −0.064 −0.045 2001:2 2000:4 2001:4 0.200 0.142 P_DEATHS 1975:3 1974:3 1976:1 0.103 0.104 0.081 1994:1 1992:3 1994:2 0.167 0.130 1997:1 1995:2 1998:3 −0.144 −0.112 1999:4 1998:1 2002:2 0.108 0.084 2001:2 1999:1 2001:4 0.178 0.139 P_CASUALTIES 1999:4 1995:2 2001:1 0.292 0.123 0.279 aLag lengths are not necessarily those shown in Table 1. bSR denotes the short-run magnitude of the break. cLR denotes the long-run magnitude of the break.

Figure 1: HOSTAGE Incidents and Forecast Errors

HOSTAGE Incidents

Inci

den

ts p

er q

uar

ter

1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 20020

5

10

15

20

25

30

35

1-Step Ahead 8-Step Ahead

1-Step and 8-Step Ahead Forecast Errors

Fore

cast

Err

ors

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003-15

-10

-5

0

5

10

15

20

25

Figure 2: DEATH Incidents and Forecast Errors

DEATH Incidents

Inci

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1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 20020

5

10

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1-Step Ahead 8-Step Ahead

1-Step and 8-Step Ahead Forecast Errors

Fore

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1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003-20

-15

-10

-5

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Figure 3: Proportion of Hostage Incidents and Forecast Errors

Proportion of Hostage Incidents

Inci

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1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 20030.00

0.08

0.16

0.24

0.32

0.40

0.48

0.56

0.64

1-Step Ahead 8-Step Ahead

1-Step and 8-Step Ahead Forecast Errors

Fore

cast

Err

ors

1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003-0.32-0.24-0.16-0.080.000.080.160.240.320.40

Transnational Terrorism: An Economic Analysis

by

Todd Sandler

School of International Relations University of Southern California

Von Kleinsmid Center 330 Los Angeles, CA 90089-0043

USA tsandler@usc.edu

Walter Enders

Department of Economics, Finance, and Legal Studies

University of Alabama Tuscaloosa, AL 35487

USA wenders@cba.ua.edu

August 2004

Abstract

Both theoretical and empirical techniques are used to put modern-day terrorism into perspective. This paper surveys past contributions, presents updated empirical findings, and suggests new directions for research. Because of strategic interactions among terrorists and targeted government, game theory and economic methods play an important role in identifying novel policy recommendations and behavioral insights. Transnational terrorism and efforts to curtail it involves externalities and market failures. The paper analyzes how terrorists alter tactics in reaction to government policies and how a no-negotiation hostage policy is difficult to institute. JEL classifications: D74, H56 Acknowledgement: This paper is an extended, updated, and modified version of “An Economic Perspective on Transnational Terrorism,” which appeared in the European Journal of Political Economy, 20(2), 2004, pp. 301-316. Portions of this article are being republished with the kind permission of Elsevier B.V. Todd Sandler is the Robert R. and Katheryn A. Dockson Professor of International Relations and Economics at the University of Southern California. Walter Enders is the Bidgood Chair of Economics and Finance at the University of Alabama. The Center for International Studies (CIS) at the University of Southern California supported the updating of the terrorism data for 2003.

I. Introduction

On 11 September 2001 (henceforth, 9/11), the world watched aghast as two commercial

airliners toppled the twin towers of the World Trade Center (WTC) and a third plowed into the

Pentagon. Yet a fourth hijacked plane landed short of its intended Washington, DC target as

passengers took matters into their own hands. Economic methods – both theoretical and

empirical – have been applied by a small and growing group of economists to understand a host

of issues associated with such terrorist events. These issues concern the policy effectiveness of

alternative responses (e.g., toughening punishments, retaliatory raids, and installing

technological barriers), negotiation responses in hostage incidents, the terrorists’ choice of target,

the economic impacts of terrorism, the provision of terrorism insurance, the curbing of

interdependent risk, and others.

Terrorism is the premeditated use, or threat of use, of extranormal violence by an

individual or a subnational group to obtain a political objective through intimidation or fear

directed at a large audience usually beyond the immediate victims. An essential aspect of this

definition concerns the presence of a political objective (e.g., getting the United States out of the

Persian Gulf states) that the terrorist acts or campaigns are designed to achieve. Incidents that

have no specific political demands are criminal rather than terrorist acts – e.g., extortion for

profit. Another crucial ingredient is the use of extranormal violence or brutality to capture news

headlines. As the public becomes numb to their acts of violence, terrorists respond with more

heinous actions to recapture media attention. Thus, the escalation experienced on 9/11 was part

of an ongoing process. Terrorists often direct their violence and threats toward a vulnerable

target group, not immediately involved with the political decision-making process that they seek

to influence. The two planes that crashed into the WTC fit this pattern, but the other two planes

were targeted against decision makers. In a deliberate attempt to create a general atmosphere of

2

fear, terrorists strike at a variety of targets with alternative modes of operations (e.g.,

assassinations, bombings, and kidnappings), thus making it difficult for the authorities to

anticipate the venue of the next incident. Such actions make attacks appear to be random, so that

a targeted society must expend large amounts of resources to protect a wide range of

vulnerabilities. This simulated randomness provides terrorists with a cost advantage over the

stronger authorities who must defend against the threat that they pose. Because people tend to

overrespond to unlikely catastrophic events while ignoring more likely daily dangers (e.g., dying

in a car accident), terrorists succeed in achieving society-wide anxiety with minimal resources.

When a terrorist incident in one country involves victims, targets, institutions,

governments, or citizens of another country, terrorism assumes a transnational character. In the

WTC tragedy, citizens from over 80 countries lost their lives at the hands of foreign terrorists

who crossed into the United States from abroad. Obviously, the four hijackings on 9/11

constitute transnational terrorist attacks. During the 1980s, the kidnappings of foreigners in

Lebanon or the near-simultaneous suicide truck bombings at the US Marines barracks and

apartment building housing French Paratroopers, as a protest against Western policies, also

represent transnational terrorism. Transnational terrorist incidents are transboundary

externalities insofar as actions conducted by terrorists or authorities in one country may impose

uncompensated costs or benefits on people or property of another country. As such, myriad

market failures are associated with collective actions to curb international terrorism.

The application of economic methods to the study of terrorism began with Landes (1978),

who applied the economics of crime and punishment to the study of domestic skyjackings in the

United States. Economic methodology is particularly well-suited to provide insights in studying

terrorism. Economic analysis can account for the strategic interactions among opposing interests

– e.g., among rival terrorists, the terrorists and the authorities, and among targeted countries.

3

Rational-choice models, based on microeconomic principles, can be applied to ascertain how

terrorists are apt to respond to policy-induced changes to their constraints. The same methods

can be used to analyze how governments react to terrorist-induced changes to their policymaking

environment. Altruistic-based intergenerational rewards can even be shown to motivate the

growing use of suicide bombings (Azam, forthcoming). Additionally, the theory of market

failures can underscore how agents’ independent optimization may be at odds with socially

efficient outcomes, so that governmental failures may result from well-intentioned policies. In

addition, various economic empirical methods can be applied to evaluate theoretical predictions

and policy recommendations. Empirical techniques can evaluate the economic consequences of

terrorism – e.g., the impact of terrorism on tourism (Enders, Sandler, and Parise, 1992), foreign

direct investment, (Enders and Sandler, 1996), and per capita GDP (Abadie and Gardeazabal,

2003).

The primary purpose of this article is to survey some crucial insights gained from

applying an economic perspective to the study of terrorism. A second purpose is to present an

updated analysis of trends and cycles, policy-induced externalities, collective action responses,

and hostage negotiation strategy. A third purpose is to identify some future research directions.

II. A Look at the Data

To provide a perspective on the nature of the transnational terrorist threat, we compile

Table 1 based on data from the US Department of State (1988-2004). This table indicates the

annual number of transnational terrorist events, the associated deaths, the number of wounded,

and the number of attacks against US people and/or property for 1968-2003. During these 36

years, there were 14,857 transnational terrorist incidents in which 14,807 people (including those

on 9/11) died. On average, there were 411 fatalities per year which is relatively few, especially

4

compared with the 41,000 or so people killed annually on US highways. Each terrorist incident

kills on average about one person. The casualties on 9/11 represent a clear outlier with deaths on

this single day approximately equal to all transnational terrorist-related deaths recorded during

the entire 1988-2000 period.

An examination of Table 1 suggests that transnational terrorism follows a cyclical pattern

with much of the 1990s being relatively calm compared to the earlier two decades.

Transnational terrorism is particularly low during 2002-2003, with incidents on par in number to

that of 1969 at the start of the era of transnational terrorism. Something that cannot be seen from

Table 1 is that a high proportion of total casualties for a given year is typically associated with a

couple of “spectacular” events – e.g., the simultaneous bombings of the US Embassies in

Nairobi, Kenya, and Dar es Salaam, Tanzania, accounted for 291 deaths and almost 5,000

injuries in 1998 (US Department of State, 1999). The right-hand column of Table 1 indicates

that approximately 40% of all transnational terrorist attacks are against US interests. This is

especially noteworthy from an externality viewpoint, because relatively few incidents take place

on US soil – i.e., during 1998-2003, only six incidents (including the four skyjackings on 9/11)

occurred in the United States (US Department of State, 2004).

By having relatively secure borders, the United States must rely on foreign governments

to protect US citizens and property while abroad. Terrorists that target US interests – e.g.,

Revolutionary Organization 17 November in Greece (known as 17 November) – may operate

with impunity if the risks to foreigners are of little concern to the local government. This leads

to underdeterrence of terrorism from a multi-country viewpoint (Lee, 1998). Until the summer

of 2002 when a 17 November terrorist injured himself in an attempted bombing, the group had

engaged in over 140 attacks and 22 assassinations since 1973 with no arrests (Wilkinson, 2001,

p. 54). If, instead, much of the threat is to a host country’s interests, then overdeterrence may

5

result as the country does not account for the transference externality of causing the terrorists to

switch their attacks to another less-protected country. In the overdeterrence scenario, each

country engages in a Prisoners’ Dilemma “arms race” to deflect the common terrorist threat to an

alternative venue (Arce and Sandler, 2004; Sandler and Lapan, 1988; Sandler and Siqueira,

2003). Unless such actions decrease the overall level of attacks, each country expends resources

without securing their citizens’ safety, which is particularly relevant when these citizens are

targeted in other countries. This is a real concern for the United States, which has deflected

almost all attacks on its interests to foreign soil.

Data

Except for some annual totals, government-collected data sets have not been made

available to researchers. Mickolus (1982) developed a data set, International Terrorism:

Attributes of Terrorist Events (ITERATE) for 1968-77. This event-based data set was extended

to cover 1978-2003 by Mickolus et al. (2004). ITERATE uses a host of sources for its

information, including the Associated Press, United Press International, Reuters tickers, the

Foreign Broadcast Information Service (FBIS) Daily Reports, and major US newspapers (e.g.,

the Washington Post, New York Times).

ITERATE poses a number of shortcomings that researchers must take into account when

testing theories. By relying on newspaper accounts, ITERATE is better at chronicling the

actions of terrorists (e.g., number of terrorists in a hit squad or terrorists’ actions during

negotiations) than in recording those of the authorities (e.g., how many commandos were used to

free a hostage). In select instances, government strategy is revealed by newspapers and is coded

by ITERATE. Because ITERATE is an events data set, researchers must rely on event counts

rather than on continuous measures of intensity unless casualty counts are used (Enders and

6

Sandler, 2000, 2002). ITERATE picks up newsworthy transnational terrorist incidents, so that

there is some bias, which must be recognized. The bias has worsened since mid-1996 when the

FBIS Daily Reports was no longer available to ITERATE coders.

Despite these difficulties, ITERATE is suited to a wide range of empirical tasks. For

example, it can display trends and cycles for events for forecasting purposes (e.g., Cauley and

Im, 1988; Enders, Parise, and Sandler, 1992). The data have even been used to investigate

terrorist and government bargaining behavior in hostage-taking events – i.e., kidnapping,

skyjackings, and takeover of facilities (barricade and hostage-taking events) – by Atkinson,

Sandler, and Tschirhart (1987). This latter study applied a time-to-failure model, where the

length of an incident is related to choice variables of the adversaries – e.g., sequential release of

hostages, allowing deadlines to pass uneventfully, and the number of hostages secured.

Based on ITERATE data, we display two quarterly time series – all transnational

incidents (All) and bombings – in Figure 1 for 1968-2003. From Figure 1, we can see that

transnational terrorism displays peaks and troughs. Bombings are the favorite mode of operation

of terrorists, accounting for about half of all transnational terrorist incidents on average in any

given year. Additionally, the bombing time series tracks the all-incident series rather well. The

latter half of the 1990s to the present represents a downturn in transnational terrorism due, in

large part, to fewer states sponsoring terrorism in the post-Cold War era (Enders and Sandler,

1999). In Figure 2, the quarterly time series for assassinations and hostage-taking events are

displayed for 1968-2003. Cycles are again apparent. The two time series display far fewer

incidents per quarter than bombings. If terrorists are rational actors, as we suppose, then they

should respond to risk and engage less frequently in those events that are more risky and

logistically complex, such as assassinations and hostage taking (Sandler, Tschirhart, and Cauley,

1983). Assassinations and hostage missions fell just prior to 9/11 and have not returned to their

7

old levels. There are probably three explanations for these drops. First, today’s terrorists are

more interested in greater carnage than an assassinated individual. Second, extra precautions at

airports have reduced skyjackings – one kind of hostage-taking mission. Third, the war on terror

has compromised al-Qaida’s leadership and its ability to execute logistically complex and costly

attacks.

In Figure 3, we display the quarterly percentage of incidents with casualties (i.e., deaths

or injuries) for the 1968-2003 period. This time series is noteworthy because it indicates that

since the early 1990s, transnational terrorist incidents, although way down in number, are more

likely to end in injuries or death for victims. Terrorist experts have documented a change in the

makeup and motivation of the general perpetrators of terrorism since the takeover of the US

Embassy in Tehran in November 1979 (Hoffman, 1998). From the late 1960s until the latter

1980s, transnational terrorism has been primarily motivated by nationalism, separatism, Marxist

ideology, and nihilism (Wilkinson, 1986). In the 1990s, the motivation of terrorism changed

with “the emergence of either obscure, idiosyncratic millennium movements” or religious-based

fundamentalist groups (Hoffman, 1997, p. 2). Since the beginning of 1980, the number of

religious-based groups has increased as a proportion of the active terrorist groups: 2 of 64

groups in 1980, 11 of 48 groups in 1992, 16 of 49 groups in 1994, and 25 of 58 groups in 1995

(Hoffman, 1997, p. 3).

With the earlier prevalence of leftist-based organizations that wanted to win the hearts

and minds of the people, such terrorist groups avoided casualties except of individuals

characterizing the establishment or the “enemy.” Today, fundamentalist terrorist groups

purposely seek out mass casualties, viewing anyone not with them as a legitimate target as 9/11

showed. Enders and Sandler (2000) show that a significant rise in casualties from transnational

incidents can be traced back to the takeover of the US Embassy in Tehran. In recent years, an

8

incident is almost 17 percentage points more likely to result in death or injury compared with the

earlier eras of leftist terrorism.

To highlight the changing patterns of transnational terrorism since 9/11, we display the

proportion of bombing incidents and the proportion of hostage-taking events for 1968-2003 in

Figure 4. Since 9/11, transnational terrorisms have decreased the proportion of hostage events

and greatly increased the proportion of bombings. This pattern is consistent with today’s

fundamentalist terrorists going for greater carnage and avoiding costly and risky hostage events.

Trends and cycles

Judging by the public’s and media’s reaction to 9/11, one might conclude that

international terrorism is on the rise, but the opposite is true as Figure 1 showed. This

misperception may be due to the increasing likelihood of an incident resulting in casualties,

making incidents on average more newsworthy. The standard procedure for ascertaining the

form of a deterministic trend is by fitting a polynomial in time (t), where additional trend terms

(i.e., t, t2, t3) are added until the associated coefficient is no longer statistically significant. For

1968-2003, we investigate trends for six time series extracted from ITERATE: hostage taking,

bombings (of all types), threats and hoaxes (i.e., threatened future incidents or a false claim for a

concurrent incident – a bomb aboard a plane, when there is no bomb), assassinations, incidents

with casualties, and all transnational terrorist incidents. Table 2 indicates the polynomial trend

estimates for these six series (where time = t), all of which are characterized by a nonlinear trend.

The t-ratios associated with the coefficient estimates are indicated in parentheses beneath the

constant and the time trend terms. Five of the six series are represented by a quadratic trend with

a negative coefficient for the squared time term. This characterization reflects the fact that series

tended to rise in the late 1960s and to decline in the late 1990s. Only the threats and hoaxes

9

series is represented by a more complicated cubic trend; nevertheless, this series also displays a

similar inverted U-shaped pattern.

In Table 2, the next-to-the-last column on the right reports the F-statistics and their

“prob” values in brackets, representing the statistical significance of the overall regression.

These significance levels are all zero to three digits, which are strongly supportive of the fitted

nonlinear trend equations. Such fitted trends are not useful for very long-term forecasting,

because there is little reason to believe that the number of incidents will continue to decline.

Instead, the fit of the nonlinear trend cautions against simple statements about a decidedly

upward or downward trend to any form of international terrorism. Such proclamations are

common in the media. The trend analysis suggests that there is persistence in each of the

incident series – high and low levels of terrorism come in waves or cycles. Shocks to any

incident series are not permanent, so that there is a reversion toward a long-run mean.

Cycles in terrorism data have been attributable to a number of factors. Alexander and

Pluchinsky (1992) explain fluctuations in terrorism using demonstration and copycat effects.

Heightened public sensitivity following a successful terrorist attack induces other terrorists to

strike when media reaction is likely to be great. The anthrax attacks following the events of 9/11

appear to correspond to this pattern. Economies of scale in planning terrorist incidents by

terrorist groups or networks may also lead to the bunching of attacks. Cycles may also stem

from the attack-counterattack process between the terrorists and authorities (Faria, 2003). Public

opinion following a spate of attacks can prompt governments’ periodic crackdowns that

temporarily create a lull in transnational terrorism. These downturns are subsequently followed

by countermeasures and recruitment by the terrorists as they prepare for a new offensive. Chalk

(1995) indicates that cycles based on public-opinion pressure swings are in the three to five year

range, insofar as time is required for the public to unite and successfully make their demands on

10

officials to do something – a prediction borne out by time series investigations (Enders and

Sandler, 1999).

In our past work, we find that each type of terrorist series has its own characteristic cycle

that hinges on the logistical complexity of the attack mode. Enders and Sandler (1999) and

Enders, Parise, and Sandler (1992) argue that logistically complex events such as skyjackings,

large suicide car bombings, and assassinations will have longer cycles than less sophisticated

events as the attack-counterattack interaction among adversaries takes longer. Such complex

missions utilize relatively large amounts of resources as compared to small explosive bombings,

threats, and hoaxes. Given their resource constraints, terrorists can more easily gear up for a

campaign dominated by small bombs than one relying on more resource-intensive events.

The theory of Fourier series allows a wide class of functions to be expressed in terms of

sine and cosine components. To uncover the underlying cycles in a series, a researcher must

regress the detrended values of a series on all frequencies in the interval [1, T/2], where T is the

number of observations. The frequency of a series indicates how fast the underlying cycle is

completed – a low (high) frequency implies a long (short) cycle. A graphical depiction the

proportionate variation explained by each frequency (called the periodogram) has large peaks

representing the crucial underlying frequencies. Some series with obvious cycles, like sunspots

or average daily temperatures, will display a periodogram with a single focal frequency. Given

the stochastic behavior of terrorists and the measures applied to curb terrorism, there is unlikely

to be one deterministic frequency that dominates the periodicity for any of the six series. Thus,

we use a different approach than trying to identify one particular frequency. Series with long

periods will have most of their variance explained by the low frequencies, whereas series with

short periods will have most of their variance explained by high frequencies.

In accordance with spectral analysis, we detrended each series using the fitted polynomial

11

trends in Table 2. The last two columns of Table 2 report the total variance of each series and

the proportion of this variance accounted for by the lowest 15 percent of the frequencies. In

particular, we report the proportion of the variance explained by the frequencies in the interval

[1, 0.15 × T/2]. We anticipate that the logistically complex incidents types will have relatively

large amounts of this proportion attributable to the low frequencies. The all-events series has a

large variance of 1256.651 with just 22.2 percent corresponding to the relatively low frequencies.

In marked contrast and in accordance with our priors, the more complex events of assassinations

and those involving casualties have smaller variances with more of this variance (39.3 and 39.1

percent, respectively) attributed to low frequencies. As predicted, threats and hoaxes of

bombings display the greatest evidence of short cycles with approximately 25 percent of their

variance explained by the longest cycles. Hostage taking is in the intermediate range with 31.1

percent of the variance explained by the low frequencies. Some hostage-taking events (e.g.,

skyjackings) are complex, while others (e.g., kidnapping) are not so complex; hence this

intermediate finding for all hostage-taking missions is sensible.

III. Game Theory and Hostage Taking

Despite the events of 9/11, hostage taking may still involve negotiations, because most

such missions involve kidnappings, where the terrorists are not suicidal. Skyjackings in Turkey

and Cuba during March 2003 demonstrate that not all such events include terrorists bent on mass

destruction. Nevertheless, suicide skyjackings and the reactions of desperate passengers to fight

back must be analyzed in the future along with a government’s decision to destroy a hijacked

plane.

To date, there have been seven economic analyses of hostage-taking events – i.e.,

Atkinson, Sandler, and Tschirhart (1987), Lapan and Sandler (1988), Selten (1988), Islam and

12

Shahin (1989), Sandler and Scott (1987), Scott (1991), and Shahin and Islam (1992). The first

three studies stress game-theoretic aspects, while the latter four studies do not. We focus our

remarks around the Lapan and Sandler (1988) study, which is the most general of these three

game-theoretic studies. The question posed by their investigation is whether or not a stated

policy by which a government precommits never to negotiate with hostage takers will have the

intended consequence of keeping terrorists from ever taking hostages. The conventional wisdom

states that if terrorists know ahead of time that they have nothing to gain that they will never

abduct hostages. This belief has become one of the four pillars of US policy with respect to

addressing transnational terrorism – i.e., “make no concessions to terrorists and strike no deals”

(US Department of State, 2001, p. iii).

The underlying game tree is displayed in Figure 5, where the government goes first and

chooses a level of deterrence, D, which then determines the likelihood, θ, of a logistical failure

(i.e., failure to secure hostages). Because deterrence expenditure (equivalent to D) must be paid

by the government in all states of the world, it is analogous to an insurance premium and is,

hence, part of the cost to the government’s payoff, listed above that of the terrorists, at the four

endpoints to this simple game in Figure 5. More risk-averse governments choose higher

deterrence levels and experience less hostage taking at home. Once deterrence is decided, the

terrorists must then choose whether or not to attack. The probability of an attack, Ω, depends on

whether the terrorists’ expected payoffs from a hostage-taking attack are positive. If

* [(1 ) ] [ (1 ) ],c c pm p m< = − θ θ × + − ! then the terrorists are better off attacking even though they

receive –cθ for a logistical failure and (1 )[ (1 ) ]pm p m− θ + − ! for a logistical success. We have c

< c* when the expected payoff from a logistical success, which accounts for negotiation success

or failure, exceeds the expected payoff from a logistical failure. In Figure 5, Ω corresponds to

13

*

0( ) ,

cf c dc∫ where f(c) is the probability density for c which reflects the unknown resolve of the

terrorists.

If hostages are apprehended (i.e., logistical success occurs), then the government must

decide whether or not to capitulate to terrorists’ demands, where p is the likelihood of

government capitulation. The probability of a hostage-taking incident increases with the

likelihood of a logistical success, the probability of a government capitulation (if hostages are

secured), and the benefit of a successful operation, m. In contrast, the likelihood of an attack

decreases with smaller terrorist payoffs associated with logistical and negotiating failures – i.e.,

smaller |c| and .m!

The conventional wisdom for the never-to-capitulate policy hinges on at least four

implicit assumptions: (i) the government’s deterrence is sufficient to stop all attacks; (ii) the

government’s pledge is fully credible to all would-be hostage takers; (iii) the terrorists’ gains

from hostage taking only derives from the fulfillment of their demands; and (iv) there is no

uncertainty concerning the payoffs. Each of these assumptions may not hold in practice.

Deterrence will not stop all attacks if the terrorists perceive that there is a positive expected

payoff from taking hostages – that ( ) ( )1 θ 1 θ 0 .pm p m c− × + − − > ! Even if the government’s

pledge is believed by the terrorists (i.e., p = 0), conditions on m! exists [i.e., ( )1 θ θm c− > −! ], so

that the terrorists can derive a positive gain from securing hostages when getting no concessions.

This may arise when media exposure from holding the hostages is sufficient reward in itself. If,

however, the government’s pledge is not completely credible (i.e., p > 0) owing to past

concessions, then the terrorists’ expected payoff is greater by ( ) ( )1 θ pm pm− − ! than in the case

of a credible governmental pledge, and so an attack becomes more imminent. When a terrorist

group is sufficiently fanatical that it views failure as having a positive payoff (i.e., 0m c> − >! ),

14

then the expected payoff is always positive even when θ = 1 and deterrence is insufficient to

make failure a certainty.

At the endpoints of the game, the payoffs may themselves be uncertain. In this regard,

we focus on the payoffs to government from the four possible outcomes to the game. With no

attack, the government incurs only the cost of deterrence. If an attack ensues but fails (i.e., no

hostages are taken), then the government incurs the cost of a (> 0) in addition to deterrence

expense; if, however, an attack succeeds, then the government experiences an added cost of h for

capitulating and n for not capitulating. The game is more interesting (and realistic) by allowing

either h or n, or both to be uncertain. When, instead, h and n are known beforehand, the

government’s response would be to not capitulate provided that h > n. In the latter case,

conventional wisdom applies. Next, suppose that n is a random variable, which may assume a

large value for some hostages (e.g., a soldier or member of parliament). The government is now

guided by comparing h with the expected value of n, and then choosing the smallest, which may

involve conceding to terrorist demands (e.g., the Israeli release of 1,150 Arab prisoners in a

negotiated swap for three Israeli soldiers in May 1985) when the expected value of n exceeds h.

For the scenario when both h and n are random, the choice then hinges on choosing the

negotiation response that minimizes the expected cost. A precommitment strategy to never

concede to hostage takers’ demands may be time inconsistent when a government later discovers

that the cost of holding firm is too high owing to cost randomness. Although the government has

every intention to fulfill its pledge, its inability to deter all incidents and the terrorists’ ability to

capture the “right” hostage means that a government may, at times, renege on its pledge.

The game representation can be made more realistic by allowing multiple periods and

reputation costs. A government concession in one period to hostage takers makes terrorists raise

their belief about future concessions. As p increases for future periods, more hostages will be

15

taken, so that there is an added cost to conceding in any period. This cost is denoted by R for

loss of reputation, and results in capitulation costs to the government, becoming h + R + D(θ) in

Figure 5. Even when reputation cost is included, conceding may not be eliminated unless h + R

exceeds n for all its realizations. Such a scenario may be achieved through rules – e.g., a

constitutional amendment that imposes sufficiently severe punishment to eliminate any

discretion of government negotiators.

The game can be made still more realistic by including additional sources of uncertainty

in terms of the terrorists’ payoffs. Hostage-taking incidents involve asymmetric information and

uncertainty on the part of both terrorists and governments (Lapan and Sandler, 1993; Overgaard,

1994). The beauty of game theory is that it permits the evaluation of policies while accounting

for uncertainty and strategic interactions of opposing interests. In so doing, easy fixes may not

be so straightforward.

IV. Game Theory and Governmental Responses

We have already discussed the transference externality when terrorists target two or more

countries and each independently chooses a level of deterrence that fails to account for associated

external costs/benefits. External costs are present when deterrence at home displaces the attack

abroad, while external benefits are relevant when deterrence at home either protects foreigners or

reduces the level of attacks globally. Depending on the opposing external effects, and there may

be others not listed, there may result too much or too little deterrence (Sandler and Arce, 2003;

Sandler and Lapan, 1988; Sandler and Siqueira, 2003). The overdeterrence/underdeterrence

problem is heightened when a terrorist network (e.g., al-Qaida) operates in upwards of 60

countries and stages their attacks worldwide (US Department of State, 2001). Underdeterrence

is particularly acute in countries sympathetic to a group’s grievances when the group focuses

16

their attack on foreigners. As the number of potential targets increase, transference efforts may

be especially large. By forming a global network, terrorists limit the effectiveness of countries’

efforts to thwart terrorism as externalities are maximized through countries’ uncoordinated

decisions. Terrorists will naturally seek out the weakest link – i.e., the country with the least

security – for the venue for their next attack. To address these weaknesses, prime targets, such

as the United States, have instituted programs to assist such weakest-link countries in bolstering

their counterterrorist capabilities. In fact, this assistance is another of the four pillars of US

antiterrorism policy (US Department of State, 2001). Ironically, US efforts to induce other

countries to secure their airports and public places make the United States a more attractive

target, as 9/11 sadly demonstrated.

If the terrorist networking advantage is to be countered, then targeted nations must learn

to coordinate their own efforts at counterterrorism. This poses a special problem because nations

resist sacrificing their autonomy over security matters to a supranational collective. With this in

mind, terrorist experts have often called for piecemeal policy where intelligence is shared but not

deterrence decisions (e.g., Kupperman, 1987, p. 577). Such piecemeal responses may be

inadvisable when the strategic incentives are taken into account. Suppose that a terrorist network

targets three countries, each of which are engaged in overdeterrence to transfer the attack abroad.

Further suppose that intelligence allows the targeted countries to better judge the marginal

effectiveness of diverting attacks by revealing the terrorists’ preference for alternative targets.

As these nations acquire this information, they become better adept at diverting attacks, thereby

augmenting the negative transference externality. The net impact of this information sharing

may be to heighten the “transference race” without providing more security, so that the added

deterrence cost simply makes the three countries worse off. This results in a second-best

outcome in which the change in one policy parameter (i.e., increased information sharing) which

17

would, under full cooperation, improve efficiency, may worsen inefficiency when a second

policy (i.e., coordination of deterrence) is not chosen optimally. A similar second-best scenario

may characterize other partial responses – e.g., greater actions to apprehend terrorists without

coordinating efforts to increase punishments. The failure to coordinate retaliatory responses

until 7 October 2001 is another piecemeal response that may have led to inefficiencies. Thus, the

application of game theory again raises policy concerns previously ignored in the literature.

V. Fighting Terrorists and Their Sponsors

Although governments are often confronted by the same terrorists who will target the

countries’ assets and people at home and abroad, countries nevertheless find it difficult to form

coalitions to attack the terrorists on their sponsors directly. Actions to coordinate retaliation

against terrorist camps are typically characterized as a Prisoners’ Dilemma (e.g., Lee, 1988;

Sandler, 1997; Sandler and Arce, 2003) where the dominant strategy, giving the greatest reward

regardless of the other countries’ action, is to do nothing. This representation follows because a

country’s own cost of attacking exceed its perceived benefits. Terrorists locate in out-of-the-way

places that give them a strategic and cost advantage – e.g., al-Qaida located in the caves and

mountains of Afghanistan. This locational advantage raises a retaliator’s costs, thus limiting a

nation’s desire to assume this role. Perceived retaliation cost may also be high relative to

derived benefits, because the retaliator often attracts subsequent terrorist attacks as a protest to its

action (Brophy-Baermann and Conybeare, 1994; Enders and Sandler, 1993). Any retaliatory

action, however, yields purely public benefits – nonexcludable and nonrival – to all potential

target countries. For example, suppose that three countries confront a common terrorist threat.

Further suppose that unilateral action by any nation costs it 6 but confers benefits of 4 on each of

the targeted nations. Thus, the retaliator nets −2, while the other nations receive a free-rider

18

benefit of 4. From a social viewpoint, each retaliator gives more total benefits to society than its

individual costs; however, from the nation’s perspective, costs exceed benefits and it will do

nothing.

Action may, however, occur if some nation is the prime target so that its actions provide

more benefits to it than to other countries. When these nation-specific benefits begin to

outweigh the associated costs, a prime-target nation acts and “privileges” other less-preferred

targets with a free ride (Arce and Sandler, 2004; Sandler, forthcoming). After 9/11, the two

countries – the United States and the United Kingdom – that lost the most were the main two

participants in the attack of the Taliban and al-Qaida in Afghanistan. These targeted countries

had to be seen by their people to be doing something to protect their lives and property against

another devastating attack. Without action, the ruling government would lose legitimacy. This

need to maintain legitimacy in the aftermath of 9/11 raised the benefits of retaliatory action

sufficiently to warrant acting alone if required. This was particularly true for the United States.

A number of lessons in building a coalition to weaken a terrorist threat can be gleaned

from the aftermath of 9/11. Asymmetric targets foster action. If some countries are the choice

targets, then they may be sufficiently motivated to act. In addition, the terrorists encourage this

coalition building by concentrating their attacks on relatively few nations and escalating the

magnitude of spectacular attacks. If they were to spread their attacks more evenly over nations,

no nation may derive sufficient benefits to privilege the rest of the group with a free ride from a

retaliatory action. Terrorists will concentrate their attacks to satisfy a constituency. Terrorists’

desire to capture the attention of the media means that they must kill lots of people with some

attacks. As death tolls mount, nations become motivated to act as benefits start to outweigh

costs.

19

VI. Rational-Choice Representations of Terrorists

Beginning with the Landes (1978) study of skyjackings, economists characterize

terrorists as rational actors who maximize expected utility or net payoffs subject to constraints.

Arguments in these constraints may consist of terrorists’ resource endowments or actions taken

by the authorities to thwart terrorism. In the Landes (1978) model, potential hijackers engage in

a hijacking provided that the associated expected utility exceeds other nonskyjacking means of

furthering their goals. Based on this utility comparison, Landes (1978) specifies an offense (i.e.,

number of skyjackings) function, whose independent variables include the hijackers’ subjective

estimate of the likelihood of apprehension, their estimate of the conditional probability of

imprisonment (if apprehended), and other actions by the authorities (e.g., the presence of US sky

marshals on flights). Using data on US hijackings for 1961-1976, Landes demonstrates that

greater prison sentences and enhanced likelihood of apprehension are significant deterrents. He

also indicates that the installation of metal detectors on 5 January 1973 led to between 41 and 50

fewer hijackings in the United States during 1973-1976.

In a subsequent analysis, Enders and Sandler (1993) examine a wide range of policy

interventions, including metal detectors, fortification of embassies, retaliatory raids, and the

Reagan “get-tough-on-terrorists” laws. The theoretical model for the terrorists that underlies

their study is analogous to the consumer-choice model. Terrorists maximize utility or expected

utility derived from the consumption of basic commodities, produced from terrorist and

nonterrorist activities. For example, al-Qaida terrorists may gain utility from a reduced political

resolve on the part of the United States to remain in the Persian Gulf as Americans lose their

lives in terrorist attacks (e.g., the destruction of the Al Khubar Towers housing US airmen and

others on 25 June 1996 near Dhahran, Saudi Arabia). This weakening of US resolve is the basic

commodity that can be produced with a number of alternative attack modes. Substitution

20

possibilities among terrorist tactics arise when alternative modes of operations produce the same

basic commodities (e.g., political instability, media attention) in varying amounts. Substitution

is enhanced when attack modes possess closely related outcomes and are logistically similar.

This is clearly the case for hijackings and other kinds of hostage events. Complementarity

results when combinations of attack modes are required to produce one or more basic

commodities. When threats follow real attacks, both actions assume a heightened effectiveness

and are thus complementary.

To produce these basic commodities, a terrorist group must choose between nonterrorist

and terrorist activities, while being constrained by resources. In the latter choice, terrorists must

further choose between different modes of terrorist attacks based on the perceived “prices”

associated with alternative operations. Choices are many and include the intended lethality of

the act, its country of location, and whom or what to target. The expenditure on any activity

consists of its per-unit price times the activity’s level. Each mode of operation has a per-unit

price that includes the value of time, resources, and anticipated risk to accomplish the act. The

securing and maintenance of a kidnapping victim in a hidden location is logistically more

complex and requires more resources than leaving a small bomb in a trash bin in a railroad

station, so that the former has a greater per-unit price. In choosing a venue, the price differs

based on security measures taken by the authorities; a country with more porous borders will be

the staging ground for attacks against targets from other more secure countries. The prices

confronting the terrorists for each tactic are determined, in large part, by the government’s

allocation of resources to thwart various acts of terrorism. If, for example, embassies are

fortified, then attacks against embassy personnel and property within the mission’s ground

become more costly for the terrorists – i.e., there is a rise in the relative price of such attacks.

Similarly, metal detectors in airports increase the relative price of skyjackings as compared with

21

other kinds of terrorist acts, including kidnappings.

Government policies aimed at a single type of terrorist event (e.g., the installation of

bomb-sniffing equipment in airports) adversely changes its relative price and results in a

substitution into now less expense modes of attack. Thus, Landes’ (1978) measure of the

success of metal detectors, in terms of fewer skyjackings, does not go far enough, because the

application of this technology may have induced a large number of other kinds of events.

Similarly, to judge the success of embassy fortification, a researcher must also examine

assassinations and other attacks against embassy personnel, once outside of the compound.

To account for these substitutions, Enders and Sandler (1993) apply vector autoregression

(VAR) analysis to allow for the potential interactions among various terrorist time series (e.g.,

skyjackings and other hostage events) in response to government policies. They find that metal

detectors decreased skyjackings and threats, but increased other kinds of hostage incidents, not

protected by detectors. The trade-off between events were about one for one (also see Enders,

Sandler, and Cauley, 1990; Im, Cauley, and Sandler, 1987). Both substitutions and

complementarities are uncovered. Fortification of US embassies and missions reduced attacks

against such installations, but were tied to a disturbing increase in assassinations of officials and

military personnel outside of protected compounds. In addition, Enders and Sandler (1993)

establish that the US retaliatory raid against Libya on April 1986 (for its suspected involvement

in La Belle Discothèque in West Berlin on 4 April 1986) was associated with an immediate

increase in terrorist attacks against US and UK interests. This increase was shortly followed by a

temporary lull as terrorists built up depleted resources. Apparently, the raid caused terrorists to

intertemporally substitute attacks planned for the future into the present to protest the retaliation.

Within a relatively few quarters, terrorist attacks resumed the same mean number of events.

There are a number of ways to institute antiterrorist policies that address these likely

22

substitutions and complementarities. First, the government must make the terrorists substitute

into less harmful events. Second, the government must go after the terrorists’ resource

endowment (i.e., its finances, its leadership, and its membership) if an overall decrease in

terrorism is to follow. Efforts to infiltrate groups or to freeze terrorists’ finances have this

consequence. Third, the government must simultaneously target a wide range of terrorist attack

modes, so that the overall rise in the prices of terrorist attacks becomes analogous to a decrease

in resources. Success in raising the price of all modes of terrorist attacks would induce terrorists

to shift into legal protests and other nonterrorist actions to air grievances. Based on the above,

we can conclude that a reliance on technological barriers merely causes a substitution into other

attack modes in the short run. In the long term, terrorists will develop ingenuous

countermeasures (i.e., plastic guns, bottles of flammable liquid) to circumvent the technology.

This terrorist response is an innovation effect, which gives rise to a dynamic strategic interaction.

Consequently, authorities must be ever vigilant to improve the technology by anticipating

terrorists’ ways of circumventing such barriers. This vigilance must lead to periodic upgrades in

the technology prior to the terrorists exposing the technology’s weakness through a successful

attack. Unfortunately, authorities have been reactive by only responding after a technological

barrier’s weakness has been exploited, so that the public remains vulnerable until a new

technological fix is found and installed.

Other kinds of substitutions

Substitution effects abound in the study of terrorism and involve not only actions of the

terrorists, as described above, but also actions of the targets. For targets, the economic literature

addresses two kinds of substitutions. First, there are studies that examine the tourists’ choice of

vacation spot based on the perceived threat of terrorism and other costs. An alteration in travel

23

risks, arising from increased terrorist incidents in a country, raises the price of a holiday there in

comparison to other vacation venues, not confronted with terrorism. In a study of Spain, Enders

and Sandler (1991) employ VAR analysis to demonstrate that a typical transnational terrorist

incident is estimated as scaring away just over 140,000 tourists when all monthly impacts are

combined. Companion studies by Enders, Sandler, and Parise (1992) and Drakos and Kutan

(2003) establish and quantify terrorism-induced substitutions in tourism for Greece, Austria,

Italy, Turkey, Israel, and other terrorism-ridden countries. Countries, like Greece, that have not

addressed transnational terrorist attacks directed at foreigners lose significant foreign-exchange

earnings as a consequence. The cost of terrorism comes in many forms.

Second, target-based substitutions involve foreign direct investment (FDI). Investors

decide where to invest based on their perceived economic risks, political risks, and monetary

returns. An increase in transnational terrorism directed at FDI (e.g., attacks by Euskadi ta

Askatasuna (ETA) in the Basque region of Spain) is sure to divert such investment. Enders and

Sandler (1996) show that an “average” year’s worth of terrorism reduced net FDI in Spain by

13.5% annually, and it reduced net FDI in Greece by 11.9% annually. These reductions

translated into declines in real net FDI of $488.9 million and $383.5 million, respectively, or the

equivalent of 7.6% and 34.8% of annual gross fixed capital formation in Spain and Greece.

Transnational terrorism displayed significant economic cost, not counting the billions spent on

barriers and deterrence. In a more recent study of the Basque region, Abadie and Gardeazal

(2003) establish that terrorism reduced per capita GDP by ten percentage points in relation to the

terrorism-free synthetic control region.

Studies of risks

After 9/11, there is greater interest in applying economic methods to study antiterrorism

24

policy choices. One useful line of study examines interdependent security (IDS) risks where the

effectiveness of the protective actions by one agent is highly dependent on those of other agents

(Heal and Kunreuther, 2004; Kunreuther and Heal, 2003). If, e.g., luggage in the cargo hold of a

commercial plane is not rechecked during transfer, then airlines’ incentives to invest in screening

their own luggage are diminished because the safety of the flight is dependent on exogenous

factors. These authors show that a variety of game forms may apply. They also make policy

recommendations to create tipping and cascading equilibriums, whereby firms become more

motivated to augment their own security as transferred luggage of key carriers (i.e., those with

the greatest number of feeder flights) become safely screened. To achieve these equilibriums,

government must target airline subsidies to key carriers. There are many IDS concerns

associated with protective measures against terrorist attacks in a globalized world.

Economists are also interested in the insurance implications of terrorism, since extreme

events such as 9/11 are very costly – about $90 billion in losses (Kunreuther, Michel-Kerjan, and

Porter, 2003) – and virtually impossible to predict. Following 9/11, most insurers dropped their

terrorism coverage or made it prohibitively expensive. Terrorism coverage raises public policy

issues – e.g., should the government provide coverage and, if so, how should public and private

coverage interface? Clearly, economics can be fruitfully applied to such problems.

VII. Toward a Benefit-Cost Analysis of Terrorist-Thwarting Policies

As a future research project, economists should assess the benefits and cost of specific

policies to thwart terrorism. Such an exercise has not been adequately done and poses some real

challenges. Costs are fairly straightforward since figures are available in, say, the United States

as to what is paid to fortify embassies and missions, or to guard US airports. Consider the cost

25

associated with airport security. The value of lost time as travelers are screened must be added

to the cost of guards and screening equipment.

On the benefit side, calculations are less transparent. One way to estimate a portion of

this benefit would be to compute the reduced loss of life attributable to airport security measures

– i.e., fewer people killed in skyjackings. If the net number of such lives saved, after adjusting

for substitutions into other life-threatening terrorist actions, can be measured, then the average

“value of a statistical life” can be applied to translate these lives into a monetary figure. To this

figure, a researcher must also compute and add the reduced losses in property values (i.e., from

destroyed planes) attributable to the fewer hijackings. In addition, a portion of the value of net

air travel revenues must be considered as a benefit arising from a heightened sense of security

stemming from security upgrades. The events of 9/11 clearly underscore that there is a cost to a

breach in airport security as the public loses its confidence in air travel. Any of these

components are fraught with measurement difficulties, because there may be intervening factors

at work – e.g., air travel was already in a slump prior to 9/11.

Every policy to thwart terrorism would entail its own stream of benefits and costs.

Invariably, the benefit calculations are problematic. The US-led retaliation against al-Qaida and

the Taliban in Afghanistan has well-defined costs in terms of deployed soldiers, ordnance,

diplomacy, and side payments to “allies.” But the true savings or benefits from fewer future acts

of terrorism, in terms of lives and property saved, is so much more difficult to calculate as they

require counterfactual information. Time-series techniques, engineered by Enders and Sandler

(1991, 1996) to measure losses to tourism or to FDI from terrorism, can be utilized following the

retaliation to roughly estimate the decline in terrorist incidents and their economic value.

VIII. Concluding Remarks

26

Although economic methods have enlightened the public on a number of issues

concerning transnational terrorism, there are many other issues to analyze. For instance, there is

a need for applying more dynamic game methods – i.e., differential game theory – if the waxing

and waning of terrorist organizations (e.g., Red Brigades and Red Army Faction) are to be

understood. Clearly, past successes and failures determine the size of these groups over time.

The terrorists try to increase their organization’s size through enhanced resources, successful

operations, and recruitment, while the government tries to limit the group’s size through raids,

intelligence, group infiltration, and actions to thwart successes. This dynamic strategic

interaction needs to be modeled and empirically tested. In addition, researchers must better

assess the role of information and intelligence on behalf of the terrorists and the authorities.

Given how little governments really know about the strength of the terrorists that they confront –

e.g., the US government had almost no clue about the size of al-Qaida (US Department of State,

2001, p. 69) prior to 9/11 – asymmetric information characterizes efforts to thwart terrorism.

Similarly, the terrorists are ill-informed about the resolve of the government and the amount of

resources that it is willing to assign to curbing terrorism. Additionally, there is a need to model

terrorist campaigns – i.e., the choice of the sequence and composition of attacks used by

terrorists. As researchers better understand these choices, more effective policy responses can be

devised that adjust for the strategic interaction. Another unresearched issue is the optimal choice

between proactive and defensive antiterrorism policies. Arce and Sandler (2004) show that

governments have a proclivity to favor defensive policies when confronting transnational

terrorism, but these authors do not indicate the optimal mix.

27

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Study of the Basque Country,” American Economic Review, 93, 113−132.

Alexander, Yonah and Dennis Pluchinsky. 1992. Europe’s Red Terrorists: The Fighting

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Enders, Walter and Todd Sandler. 1991. “Causality Between Transnational Terrorism and

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28

_____. 1993. “The Effectiveness of Anti-Terrorism Policies: Vector-Autoregression

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_____. 1996. “Terrorism and Foreign Direct Investment in Spain and Greece,” Kyklos, 49,

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_____. 2000. “Is Transnational Terrorism Becoming More Threatening,” Journal of Conflict

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_____. 2002. “Patterns of Transnational Terrorism 1970-99: Alternative Time Series

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Enders, Walter, Gerald F. Parise, and Todd Sandler. 1992. “A Time-Series Analysis of

Transnational Terrorism: Trends and Cycles,” Defence Economics, 3, 305−320.

Enders, Walter, Todd Sandler, and Jon Cauley. 1990. “UN Conventions, Technology and

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Heal, Geoffrey and Howard Kunreuther. 2004. “IDS Models and Airline Security,” New York,

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Hoffman, Bruce. 1997. “The Confluence of International and Domestic Trends in Terrorism,”

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_____. 1998. Inside Terrorism. New York: Columbia Univ. Press.

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Question,” American Economic Association Papers and Proceedings, 78, 16−20.

_____. 1993. “Terrorism and Signalling,” European Journal of Political Economy, 9, 383−397.

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Terrorists’ Choice of Targets,” Synthèse, 76, 245-261.

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Sandler, Todd and Kevin Siqueira. 2003. “Global Terrorism: Deterrence versus Preemption,”

Los Angeles: School of International Relations, University of Southern California

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Transnational Terrorism,” American Political Science Review, 77, 36−54.

Scott, John L. 1991. “Reputation Building in Hostage Incidents,” Defence Economics, 2,

209−218.

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Models of Strategic Rationality, Boston: Kluwer Academic, pp. 77−93.

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Alternative Approach,” Defence Economics, 3, 321−7.

United States Department of State, Various years. Patterns of Global Terrorism. Washington,

31

DC: US Department of State.

Wilkinson, Paul. 1986. Terrorism and the Liberal State, rev. ed. London: Macmillan.

_____. 2001. Terrorism versus Democracy: The Liberal State Response. London: Frank Cass.

TABLE 1: Transnational Terrorism: Events 1968-2003

Year Number of Events Deaths Wounded Attacks on US Interests 2003 208 625 3,646 84 2002 202 725 2,013 77 2001 355 3,296 2,283 219 2000 426 405 791 200

1999 395 233 706 169 1998 274 741 5,952 111

1997 304 221 693 123 1996 296 314 2,652 73

1995 440 163 6,291 90

1994 322 314 663 66 1993 431 109 1,393 88

1992 363 93 636 142 1991 565 102 233 308 1990 437 200 675 197

1989 375 193 397 193

1988 605 407 1,131 185 1987 665 612 2,272 149

1986 612 604 1,717 204 1985 635 825 1,217 170

1984 565 312 967 133 1983 497 637 1,267 199

1982 487 128 755 208 1981 489 168 804 159

1980 499 507 1,062 169 1979 434 697 542 157

1978 530 435 629 215

1977 419 230 404 158 1976 457 409 806 164 1975 382 266 516 139

1974 394 311 879 151

1973 345 121 199 152 1972 558 151 390 177

1971 264 36 225 190 1970 309 127 209 202

1969 193 56 190 110 1968 125 34 207 57 Source: US Department of State, Patterns of Global Terrorism (1988-2003) and tables provided to Todd Sandler in 1988 by the US Department of State, Office of the Ambassador at Large for Counterterrorism.

0

50

100

150

200

250

300

350

1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Inci

den

ts p

er Q

uar

ter

All

Bombings

FIGURE 1: All Incidents and Bombings, 1968-2003

0

5

10

15

20

25

30

35

1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Inci

den

ts p

er Q

uar

ter

Assassinations

Hostage Incidents

FIGURE 2: Assassinations and Hostage Incidents, 1968-2003

0

10

20

30

40

50

60

70

80

90

100

1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Per

cen

t

FIGURE 3: Proportion of Incidents with Casualities, 1968-2003

0

10

20

30

40

50

60

70

80

90

100

1968 1970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000 2002

Per

cen

t

Hostage IncidentsBombings

FIGURE 4: Proportions of Bombings and Hostage Incidents, 1968-2003

TABLE 2: Trend and Other Statistical Properties of Transnational Terrorist Incidents, 1968-2003

Incident Type Constanta Time (Time)2 (Time)3 F–statb Variance Percentc

Hostage taking 2.916 0.244 –0.002 13.83 31.837 0.311 (2.009) (5.120) (–4.839) [0.000] Bombings 37.710 0.954 –0.008 30.296 624.310 0.241 (5.916) (4.637) (–6.040) [0.000] Threats & Hoaxes 6.024 –0.061 0.006 –0.000 15.011 79.431 0.263 (1.940) (–0.326) (1.811) (–2.854) [0.000] Assassinations –1.069 0.379 –0.003 65.367 18.126 0.393 (–0.976 (10.716) (–11.371) [0.000] Casualties 5.112 0.810 –0.006 58.444 86.454 0.391 (2.138) (10.494) (–10.811) [0.000] All Events 43.075 2.293 –0.018 44.240 1256.651 0.222 (4.725) (7.790) (–8.855) [0.000] a t-ratios are in parentheses. b Prob values are in brackets under the F-statistics. c Proportion of variance of the detrended, fitted-polynomial series that is accounted for by the lowest

15 percent of the frequencies (i.e., the longest cycles).

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10.1177/0022002704272863ARTICLEJOURNAL OF CONFLICT RESOLUTIONArce M., Sandler / COUNTERTERRORISM

Counterterrorism

A GAME-THEORETIC ANALYSIS

DANIEL G. ARCE M.Department of Economics

Rhodes College

TODD SANDLERSchool of International Relations

University of Southern California

This article establishes the prevalence of deterrence over preemption when targeted governments canchoose between either policies or employ both. There is a similar proclivity to favor defensive counter-terrorist measures over proactive policies. Unfortunately, this predisposition results in an equilibrium withsocially inferior payoffs when compared with proactive responses. Proactive policies tend to provide purelypublic benefits to all potential targets and are usually undersupplied, whereas defensive policies tend to yielda strong share of provider-specific benefits and are often oversupplied. When terrorists direct a dispropor-tionate number of attacks at one government, its reliance on defensive measures can disappear. Ironically,terrorists can assist governments in addressing coordination dilemmas associated with some antiterroristpolicies by targeting some countries more often than others.

Keywords: counterterrorism; deterrence; preemption; terrorism; noncooperative game; Nashequilibrium

Terrorism is the premeditated use or threat of use of violence by individuals orsubnational groups to obtain political, religious, or ideological objectives throughintimidation of a large audience usually beyond that of the immediate victims.1 Bysimulating randomness, terrorists create an atmosphere of fear where everyone feelsvulnerable, thereby extending their sphere of influence as far as possible. Suicide mis-sions can heighten this air of anxiety and place greater pressures on governments tocapitulate to terrorist demands owing to the greater casualties, on average, associatedwith such events—thirteen deaths per suicide attack compared with less than one

183

AUTHORS’NOTE: Daniel G. Arce M. is the Robert D. McCallum Distinguished Professor of Econom-ics and Business at Rhodes College. Todd Sandler is the Robert R. and Katheryn A. Dockson Professor ofInternational Relations and Economics at the University of Southern California. The authors have profitedfrom the comments of two anonymous reviewers.

JOURNAL OF CONFLICT RESOLUTION, Vol. 49 No. 2, April 2005 183-200DOI: 10.1177/0022002704272863© 2005 Sage Publications

1. This definition combines essential features of definitions in the literature; see Hoffman (1998,chap. 1) and Schmid and Jongman (1988).

death per nonsuicide attack (Pape 2003). In this regards, the events of September 11,2001 (henceforth 9/11), made the public and governments painfully aware of the risksposed by the new breed of suicide and fundamentalist terrorists bent on maximal casu-alties. Following 9/11, governments have spent tens of billions of dollars on a varietyof antiterrorist policies. Since 2002, the budget supporting the newly created U.S.Department of Homeland Security grew by more than 60 percent to $36.2 billion forfiscal year 2004 (Office of Management and Budget 2003).

Counterterrorist policies may involve taking direct actions against terrorists or theirsponsors. Such proactive policies may include destroying terrorist training camps,retaliating against a state sponsor, infiltrating terrorist groups, gathering intelligence,or freezing terrorist assets. Preemption is the quintessential proactive policy in whichterrorists and their assets are attacked to curb subsequent terrorist campaigns. Moredefensive or passive counterterrorist measures include erecting technological barriers(e.g., metal detectors or bomb-sniffing equipment at airports), fortifying potential tar-gets, and securing borders. These defensive policies are intended to deter an attack byeither making success more difficult or increasing the likely negative consequences tothe perpetrator.2 Efforts to deter terrorist events often displace the attack to other ven-ues, modes of attack (e.g., from a skyjacking to a kidnapping), countries, or regions,where targets are relatively softer (Drakos and Kutan 2003; Enders and Sandler 1993;Sandler and Enders 2004; Sandler 2003).

By protecting all potential targets, preemption provides public benefits; in contrast,by deflecting the attack to relatively less-guarded targets, deterrence and/or defensivemeasures impose public costs. The irony arises because nations have a pronouncedproclivity to resort to deterrence rather than preemption despite the greater social gainsusually associated with the latter. The primary purpose of this article is to apply ele-mentary game theory to explain this tendency. Unlike a recent paper (Sandler andSiqueira 2003) that examines deterrence and preemption in isolation, the current exer-cise allows governments to choose between these policies or to employ them together.Although we allow alternative game forms to characterize both policies, deterrence isshown to have an unfortunate dominance over preemption, consistent with what isobserved in the real world. A second major purpose is to investigate the game structureof other defensive and proactive counterterrorist policies. A variety of game forms arerelevant, not only among different antiterrorist measures but also for the same measureunder alternative scenarios. The analysis also identifies the circumstances whenpreemption may result owing to payoff asymmetries between targets or policies.

Game theory is an appropriate tool for investigating counterterrorism because itcaptures the strategic interactions between terrorists and targeted governments whosechoices are interdependent.3 In so doing, game theory permits a rich range of strategic

184 JOURNAL OF CONFLICT RESOLUTION

2. Our use of deterrence follows that in the terrorist literature (Sandler and Enders 2004), in whichdeterrence limits or restrains a particular action (e.g., metal detectors made hijackings more difficult andgreatly reduced attempted hijackings). We do not use deterrence in the cold war sense of inhibiting an actionnecessarily through a threatened punishment.

3. Past articles have applied game theory to evaluate hostage negotiations (Atkinson, Sandler, andTschirhart 1987; Lapan and Sandler 1988; Sandler, Tschirhart, and Cauley 1983; Selten 1988), terrorists’choice of targets (Sandler and Arce M. 2003; Sandler and Lapan 1988), and terrorists’allocation of resourcesunder asymmetric information (Lapan and Sandler 1993; Overgaard 1994).

environments and policy choices in keeping with modern-day terrorist threats. More-over, game theory assumes that each player is rational and must second-guess itsadversaries; thus, a government must place itself in its opponents’ position beforedeciding the appropriate strategic response. To decide the best strategy, a governmentmust anticipate not only the actions of terrorists but also those of other governmentsthat might work at cross-purposes or take advantage of another government’s action.In today’s world of networked terrorists where the threat is global, accounting forthese reactions of other governments is essential to the formulation of effectivecounterterrorist policies.

PREEMPTION OR DETERRENCE: SPECIFIC EXAMPLE

Any strategic analysis of the choice between preemption or deterrence mustaccount for preemption’s purely public benefits to all potential targets: direct actionagainst terrorists or their sponsors makes everyone safer.4 In contrast, a strategic repre-sentation of deterrence must account for the costs imposed on the nation that deters anattack as well as the public costs incurred by others from the increased likelihood ofhaving an attack deflected to their soil. The deterrer must not only expend resources tomake its territory a less attractive venue but also suffers costs from having its people orproperty targeted abroad. Deterrence spending is analogous to an insurance policy thatis paid regardless of the outcome, but in bad states (when an attack ensues), deterrencecurbs the expected damage at home, which is the deterrer’s private benefit.

Arce M., Sandler / COUNTERTERRORISM 185

EU Preempt Status quo Deter

Preempt 2,2 2,4 6,6

Status quo 4, 2 0,0 4,2 US

Deter 6, 6 2, 4 Nash

2, 2

− −

−−

−−−−

Figure 1: Deterrence versus Preemption: Symmetric Benefits and CostsNOTE: EU = European Union.

4. Everyone is safer insofar as a weakened terrorist threat means that all potential targets have less tofear. There is, however, a qualification: heavy-handed preemption may create anger and new recruits,thereby jointly producing a public bad (Rosendorff and Sandler 2004). The analysis here holds, provided thatthe pure public benefit from preemption-induced threat reduction outweighs any associated public costsfrom new recruits to the terrorist cause. Inclusion of recruitment costs would reinforce our findings thatdeterrence is favored to preemption.

To illustrate the dilemma posed by counterterrorist policies, we use a specificexample in which two targets—the United States and the European Union (EU)—must choose preemption or deterrence. Both players can also do nothing, denoted bythe status quo. The passive player is the terrorist group that is bent on attacking theweaker of the two targets or flipping a coin if neither is weaker. For illustration, eachpreemptive action provides a public benefit of 4 for the United States and EU at a pri-vate cost of 6 to the preemptor. In Figure 1, the preemption game is captured by thenorthwest 2 × 2 bold-bordered matrix, in which each government can preempt ormaintain the status quo. If, say, the United States preempts, then it gains a net benefit of–2 (= 4 – 6) while conferring a free-rider gain of 4 on the EU. These payoffs arereversed if the roles are switched. When both governments preempt, each receives anet gain of 2 as its preemption expense of 6 is deducted from gains of 8 (= 4 × 2)derived from both targets’ efforts. Neither country acting gives zero net benefits toboth players. This 2 × 2 preemption game is a prisoner’s dilemma (PD) with inaction asthe dominant strategy since 4 > 2 and 0 > −2. The resulting Nash equilibrium is mutualstatus quo—(Status Quo, Status Quo)—from which neither target would unilaterallymove. This equilibrium is Pareto dominated by mutual action (preemption).

Next, we turn to the 2 × 2 deterrence game displayed by the southeast 2 × 2 bold-bordered matrix in Figure 1, in which the players have two strategies: do nothing ordeter an attack at home. In this stylized symmetric example, we assume that deterrenceis associated with a public cost of 4 experienced by the deterrer and the other country.The deterrer’s costs arise from the action and its potential losses from a deflectedattack (say, from its citizens residing abroad), while the nondeterrer suffers the deflec-tion costs of being the target of choice. A deterrer is motivated by private gains of 6prior to costs being deducted. If, say, the EU deters alone, then it nets 2 (= 6 – 4), whilethe United States loses 4 by becoming the target of choice. Payoffs are switched whenthe United States deters alone. Net benefits are zero if neither acts, while each receivesa net payoff of –2 [= 6 – (4 × 2)] from mutual deterrence as costs of 8 are deducted froma private gain of 6. Once again, a PD game results. Now, the dominant strategy is action(Deter) rather than inaction, and the Nash equilibrium is (Deter, Deter).

The real issue is which counterterrorism policy dominates if each target can chooseeither policy or the status quo. This can be addressed by consulting the 3 × 3 matrix ofFigure 1 with its two embedded PD games. If one player deters and the other preempts,then the deterrer gains 6 (= 6 + 4 – 4), while the preemptor receives –6 (= 4 – 6 – 4). Thedeterrer gets a private benefit of 6 from its deterrence and a public benefit of 4 from theother player’s preemption but must cover its deterrence cost of 4. In contrast, the solepreemptor suffers a cost of 4 from the other player’s deterrence and a cost of 6 from itsown efforts but only receives a private benefit of 4 from preempting. The other payoffsin the matrix remain as before.

The dominant strategy is for both players to deter since the payoffs are higher thanthe corresponding payoffs associated with the other two strategies. As both targetsexercise their dominant strategy, the Nash equilibrium of (Deter, Deter) follows. Thisoutcome is like a double PD game in which the smallest summed payoff results—every other strategic combination is socially preferred from an aggregate payoff view-point. Of the two Nash equilibria of the embedded and overlapping 2 × 2 PD games,

186 JOURNAL OF CONFLICT RESOLUTION

the Pareto-inferior equilibrium reigns. In the 3 × 3 game, the sum of the payoffsdecreases when moving down the columns, but the strategy in the bottom row domi-nates; similarly, the sums of the payoffs decrease when moving rightward along a row,but the strategy in the right-most column dominates. This outcome is rather fascinatingand disturbing; it implies that deterrence wins out over preemption when payoffs mir-ror one another in that the public versus private roles of benefits and costs areswitched.5 There is an implied resilience to deterrence in this stylized example. Is thisexample reflective of more generalized situations where benefits and costs do notmerely switch roles in terms of values for the two policies, or alternative game formsapply, or players are asymmetric? We now analyze more general representations toaddress this question.

GENERALIZED DETERRENCE-PREEMPTION ANALYSIS

In this section, the generalized game no longer assumes that the public costs ofdeterrence equal the public benefits of preemption or that the private benefits of deter-rence equal the private costs of preemption. In terms of notation, B denotes the publicbenefits of preemption, c represents the private costs of preemption; C denotes thepublic costs of deterrence, and b represents the private benefits of deterrence. The(re)actions of terrorists in this model are suppressed because they are consistent withthe public aspects of deterrence and preemption produced in conjunction with terroristactivity, as explicitly derived by Sandler and Siqueira (2003) and Sandler and Arce(2003).6 The generalized game is in Figure 2, where the overlapping 2 × 2 preemptionand deterrence games are again highlighted by boldfaced borders. In the northwest 2 ×2 preemption game, the pure publicness of preemption is a key feature. If there is a solepreemptor, then that player affords a free ride worth B to the other nation and receives a

Arce M., Sandler / COUNTERTERRORISM 187

EU Preempt Status quo Deter

Preempt

2 ,2B c B c

,B−c B ,B c C B b C+

Status quo ,B B c 0,0 ,C b C US

Deter

,B b C B c C+

,b C C

Nash

2 , 2b C b C −−−−

−−−

−−−

−−−

Figure 2: Generalized Deterrence-Preemption Game, 2B > c > B and 2C > b > CNOTE: EU = European Union.

5. With an alternative solution concept, such as nonmyopic equilibria in the “theory of moves”(Brams 1994), the Pareto-efficient solution might be achieved. This investigation is left to our future work.

6. Heal and Kunreuther (2005 [this issue]) make a similar assumption in a study that focused only ondefensive policies.

net benefit of B – c. We initially assume that the costs of preemption exceed the associ-ated benefits so that c > B. If both countries preempt, then each receives 2B – c as costsare deducted from the benefits derived from the combined actions of the two govern-ments (i.e., B from each preemption for a total of 2B). To ensure that a PD game results,we must assume that B > 2B – c, which again implies that c > B. Also, we assume thatthe payoff from mutual preemption is greater than that from mutual inaction so that 2B– c > 0.7 Taken together, the inequality 2B > c > B is sufficient to ensure that a PD gamecharacterizes the northwest 2 × 2 preemption game. The dominant strategy for thisembedded game is to do nothing, which results in the Nash inactivity equilibrium witha payoff of (0, 0). The southeast 2 × 2 bold-bordered matrix indicates the deterrencegame, in which payoffs are computed as before. To ensure a PD game, we assume that2C > b > C. The dominant strategy of this embedded game is to deter, and the Nashequilibrium is mutual deterrence.

For the 3 × 3 game, there are also the two strategic combinations in which oneplayer deters and the other preempts. The deterrer then receives B + b – C from theassociated public gain from preempting, B, and the private gain from deterring, b,minus the public deterrence costs, C. The preemptor gains the public preemption ben-efit but must cover the private costs of preempting and the public costs of its counter-part’s deterrence for a payoff of B – c – C. The two sets of inequalities ensure that thedominant strategy is to deter for both governments so that the Nash equilibrium ofmutual deterrence results, which is Pareto inferior to doing nothing or mutual preemp-tion. Thus, this first generalization of the game, denoted as the baseline game, does noteliminate the persistence of deterrence.8

Because targeted countries may face the same situation in each period, we examinewhen mutual preemption can be supported in an infinitely repeated game with a dis-count factor of δ. Suppose that a grim-trigger strategy is employed in which a playerbegins by preempting but will henceforth switch to deterrence if the other player everfails to preempt, so that a “deterrence trigger” is employed. Preemption is then sus-tained if 9

188 JOURNAL OF CONFLICT RESOLUTION

7. This last inequality also rules out any oscillatory supergame equilibrium in which alternatingbetween the off-diagonal cells does better than mutual preemption. This means that 2B – c > .5B + .5(B – c),which implies that 2B > c.

8. The same bias against proactive policy and reliance on defensive measures is not anticipated fordomestic antiterrorist policy because the central government can internalize the public benefit fromproactive responses. A weakened domestic terrorist group benefits just the host country, whose taxes cansupport a proactive campaign. Similarly, a central government can balance the external deflection costs fromdefensive actions. For transnational terrorism, there is no supranational government that can internalizeexternal benefits and costs from proactive and defensive policies, respectively.

9. To derive this inequality, we must assume that the present value of the perpetual gain from mutualpreemption, (2B – c)/(1 – δ), exceeds the gain from deterring in the first period and then suffering the punish-ment payoff of mutual deterrence thereafter. This implies that

2

12 2 2B c

B b C b C b C−

−≥ + − + − + − +

δδ δ( ) ( ) ... ,

or

2

12

2

1

B cB b C b C

b C−−

≥ + − − − + −−δ δ

( )( )

,

from which equation (1) follows with some algebra.

δ ≥ [(b – C) – (B – c)]/(B + C). (1)

Based on equation (1), the smaller is the incentive for unilateral deterrence, b – C, andthe smaller is the net cost of unilateral preemption, B – c, the more likely it is to sustainmutual preemption through a threat-based trigger. This inequality also holds if

δ ≥ [(b + c) – (B + C)]/(B + C). (2)

which indicates that mutual preemption has a better chance when the sum of publiccosts and benefits is large compared with the sum of private costs and benefits. Equa-tion (2) highlights that private motivation must be small compared with external influ-ences for a threat-based trigger to induce cooperation. Of course, the sustainability ofmutual preemption also hinges on the discount factor being large so that the future isvalued sufficiently.

Two problems must be resolved to secure mutual preemption through a threat-based trigger. First, mutual deterrence remains an equilibrium; thus, parties mustagree to coordinate and move from deterrence to preemption. Second, sustainingmutual preemption may conflict with the short-run viewpoint taken by governmentsowing to election periods that limit tenure. The results for the infinitely repeated ver-sion of Figure 2 are equivalent to those for a finite, but indefinitely, repeated versionwhere δ is the probability that the current period is not the last.10 If δ represents theprobability of reelection, then this may be quite low owing to term limits or other con-siderations, which then work against sustaining preemption through threat-based trig-gers. Thus, we must look elsewhere for supporting preemption. Ironically, the lifetimetenure of terrorist leaders supports the widespread cooperation that characterizes ter-rorist groups since the 1960s.11

MUTUAL INACTION IS DISASTROUS

Next, we change one payoff combination in Figure 2—that of mutual status quo,where the two embedded 2 × 2 games overlap. In particular, we change this payoff to(–D, –D) (not shown in Figure 2) so that mutual inaction is disastrous in the sensethat this payoff is less than the sucker payoffs of the embedded preemption and deter-rence games. Thus, the payoff, Π, from the mutual status quo must satisfy

–D = Π(Status Quo, Status Quo) < minB – c, –C. (3)

This inequality ensures that the 2 × 2 preemption game is now a chicken game withpure-strategy Nash equilibria of unilateral preemption. The dominant strategy for theassociated 3 × 3 game is still deterrence with a single Nash equilibrium of (Deter,Deter) that makes at least one player worse off than the equilibria of the embedded 2 ×2 preemption chicken game.12 The Nash equilibrium of the embedded deterrence

Arce M., Sandler / COUNTERTERRORISM 189

10. The expected length of such a game is 1/(1 – δ).11. On terrorist networks, see Alexander and Pluchinsky (1992), Arquilla and Ronfeldt (2001),

Hoffman (1998), and Sandler (2003).12. This equilibrium could make both players worse off than the equilibria of the chicken game if

B – c > b – 2C, both of which are negative by assumption.

game wins out over those of the embedded preemption game. Thus, the persistence ofdeterrence is again demonstrated.

DETERRENCE AND THRESHOLD PREEMPTION GAME

To further study the resilience of the mutual deterrence equilibrium, we now tie thecountries’ interests for preemption closer together by assuming a threshold preemp-tion game in which benefits of B per preemption effort are only realized once there aretwo preemptors. This suggests that a sufficient effort must be expended or else nothingis achieved. Thus, a token operation such as the U.S. retaliatory raid on Libya in April1986 may have no lasting impact—an outcome later demonstrated by empirical analy-sis (Enders and Sandler 1993). In Figure 3, two payoffs change in the northwest 2 × 2matrix as compared with Figure 2—a sole preemptor only incurs costs of c, and thereare no free-rider benefits. This embedded preemption matrix is an assurance or staghunt game in which players will match actions at the Nash equilibria: either both pre-empt or both maintain the status quo. Strategy choices must be coordinated. The 2 × 2embedded deterrence game remains unchanged.

For the 3 × 3 game, we must also alter the payoffs associated with (Deter, Preempt)and (Preempt, Deter) in Figure 3. If the United States deters and the EU preempts, thenthe United States gains b – C, and the EU endures the public costs of U.S. deterrenceand the private costs of its own preemption. The EU receives no benefits from its pre-emption because the threshold has not been attained. In the upper right-hand cell of thematrix, the roles and payoffs are reversed. Deter still dominates over the status quo butmay not dominate over preempt. The strategic combination (Deter, Deter) remains aNash equilibrium. If 2B – c ≥ b – C, then (Preempt, Preempt) is a second Nash equilib-rium. This inequality requires that mutual preemption provides payoffs at least as largeas those from deterring alone. It also implies that the sum of public benefits and costsof preemption and deterrence, 2B + C, exceeds the corresponding sum of privatebenefits and costs, b + c. If we use the benefits and costs underlying Figure 1, we get

190 JOURNAL OF CONFLICT RESOLUTION

EU Preempt Status quo Deter

Preempt

2 , 2B c B c

,0c ,c C b C

Status quo 0, c 0,0 ,C b C US

Deter ,b C c C ,b C C 2 , 2b C b C

Figure 3: Deterrence and Threshold Preemption Game, 2B > c > B and 2C > b > CNOTE: EU = European Union.

2B – c = 2 = b – C, so that deter weakly dominates preempt, and the likely equilibriumis (Deter, Deter), which is Pareto inferior to (Preempt, Preempt). Unless payoffs reallyfavor preemption, mutual deterrence is anticipated.

ASYMMETRIC PREEMPTION

Countries that have engaged in preemption have one major commonality: they haveattracted the lion’s share of terrorist attacks. Thus, Israel is known for attacking terror-ist groups and their infrastructure in the hopes of weakening them. Since 9/11, theUnited States has also greatly increased its preemptive actions against terrorists. U.S.action is understandable given that approximately 40% of transnational terroristattacks are directed at U.S. people and property (Sandler 2003, Table 1). For domesticterrorism, countries engage in preemption because limiting such attacks solely bene-fits them. For transnational terrorism on home soil, governments have been moreaggressive at pursuing groups that pose a significant threat to domestic interests (e.g.,Red Brigades in Italy, Direct Action in France, and Red Army Faction in West Ger-many) and have done little to crush groups with little risk to domestic concerns (e.g.,November 17 in Greece).

To model asymmetric gains from preemption, we alter the baseline game so that theUnited States receives greater benefits from its own preemption than it confers on theEU. In particular, U.S. preemption yields a benefit of 2B to itself and a spillover benefitof B to the EU at a cost of c to the United States. EU preemption still provides a publicbenefit of B at a preemption cost of c. Deterrence remains as before: each deterrerreceives private benefits of b and confers a public cost of C to both countries. We againassume the same two sets of inequalities indicated in the caption to Figure 4.

In Figure 4, the 2 × 2 deterrence PD game has the same payoffs as in the baselinegame of Figure 2. If the United States preempts alone, it now receives 2B – c while stillconferring a free-rider benefit of B on the EU. Compared with the baseline game, theasymmetry adds B to each of the U.S. payoffs in the top row—all other payoffs remainunchanged. The EU still has a dominant strategy to deter, so that the only possible

Arce M., Sandler / COUNTERTERRORISM 191

EU Preempt Status quo Deter

Preempt

3 ,2B c B c

2 ,B c B 2 ,B c C B b C+

Status quo ,B B c 0,0 ,C b C US

Deter ,B b C B c C+ ,b C C 2 , 2b C b C

Figure 4: Asymmetric Deterrence-Preemption Game, 2B > c > B and 2C > b > CNOTE: EU = European Union.

Nash equilibria must be (Preempt, Deter) or (Deter, Deter) in the right-hand column.The former is the equilibrium if 2B – c > b – C, so that the United States gains morefrom preempting alone than from deterring alone. In fact, satisfaction of this inequal-ity makes preempt the dominant strategy for the United States. After 9/11, thisinequality likely held for a preferred-target country such as the United States sincedeterring alone merely transfers the attack abroad where its people and property arestill attacked, thus greatly limiting U.S. gains from relying on deterrence alone. Targetasymmetry can explain the current state of affairs with the United States using preemp-tion and deterrence, while less-preferred targets engage in just deterrence. As terror-ists display less bias for a single target, there is less apt to be a preemptive response. Itis asymmetric targeting by terrorists that induces countries to resort to preemption.The relevant asymmetry involves whose assets are targeted and not where they are tar-geted—an attack against Israelis in Kenya will be viewed by the Israeli government asan attack against Israel.

DOING BOTH

Next, we allow for a fourth strategic choice of doing both preemption and deter-rence. The payoffs for preempting and deterring are those of the baseline game. Therelevant 4 × 4 game matrix is displayed in Figure 5, in which the northwest bold-bordered 3 × 3 matrix is that of the baseline game. There are four new payoff combina-tions. If, for example, a government does both policies unilaterally, then it receives B –c + b – C and provides the other government with a net payoff of B – C. When one gov-ernment does both and the other just preempts, the first receives 2B – c + b – C, and thepreemptor gets 2B – c – C. The other two payoff combinations are computed similarly.

Deterrence dominates if it provides a player a higher payoff than doing both whenthe other player does both, that is, B + b – 2C ≥ 2B – c + b – 2C. This inequality reducesto c ≥ B, which is clearly true for our example because c > B by assumption. The persis-tence of deterrence is again displayed. Thus we are led back to the realization of thelast section that asymmetric preemption benefits are often essential to stem this ten-dency. In short, preemption benefits must outweigh associated costs if targeted gov-ernment such as the United States is to engage in both deterrence and preemptionagainst a terrorist threat. Only those countries experiencing a disproportionate numberof attacks may fall into this category. All others will rely on deterrence and hope thatsome prime target will privilege them to some purely public preemption benefits.

OTHER PROACTIVE ANDDEFENSIVE COUNTERTERRORIST POLICIES

Thus far, we have shown that for the choice between preemption and deterrence,there is a marked tendency to rely on Pareto-inferior deterrence. Preemption abides bya variety of game forms—PD, chicken, assurance (threshold), asymmetric domi-

192 JOURNAL OF CONFLICT RESOLUTION

193

EU Preempt Status quo Deter Both

Preempt

2 , 2B c B c

,B c B

,B c C B b C+

2 , 2B c C B c b C+

Status quo

,B B c

0,0

,C b C

,B C B c b C+

Deter ,B b C B c C+

,b C C

2 , 2b C b C

2 , 2B b C B c b C+ +

US

Both

2 , 2B c b C B c C+

,B c b C B C+

2 , 2B c b C B b C+ +

2 2 , 2 2B c b C B c b C+ +

Figure 5: Four-Strategy Deterrence-Preemption Game, 2B > c > B and 2C > b > CNOTE: EU = European Union.

nance, and others indicated below—while deterrence typically adheres to a PD game.The issue here is whether these tendencies also characterize other proactive and defen-sive counterterrorism policies.

PROACTIVE POLICIES

In Figure 6, we display the game-theoretic aspects of four additional proactive poli-cies. Each two-player, normal-form game is in ordinal (rank-ordered) form, where thelargest number (i.e., 4) in the cells is the best payoff, and the smallest (i.e., 1) is theworst payoff. Consider two governments contemplating freezing terrorist assets,shown in panel a. Each government has two choices: to freeze assets or not to freezeassets. If a weakest-link situation (Hirshleifer 1983) applies, then nothing is accom-plished unless both players take action—sole action merely induces the terrorists toput assets in the other country. The best payoff for each government arises when bothfreeze assets, thus eliminating a safe haven for the terrorist assets. The worst payoff isreceived by the government that freezes assets unilaterally since it suffers an economicloss without any safety gain. The government that does nothing then gets the second-greatest ordinal payoff of 3 from the banking profits derived from doing business withthe terrorists. This latter government does not get a free ride because no safety isachieved—the lowest level of action determines the safety of everyone in a weakest-link scenario. The second-lowest payoffs are associated with mutual inaction. Thereare then two Nash equilibria—mutual freeze and mutual inaction—indicated by thecells with boldfaced payoffs. With a weakest-link situation, leadership by one countrycan coordinate efforts. If, therefore, the United States freezes assets, the EU is betteroff matching U.S. resolve because the EU prefers a payoff of 4 over 3.

When the noncooperating country is not worried about terrorist attacks and cangain greatly by sequestrating terrorist funds, then its ordinal payoffs in the off-diago-nal cells change from 3 to 4—the temptation payoff—and the mutual action payoffschange from 4 to 3. A PD game results with a no-action equilibrium. Like preemption,freezing assets can be associated with numerous game structures such as PD, chicken,assurance, and asymmetric dominance. Asymmetric dominance applies when onecountry confronts a greater terrorist threat and achieves some protection from unilat-eral action. Given the strategic similarity between preemption and freezing assets, acountry that must choose between freezing assets and deterrence will favor deterrenceunless there is a significant asymmetry or a weakest-link consideration motivatescooperation.

Next, consider the proactive policy of retaliating against a state sponsor of terror-ism. This policy has virtually the same strategic structure as preemption and is often aPD game. It is a chicken game if mutual inaction results in a spate of terrorist attacks inwhich the status quo is the worst outcome. In panel b of Figure 6, we characterize theUnited States as the prime target of a state sponsor, so that it has a dominant strategy toretaliate (4 > 3 and 2 > 1), while the EU has a dominant strategy not to retaliate. Whenboth targets exercise their dominant strategy, the Nash equilibrium (whose payoffs areboldfaced) results, with the United States retaliating unilaterally. Retaliation may alsoabide by a threshold assurance game. Once again, a policy choice between retaliation

194 JOURNAL OF CONFLICT RESOLUTION

195

a. Freezing assets: weakest link

EU Gather Does not

Gather

2,2

4,3

US

Does not

3,4

1,1

c. Intelligence: hero

EU Retaliate Does not

Retaliate

4,3

2,4

US

Does not

3,1

1,2

b. Retaliation: asymmetric dominance

EU Infiltrate Does not

Infiltrate

2,2

3,4

US

Does not

4,3

1,1

d. Infiltration: leader

EU Freeze Does not

Freeze

4,4

1,3

US

Does not

3,1

2,2

Figure 6: Some Alternative Proactive Policies and Their Ordinal Game FormsNOTE: EU = European Union.

and deterrence is apt to favor deterrence. After 9/11, the U.S.-led attack against theTaliban, who harbored al-Qaida, follows this pattern, with most European countriesresponding by tightening security to deter attacks.

We now turn to two proactive policies that can be associated with a quite differentstrategic structure than the proactive policies considered thus far. In the case of gather-ing intelligence, the ordinal-payoff matrix for a two-government scenario may corre-spond to panel c of Figure 6. Each government must decide whether to gather intelli-gence on a terrorist threat or group. The intelligence game gives the greatest advantageto the government that gathers the information and the second-greatest payoff to thefree rider. The gatherer achieves some additional benefit from being in control of theinformation that is not obtained by the free rider. In a world of globalized terror, theinformed government will want to share much of its intelligence to protect its coun-try’s citizens and assets abroad. If both governments gather the same intelligence,there is wasted effort, and each may jeopardize the other’s covert operation. Thusmutual action may result in the second-lowest payoff. Finally, mutual inaction leavesboth governments vulnerable, and this gives the lowest payoff. In panel c, the resultingequilibria are the two off-diagonal cells in which just one country gathers the intelli-gence. This game structure is known as “hero” (Coleman 1999) because the playerwho unilaterally moves away from the maximin solution of mutual gathering is a heroby taking a lower return while conferring a higher return on the other player. Hero is acoordination game in which players must coordinate their choices or else be saddledwith undesirable outcomes. This coordination requires a loss in autonomy that nationshave often been unwilling to display on security matters except in the direst ofcircumstances. Furthermore, there is no room for two heroes as two heroes result in thesmallest payoffs.

If payoffs from intelligence are asymmetric because terrorists’ targeting decisionsfocus on some governments, then an asymmetric-dominance scenario may arise. Inthis case, the coordination dilemma is solved by the likely target providing intelligencefor itself and others. Ironically, the terrorists can greatly assist governments in address-ing the coordination dilemma by having favorite targets that attract a disproportionateshare of attacks. As for other proactive policies, asymmetries may be essential if gov-ernments are to engage in intelligence gathering and deterrence and not rely on deter-rence. Another asymmetry may arise from capacity when one country is betterequipped than the other for the mission. The latter may then be willing to let its coun-terpart gather the intelligence. For choices involving intelligence and deterrence, therelatively high payoffs for both players mean that intelligence may win out when adecision between them must be made. In situations where doing both is an option, oneor more players may do both, which again brings up a coordination problem.

In panel d of Figure 6, strategic aspects of infiltrating a terrorist group are indicatedin a 2 × 2 game representation. Taking the action outweighs the costs but not relative tothe net gain of free riding, which is associated with the greatest ordinal payoff. Thesecond-smallest payoff arises when both governments infiltrate a terrorist groupbecause mutual action may jeopardize the other government’s operation. Agents maybe killed if governments do not know of their counterpart’s action. Moreover,resources are wasted since nothing is gained from duplicating the mission. The small-

196 JOURNAL OF CONFLICT RESOLUTION

est payoffs arise from mutual inaction. The game is known as “leader,” in which theplayer who moves away from the maximin solution of mutual action receives thegreatest gain (Coleman 1999). The two Nash equilibria are again the off-diagonal cellswith the boldfaced payoffs, in which one government infiltrates and the other freerides. As in the case of hero, coordination is required or else low-paying diagonal cellswill be reached. The coordination can be provided de facto if one target has insufficientcapacity or expertise to provide infiltration. Coordination is also not an issue when onecountry perceives a much greater threat from the group, so that an asymmetric domi-nance applies as in panel b. If infiltration abides by a leader game, then extending theanalysis to allow infiltration to be chosen along with deterrence may lead to equilibriawith both being chosen, as in the case of intelligence.

A final proactive policy concerns the development of new counterterrorism tech-nologies (e.g., bomb-sniffing devices, plastic explosive tags, and new databases).Such actions are “best-shot” public goods for which the greatest effort determines theprovision level (Hirshleifer 1983). Suppose that each of two governments can discoverthe new technology. Further suppose that the technology gives 6 in benefits to every-one once discovered but provides no additional benefits for a redundant discovery. Thecost of discovery is, say, 4. If one computes the cardinal payoffs, they are (2, 6) and (6,2) in the off-diagonal cells and (2, 2) and (0, 0) along the main diagonal. The greatestpayoff is gained by the free-riding government when the other government achievesthe technological breakthrough. In ordinal form, the game is that of panel c in Figure 6,provided that the 4s are changed to 2s. The Nash equilibria are the off-diagonal cells inwhich only one government acts; coordination is required to avoid duplication, notunlike intelligence or group infiltration.

A number of findings are associated with proactive policies. First, most proactivepolicies are purely public goods. If governments’ proactive policies are cumulative(i.e., actions add to the total level achieved rather than weakest link, threshold, or bestshot), then a PD game applies, and inaction is the dominant strategy. Second, a varietyof game forms can characterize the same proactive policy owing to alternative waysthat effort levels of the governments are aggregated. Third, coordination games figureprominently, meaning that some communication and joint efforts are necessary toavoid wasteful duplication. Fourth, asymmetric targeting by terrorists can motivateaction by a government to privilege the rest of the governments with benefits from itsresponse.

DEFENSIVE POLICIES

Defensive policies include deterrence in which a PD game applies and the domi-nant strategy is to deter. Deterrence can result in a “deterrence race” whereby action byone potential target induces another target to take similar steps to reduce the terrorists’likelihood of success or their payoffs. A race occurs because failure to act makes a gov-ernment a soft target that will draw an attack. Another defensive policy is to harden atarget (e.g., fortifying embassies and diplomatic missions). Such security upgradesagain deflect an attack to other less fortified targets, thereby inducing potential targetsto compete in terms of fortification. Once again, a PD game applies. Both deterrence

Arce M., Sandler / COUNTERTERRORISM 197

and security enhancement are instances of “strategic complements” whereby actionby one government encourages similar actions by another government.

A somewhat different defensive scenario characterizes efforts to shore up a weak-est-link or vulnerable country. Countries have an interest in bolstering such countries’defensive measures because foreign residents are in harm’s way as terrorists use “soft”venues to hit other countries’ assets. Thus, one of the four pillars of U.S. counter-terrorism policy is to offer assistance to countries whose capacity is inadequate tocounter terrorism (U.S. Department of State 2003). Shoring up vulnerable targetsabroad is a pure public good in which inaction is a dominant strategy unless a country’sassets are the targets of choice. Thus, shoring up the weakest link gives rise to a PDgame, chicken game (if doing nothing is disastrous), or asymmetric dominance. Incontrast to the other two defensive actions, efforts to achieve an acceptable securitystandard abroad yield purely public benefits. As such, this defensive policy has muchin common with proactive policies of preemption, freezing assets, and retaliatingagainst state sponsors.

CONCLUDING REMARKS

By way of summary, Table 1 lists six proactive and three defensive counter-terrorism policies along with their corresponding game forms. Counterterrorism poli-cies fall in four classes: PD scenarios with public benefits in which too little action fol-lows, PD scenarios with public costs in which too much action follows, coordinationgames (e.g., assurance, best shot, leader, and hero) in which bad outcomes must beavoided, and asymmetric dominance in which a prime target provides protection forall. When compared to defensive measures, proactive counterterrorist policies display

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TABLE 1

Policy Choices and Underlying Games

Policy Type Alternative Game Forms

Proactive policiesPreemption Prisoner’s dilemma, chicken, assurance (threshold), coordination

(best shot), asymmetric dominanceFreezing assets Prisoner’s dilemma, chicken, asymmetric dominance, assurance

(weakest link)Retaliation Prisoner’s dilemma, chicken, assurance (threshold), coordination

(best shot), asymmetric dominanceGroup infiltration Leader, asymmetric dominanceIntelligence Hero, asymmetric dominanceNew technological barriers Coordination (best shot)

Defensive policiesDeterrence Prisoner’s dilemma (deterrence race)Hardening targets Prisoner’s dilemma (fortification race)Shoring up weakest link Prisoner’s dilemma, chicken, asymmetric dominance

the greater variety of underlying game forms, which implies a richer set of policyresponses. Efforts to facilitate more appropriate responses must be tailored to the asso-ciated strategic structure (e.g., with asymmetric dominance, no policy interventionmay be needed if the acting country responds sufficiently for all, while for a chickengame, responses must be coordinated to avoid a disastrous outcome).

Earlier, we examined the choices between preemption and deterrence and demon-strated the resilience of deterrence even though the associated Nash equilibrium wasthe worse of the two embedded PD games. When a proactive policy such as retaliationis combined with a defensive policy such as hardening targets, the associated 3 × 3game has target hardening being the dominant strategy, analogous to the preemption-deterrence choice. For the pattern of benefits and costs examined here, defensive poli-cies of deterrence and hardening targets generally dominate many proactive policies,except for intelligence and infiltration. For the latter two policies, equilibria involve acoordination of efforts to avoid wasteful duplication or nations working at cross pur-poses. This coordination requires better communications between intelligence organi-zations or some type of signaling mechanism to indicate whose turn it is to act.

Many proactive policies yield purely public benefits in which free riding is a prob-lem. In contrast, most defensive policies give private benefits and public costs, withcountries competing to match one another’s actions to not draw the attack. Govern-ments are predisposed to engage in too little proactive effort and too much defensiveeffort—thus the general prevalence of the latter. Proactive policies are encouragedprimarily by asymmetric targeting, in which a few nations draw a larger share ofthe attacks. This asymmetry raises these countries’ net benefits from proactivemeasures that can potentially reduce the terrorist threat for everyone. Thus, asymmet-ric targeting works against terrorists’ interests. When asymmetries are sufficientlygreat, a nation will engage in both proactive and defensive actions. A more optimalresponse may ensue if the international community fosters the prime target’s proactiveresponses through subsidies or other support. Too much reliance on a prime target maylead to either fatigue or the pursuit of an agenda not in keeping with other countries’interest; thus, free riding has its own costs.

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Arquilla, John, and David Ronfeldt. 2001. The advent of netwar (revisited). In Networks and netwars, editedby John Arquilla and David Ronfeldt, 1-25. Santa Monica, CA: RAND.

Atkinson, Scott E., Todd Sandler, and John Tschirhart. 1987. Terrorism in a bargaining framework. Journalof Law and Economics 30 (1): 1-21.

Brams, Steven J. 1994. Theory of moves. Cambridge, UK: Cambridge University Press.Coleman, Andrew M. 1999. Game theory and its applications in the social and biological sciences. New

York: Routledge.Drakos, Konstantinos, and Ali M. Kutan. 2003. Regional effects of terrorism on tourism in three Mediterra-

nean countries. Journal of Conflict Resolution 47 (5): 621-41.Enders, Walter, and Todd Sandler. 1993. Effectiveness of anti-terrorism policies: Vector-autoregression-

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Heal, Geoffrey, and Howard Kunreuther. 2005. IDS models of airline security. Journal of Conflict Resolu-tion 49 (2): 201-17.

Hirshleifer, Jack. 1983. From weakest link to best shot: The voluntary provision of public goods. PublicChoice 41 (3): 371-86.

Hoffman, Bruce. 1998. Inside terrorism. New York: Columbia University Press.Lapan, Harvey E., and Todd Sandler. 1988. To bargain or not to bargain: That is the question. American Eco-

nomic Review 78 (2): 16-20.. 1993. Terrorism and signaling. European Journal of Political Economy 9 (3): 383-97.Office of Management and Budget. 2003. Department of Homeland Security. Accessed August 25, 2003, at

http://www.whitehouse.gov/omb/budget/fy2004/homeland.htmlOvergaard, Per B. 1994. Terrorist attacks as a signal of resources. Journal of Conflict Resolution 38 (3):

452-78.Pape, Robert A. 2003. The strategic logic of suicide terrorism. American Political Science Review 97 (3):

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Reinhard Selten, 77-93. Boston: Kluwer Academic.U.S. Department of State. 2003. Patterns of global terrorism. Washington, DC: U.S. Department of State.

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Public Choice (2005) 124: 75–93DOI: 10.1007/s11127-005-4747-y C© Springer 2005

Collective versus unilateral responses to terrorism

TODD SANDLERSchool of International Relations, University of Southern California, Von Kleinsmid Center 330, LosAngeles, CA 90089-0043, USA (E-mail: tsandler@usc.edu)

Accepted March 2005

Abstract. Global terrorism presents collective action issues for targeted nations. Proactivemeasures (e.g., preemptive strikes) against terrorists create external benefits for all at-risknations. In contrast, defensive actions deflect attacks to softer targets, thereby giving rise toexternal benefits to protected foreign residents and external costs to venues abroad. Coordinatedantiterrorism measures are particularly difficult to achieve when many nations must participateand nonparticipants can undo the efforts of others. Thus, freezing terrorists’ assets or abidingby a no-negotiation pledge pose difficult collective action problems. These same concerns donot plague decisive action against domestic terrorism.

1. Introduction

Terrorism is the premeditated use or threat of use of violence by individualsor subnational groups to obtain a political or social objective through intimi-dation of a large audience beyond that of the immediate victims. Terrorists tryto circumvent the normal political process through violence perpetrated ona public who may then pressure the government to concede to the terrorists’demands. On 11 September 2001 (henceforth, 9/11), the four hijacked planesgraphically illustrated the havoc and destruction that terrorists can wreak onsociety. If a targeted government views its future (discounted) costs from asustained terrorist campaign as greater than that of conceding to terrorists’demands (including reputation costs), then a government may grant conces-sions (Lapan & Sandler, 1993). In the absence of caving in, governments mustinstitute antiterrorist measures.

The modern era of transnational terrorism began in 1968 with terroriststraveling between countries and maintaining a presence in multiple countriesto achieve their greatest impact. A watershed transnational terrorist event wasthe 22 July 1968 hijacking of an El A1 Boeing 707 en route from Rome toTel Aviv with 10 crew members and 38 passengers, including three hijack-ers identified with the Popular Front for the Liberation of Palestine (PFLP)(Mickolus, 1980, pp. 93–94). This event is noteworthy for a number of reasons.First, there was clear evidence of state-sponsorship after the plane landed inAlgiers, because Algeria took advantage of the situation and held some of thehostages until 1 September 1968 when a deal was finally struck.1 Second, theincident forced the Israelis to negotiate directly with the Palestinian terrorists

76

(Hoffman, 1998, p. 68). Third, massive media coverage demonstrated to otherterrorists that such events could capture worldwide attention. Fourth, one ofthe terrorists helped land the plane in Algiers; hence, 9/11 was not the firstinstance where a terrorist flew a hijacked airplane (Mickolus, 1980, p. 94).Fifth, a ransom of $7.5 million was paid by the French to the hijackers and16 Arab prisoners from the 1967 Arab-Israeli war were released by Israel.The hijackers were flown to a safe location with their ransom; two of thehijackers subsequently were involved in hijackings in 1972 (Mickolus, 1980).This incident clearly depicts the transnational externality (i.e., uncompen-sated interdependency involving multiple countries) that modern terrorismcan imply where, e.g., a grievance in the Middle East affects a flight leavinga European airport. To protect against such events, airports must institute ad-equate security measures against the spillover of terrorism from abroad. Thenews coverage resulted in an externality in the form of additional hijackings.Moreover, paid ransoms encouraged further incidents worldwide owing to thepromise of high rewards.

More recently, the skyjackings of 9/11 created transnational externalitiesbecause the deaths and property losses at the World Trade Center (WTC) in-volved upwards of 80 countries. Subsequent efforts to bolster security in theUnited States and Europe appear to be shifting attacks to developing coun-tries – e.g., Indonesia, Morocco, Saudi Arabia, Kenya, Turkey and Malaysia(Sandler, 2005). The devastation of 9/11 raised the bar in terms of the kind ofcarnage that a future terrorist act must produce to capture similar news cover-age. That, in turn, induces the terrorists to innovate in order to find new meansto cause even greater destruction. This innovation process is an intertemporalexternality that today’s terrorists impose on tomorrow’s victims.

Modern-day transnational terrorism raises some essential dilemmas. Ter-rorists appear able to address their collective action concerns through co-operation among themselves, while governments are less adept at collec-tive responses and primarily resort to unilateral (suboptimal) responses. Fortransnational terrorism, there is a propensity for nations to focus on defensiverather than proactive countermeasures. Defensive actions may merely deflectattacks to less-protected venues, leading nations to work at cross-purposes(Arce & Sandler, 2005; Sandler & Lapan, 1988; Sandler & Siqueira, 2003).Moreover, there is a clear tendency for at-risk nations to rely on a prime-targetnation to carry the burden for direct action against the terrorists. In contrast,governments appear properly motivated to strike the right balance betweendefensive and proactive responses against domestic terrorism.

The primary purpose of this paper is to explain the collective action failuresthat plague targeted countries in their efforts to respond to global terrorism. Toaccomplish this task, I employ some simple game theory to examine alternativeantiterrorism responses to a common transnational terrorism threat. Threegame forms are prevalent: prisoners’ dilemma, asymmetric dominance and

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stag hunt. The last is particularly germane for analyzing cases where a degreeof coordination is required to accomplish some gain. For example, countriesthat do not freeze terrorists’ assets can greatly undo the actions of those that do.I address the asymmetries between governments and terrorists that underliemany collective action concerns, driven by opposing externalities relevant totoday’s networked terrorists who harbor common grievances. Terrorists’ ownactions may foster efforts for nations to address collective action concerns.As the severity of attacks escalates, nations become more willing to followthe lead of prime-target nations to take actions such as freezing terrorists’assets. I also underscore some of the public choice dilemmas where politicalfreedoms provide a favorable environment that some terrorists may exploit.

2. Preliminaries

At the outset, domestic terrorism must be distinguished from transnational ter-rorism. The former is solely a host country affair where its citizens resort toterrorist attacks on other citizens or their property with the intention of further-ing a domestic political or social agenda through violence and intimidation.The bombing of the Alfred P. Murrah Federal Building in Oklahoma Cityon 19 April 1995 was a domestic terrorist event, because Timothy McVeighand his accomplices were American citizens, as were the victims of the blast.Moreover, this bombing did not have ramifications for other countries.

By virtue of its victims, targets, institutions, supporters, terrorists’ de-mands, or perpetrators, transnational terrorism involves more than a singlecountry. The train bombings in Madrid on 11 March 2004 were transnationalterrorist incidents because many of the terrorists were foreign nationals whocame to Madrid to stage their attack. Moreover, the bombing victims in-cluded some non-Spanish citizens. In addition, the bombing had far-reachingimplications for other European countries that then had to take precautionsagainst similar attacks. The four hijackings on 9/11 also were transnationalterrorist acts with global consequences as to their victims, security concerns,and financial impact. Although domestic terrorism is far more prevalent thantransnational terrorism (National Memorial Institute for the Prevention of Ter-rorism, 2004), the latter generates cross-border externalities that are difficultto address, and leads to collective action failures when unilateral responses bygovernments work against global welfare. For example, US efforts to secureits borders have transferred most terrorist incidents against US interests toforeign venues. Although 40% of all transnational terrorist attacks are againstUS people or property, few have occurred on US soil in recent years (Sandler,2003). Transnational terrorism, as practiced by Al-Qaida and its loose networkof affiliates, poses a greater threat than domestic terrorism to world securityas fundamentalist groups seek maximum carnage and financial repercussions(Hoffman, 1998).

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Counterterrorism consists of government actions to inhibit terrorist attacksor curtail their consequences. There are two main categories of antiterrorismpolicies – proactive and defensive. Proactive or offensive measures targetthe terrorists, their resources, or their supporters directly. By weakening theability of terrorists to operate, proactive policies reduce the frequency andprevalence of attacks against all at-risk targets. Such actions include attack-ing terrorist camps, assassinating terrorist leaders, freezing terrorist assets,retaliating against a state-sponsor, gathering intelligence, and infiltrating aterrorist group.

Defensive or passive policies try to protect a potential target against anattack or to ameliorate the damage in case of an attack. Defensive measuresmay involve the installation of technological barriers (e.g., bomb-sniffing de-vices, metal detectors, or biometric identification), the hardening of targets(e.g., barriers in front of federal buildings), the deployment of security person-nel (e.g., sky marshals on commercial flights), and the institution of terroristalerts. While some proactive policies may provoke a terrorist backlash, de-fensive measures usually do not have this potential downside (Rosendorff &Sandler, 2004). By reducing the terrorists’ probability of success and increas-ing their operations’ costs, defensive actions attempt to dissuade terrorists byreducing their expected net benefits from attacks. If, however, the authoritiesmake one type of attack harder without affecting the costliness of other typesof attacks, then such partial measures can merely induce terrorists to substituteone mode of attack for another relatively cheaper one – e.g., the installationof metal detectors at airports reduced skyjackings but increased other types ofhostage-taking missions (Enders & Sandler, 1993, 1995, 2004; Enders et al.,1990). Similarly, defensive actions that make one country more secure maymerely transfer attacks to less-secure venues abroad.

3. Asymmetries Between Nations and Terrorists

To appreciate the collective action problems posed by transnational terrorism,one must recognize the asymmetries that distinguish the behavior of targetednations and their terrorist adversaries. These asymmetries provide tacticaladvantages to terrorists who target assets from powerful nations.

Nations must guard everywhere, while terrorists can identify and attackthe softest targets. Efforts by nations to harden targets induce terrorists toredirect their attacks to less-protected venues. As rich countries mobilizedtheir defensive measures following 9/11, the developing world stayed thevenue of choice from which to attack Western interests. In 2003, there were 190transnational terrorist attacks, with none in North America and 24 incidentsin Europe.2 There were, however, 70 attacks in Asia, 53 in Latin America,and 37 in the Middle East. Although there were no transnational attacks inthe United States in 2003, there were 82 anti-US attacks on foreign soil: 46,

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Latin America; one, Eurasia; two, Africa; six, Asia; 11, Middle East; and 16,Western Europe. During 2002, there were 198 transnational terrorist incidents,with none in North America and only nine in Western Europe. Asia was thepreferred venue with 101 attacks.

Nations are target-rich; terrorists are target-poor. Terrorists may hide in thegeneral population in urban centers, thereby maximizing collateral damageduring government raids to capture them. Nations have to be fortunate on adaily basis, while terrorists only have to be fortunate occasionally.3 As such,terrorists can sit back and pick the most opportune time to strike, as they did on9/11. Unlike liberal democracies that are constrained in their reaction to ter-rorist threats, terrorists can be unrestrained in their brutality, as demonstratedby attacks perpetrated by fundamentalist terrorists in recent years. Nationsare not well-informed about terrorists’ strength, whereas terrorists can easilydiscover how many governmental resources are being allocated to antiterroristactivities. In the United States, this information is a matter of public record.This asymmetric information is amply illustrated by US estimates of al-Qaidastrength as “several hundred to several thousand members”, reported by the USDepartment of State (2001, p. 68) just five months before 9/11. The 7 October2001 invasion of Afghanistan indicated that Al-Qaida had far more membersthan the State Department’s upper-bound estimate. Such misleading figuresnot only hamper the military in terms of planning antiterrorist operations,but they also make it more difficult to convince other countries to contributetroops to preemptive raids on training camps and terrorist infrastructure.

Another asymmetry concerns the organizational structure adopted by gov-ernments and terrorists. Governments are hierarchical, whereas terrorist orga-nizations are nonhierarchical with loosely tied networks of cells and affiliatedterrorist groups (Arquilla & Ronfeldt, 2001). Terrorist cells and groups canoperate independently of one another. Moreover, captured terrorist leaders canprovide only limited intelligence owing to the looseness of the network andthe virtual autonomy of many of its components. Recent espionage scandalsindicate that government informants can do much damage to the integrity ofan intelligence organization.

Beyond some point, government size can limit its effectiveness in wag-ing an antiterrorist campaign. Also, a larger government has more targetsto protect and can create greater grievances from taxes used to finance thebureaucracy. In contrast, a larger terrorist group can engage in a more ef-fective campaign that may signal to the government that an accommodationis less costly. Hirshleifer (1991) introduced the notion of the “paradox ofpower” in conflict situations, where smaller forces may have a strategic advan-tage over larger, militarily superior forces. In particular, small insurgencies,including terrorists, can cause more damage per operative insofar as sometechnologies of conflict favor the small force that can hide and strike largetargets.

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A final asymmetry is the most essential for understanding why nationshave greater difficulty in addressing their collective action problem than theterrorists. National strength provides a false sense of security, thereby inhibit-ing governments from appreciating the need for coordinated action. Nationsalso do not agree on which groups are terrorists – e.g., until fairly recently,the European Union (EU) did not view Hamas as a terrorist organization de-spite its suicide bombing campaign. In democracies, leaders’ interests in thefuture are limited by the length of the election cycle and their likelihood ofreelection. Agreements made with leaders of other countries to combat ter-rorism may be rather short-lived if a government changes. For example, thenew Spanish Prime Minister Zapatero pulled the country’s troops out of Iraqfollowing his surprise win in the national elections stemming from the al-leged link between the 11 March 2004 train bombing and Spanish support forthe US-led war on terror. This short-term viewpoint limits intergovernmentalcooperative arrangements that could follow from a repeated-game analysis,based on a tit-for-tat strategy. Because many counterterrorism actions amonggovernments abide by a prisoners’ dilemma game structure (see Section 4), amyopic viewpoint works against solving the problem through repeated inter-actions, unless agreements can have a permanency that transcends a changein governments. The high value that governments place on their autonomyover security matters also inhibits their addressing collective action issuessuccessfully.

A much different situation characterizes the terrorists who have coop-erated in networks since the onset of modern-day terrorism. From the late1960s, terrorist groups have shared personnel, intelligence, logistics, trainingcamps and resources (Alexander & Pluchinsky, 1992; Hoffman, 1998). Morerecently, Al-Qaida forged a loosely linked network when Osama bin Laden be-gan franchising other Islamic groups (Raufer, 2003; Hoffman, 2003). Despitedifferent political agendas, terrorist groups share similar opponents – e.g., theUnited States and Israel – that provide some unity of purpose. For example,the left-wing terrorists groups in Europe during the 1970s and 1980s wereunited in their political orientation and their goal to overthrow a capitalisticsystem (Alexander & Pluchinsky, 1992). Terrorist groups cooperate becauseof their relative weakness compared with the well-armed governments thatthey confront. Given their limited resources and grave risks, terrorists havelittle choice but to cooperate to stretch resources. Terrorist leaders tend to betenured for life so that they view intergroup interactions as continual. Thislong-term orientation means that terrorist groups can successfully addressprisoners’ dilemma interactions through punishment-based tit-for-tat strate-gies. The temptation to renege on an agreement with another terrorist groupfor a short-term gain is tempered by the long-run losses from the lack of futurecooperative gains. Terrorists appear to place less weight than governments ontheir autonomy, provided that shared actions further their goals. Unlike their

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government adversaries, terrorists are motivated to address their collectiveaction concerns.

4. Proactive Versus Defensive Policies

As a generic proactive policy, I examine efforts to preempt a terrorist groupby, say, attacking the terrorists’ bases and training camps. I then compare andcontrast preemption with a generic defensive policy – i.e., actions to deter anattack by fortifying vulnerable targets.

4.1. Preemption

In panel a of Figure 1, a symmetric preemption game is displayed for twotargeted countries (i.e., nations 1 and 2), each of which must decide whether ornot to launch a preemptive strike against a common terrorist or state-sponsorthreat. The attack is meant to weaken the terrorists and limit their futureactions. Given the common threat posed by the terrorists, each preemptingcountry provides a pure public benefit of B for itself and the other at-risknation. More benefits are achieved when both countries attack the terrorists,as combined action does more harm to the terrorists.

In each cell of the 2 × 2 game matrix, the left-hand payoff is that of nation1 and the right-hand payoff is that of nation 2. The cost of preemption is cfor each preemptor, where c > B. I assume that isolated action results inless benefits than costs so that a collective action problem occurs.4 If nation

Figure 1. Alternative preemption scenarios.

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1 preempts alone and nation 2 maintains the status quo, then nation 1 netsB − c < 0, while nation 2 receives the free-rider benefit of B. These payoffsare interchanged when the nations’ roles are reversed in the bottom left-handcell. When both nations join forces, each nets 2B −c from the two preemptionactions, where 2B is assumed to be greater than c. All-around inaction givespayoffs of 0 to both nations. Given these assumptions, each nation’s dominantstrategy is to do nothing, because B > 2B −c and 0 > B −c. The underlyinggame is a prisoners’ dilemma with a Nash equilibrium of mutual inaction. Ifthe symmetric case is extended to n nations with each preemptor providing Bin benefits for all at-risk nations at a provision cost of c > B to the preemptor,then the outcome is for no nation to act. A repeated-game version is notpromising owing to the short-run view that nations take of such interactionswith other governments.

A more optimistic case arises in the asymmetric version in panel b ofFigure 1, where benefits and costs are tailored by subscripts to the two nations.Nation 1 is a prime target of the terrorists with more to gain from any actionthat weakens the terrorists. Suppose that nation 1 receives a benefit of B1

from its own preemptive action or that of nation 2. Moreover, B1 exceedsits preemption costs of c1. Since B1 > c1, nation 1’s dominant strategy nowis to preempt, which is analogous to the United States after 9/11. Nation 2is in an analogous situation to that in panel a; thus, 2B2 > c2 > B2 andnation 2’s dominant strategy is still to do nothing. As each nation exercisesits dominant strategy, the Nash equilibrium results in nation 1 preemptingunilaterally. The underlying game is one of “asymmetric dominance”. Withthe United States sustaining 40% of transnational terrorist attacks worldwide,its willingness to preempt alone or to lead a coalition is easy to understand. Byfocusing so many attacks on US interests, the terrorists motivate US proactiveresponses. If terrorists had not concentrated their campaign on a couple ofnations, there would be even fewer proactive measures against terrorism. TheNash equilibrium in panel b is not necessarily the social optimum (based on thecompensation principle) insofar as the sum of benefits from mutual preemptionmay exceed that of the Nash equilibrium. Matrix b can be extended to n nationswith m prime targets and n −m nonprime targets. As such, the subset of primetargets is motivated to take aggressive actions against the terrorists.

Next suppose that some at-risk nation adopts proactive measures (evensymbolic ones) to support a prime-target nation’s actions, as Spain and Japandid in the US war on terror. Their supportive efforts put their people in greaterjeopardy. In this scenario, nation 2’s assumed inequality changes to c2 > 2B2

in panel b of Figure 1. Nation 2’s dominant strategy is to do nothing – asillustrated by Spain’s withdrawal from Iraq following the 11 March 2004train bombing where this inequality became apparent. Terrorists have a clearmotive to attack countries that bolster the proactive measures of prime-targetcountries.

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Figure 2. Deterrence: Symmetric prisoners’ dilemma

4.2. Defensive measures

Next, I consider deterrence as a means to limit terrorists’ success by hardeninga target at an expense of C to the deterrer. In Figure 2, such action provides abenefit of b greater than C for the deterrer. Unlike preemption with its publicbenefits, defensive measures have a public cost of Ci because the attack maybe deflected to country i as country j takes precautionary actions. If nation1 deters alone, then it gains b − C , while nation 2 suffers a cost of −C2 asit becomes a more desirable target. When nation 2 deters alone, the payoffsare reversed with nation 1 sustaining a deflection cost of −C1. No actiongives 0 payoffs, while mutual deterrence provides payoffs of b − C − Ci fornation i, i = 1, 2. Since b > C , the dominant strategy in the game matrixis for both countries to deter. As each nation plays its dominant strategy, theNash equilibrium of this prisoners’ dilemma is for everyone to deter, whichgives both nations a negative payoff based on the parameters assumed. Thepayoffs for mutual deterrence include −Ci because I implicitly assume onlytwo countries and that the terrorists are bent on attacking some target nomatter how well protected. Thus, matching deterrence upgrades leads to netcosts, so that C + Ci > b, as assumed. The deterrence game is analogous tothe problem of the commons, with all players trying to achieve a gain whileignoring the external-cost consequences of their actions.

If this game is extended to n nations with analogous parameters, then thesuboptimality of the Nash equilibrium worsens as more nations take defen-sive measures to shift the attack elsewhere. In today’s world of globalizedterrorism, the game’s outcome is that the terrorists will stage their attacksin those nations with the least defensive measures – the so-called soft tar-gets. In these venues, the terrorists will hit the interests of those nationsagainst which they have the greatest grievances. Thus, the paucity of attacksin North America and Europe in 2002–2003 is consistent with this predic-tion, as is the large percentage of attacks against US people and propertyabroad.

Shoring up the softest target implies its own collective action problem.Bolstering the defense of soft targets provides purely public benefits to all

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nations whose people or property are in jeopardy. In a globalized world, thismay involve improving many nations’ defensive capabilities. The underly-ing symmetric game for shoring up the softest target is surely a prisoners’dilemma with no action at the equilibrium. With nonsymmetric players, theprime-target nations have the most to gain from increasing the capabilities ofsoft targets. Thus, one of the four pillars of US counterterrorism policy is toimprove the antiterrorism abilities of those countries that seek assistance (USDepartment of State, 2004). No country – not even the United States – hasthe requisite resources to enhance all countries’ counterterrorism activities.Since 9/11, the United States has been spending large amounts on its ownproactive and defensive responses, which limits its capacity to help others.There is also a moral-hazard problem associated with strengthening anothercountry’s capabilities, since the latter may purposely use this money for do-mestic concerns and not protect the providing country’s interests. Thus, USaid to country X might either be used to protect non-US targets in X or elsereplace X’s usual security expenditures.

4.3. Choice between preemption and deterrence

Even though preemption implies public benefits and private costs, while deter-rence implies public costs and private benefits, the prisoners’ dilemma appliesto both situations in their symmetric presentation. What would happen if anation has three strategic options: deter, status quo, and preempt? Arce andSandler (2005) examined this question and found that the deter strategy dom-inates in two-nation symmetric scenarios. Ironically, the mutual-deter Nashequilibrium provides the smallest summed payoff in the associated 3×3 gamematrix. These authors vary the game form for the embedded preemption game(e.g., chicken is allowed) but uncover a robustness of their results. Even whena fourth policy choice – deterring and preempting – is included, the deterchoice dominates.

For domestic terrorism, nations are able to balance proactive and defensivemeasures. Israel clearly applies both in its domestic struggle against Hamasand Hezbollah. In their fight against leftist terrorists in the 1970s and 1980s,countries in Europe used proactive and defensive campaigns. The former re-sulted in the capture of Direct Action in France, the Red Brigades in Italy,and the Combatant Communist Cells in Belgium in the 1980s (Alexander& Pluchinsky, 1992). Why do tactics to combat domestic terrorism gener-ally differ from those used by non-prime-target nations to fight transnationalterrorism? First, the host nation is the only target of domestic terrorism. De-fensive actions are not applied to transfer the attack abroad as in the caseof transnational terrorism. Any transference of domestic attacks takes placeamong targets within the nation. A centralized government can internalize anytransference externality when deciding defensive allocations for the country.

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There is no centralized supranational government to serve the same purpose fortransnational terrorism. Second, the benefits of a proactive campaign againstdomestic terrorism are private to the venue nation. As such, the nation cannotfree ride on any other nation’s efforts, since other nations are not in jeop-ardy. For domestic terrorism, the central government removes much of thestrategic maneuvering that characterizes policy decisions for transnationalterrorism.5 Third, defensive measures require protecting all potential targets,while proactive responses only necessitate intelligence-based raids againstthe terrorists or their resources. There is a cost-effectiveness in instituting afocused proactive campaign; defensive action may lead to virtually limitlessspending.

5. Coordination Dilemma: Freezing of Terrorists’ Assets

Obviously, other game forms can apply to countermeasures in the war on ter-ror. A common game form for some policy choices is a “stag-hunt” assurancegame, where both parties are best off if they take identical measures. When aplayer takes the measure alone, this player receives the smallest payoff and theplayer who does nothing earns the second-greatest payoff. This kind of sce-nario is descriptive of a host of counterterrorism policies where two or morenations must act in unison for the best payoffs to result. Examples includefreezing terrorist assets, denying safe haven to terrorists, applying sanctionsto state-sponsors, or holding to a no-negotiation policy. Even one nation thatbreaks ranks can ruin the policy’s effectiveness for all others. To illustratesuch scenarios, I use freezing terrorist assets as a generic example and beginwith a two-nation symmetric case.

Matrix a in the top of Figure 3 displays this scenario where the highestpayoff of F results from mutual action, followed by a payoff of A from doingnothing either alone or together. The smallest payoff, B, comes from freezingassets alone since the terrorists can merely transfer their assets elsewhere,leaving the acting country with some banking losses but few safety gains. SinceF > A > B, there is no dominant strategy. There are, however, two pure-strategy Nash equilibriums: both countries freeze assets or neither freezesassets.

A third Nash equilibrium involves mixed strategies in which each purestrategy is played in a probabilistic fashion. To identify this mixed-strategyequilibrium, I determine the probability q of nation 2 freezing terrorist as-sets that make nation 1 indifferent between freezing terrorist assets and doingnothing. Similarly, I derive the probability p of action on the part of nation1 that makes nation 2 indifferent between the two strategies. Once p and qare identified, equilibrium probabilities for maintaining the status quo simplyequal 1 − q and 1 − p for nations 2 and 1, respectively. The relevant proba-bilities are indicated for matrix a besides the respective column and row. The

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Figure 3. Alternative freezing assets scenarios.

calculations for q (or p not shown) go as follows:

q F + (1 − q)B = q A + (1 − q)A, (1)

from which we have

q = (A − B)/(F − B). (2)

when q exceeds this value, cooperation in the form of both countries freezingterrorist assets is the best strategic choice. An identical expression holds forp owing to symmetry. The ratio in (2) represents the adherence probabilitythat each nation requires of the other to want to coordinate its freeze policy.6

A smaller equilibrium probability favors successful coordination, because anation requires less certainty of its counterpart’s intention to freeze assets inorder to reciprocate.

From Equation (2), either a larger gain (F) from a mutual freeze or a smallerstatus-quo payoff (A) promotes the coordination equilibrium by reducing therequired adherence probability. An event like 9/11 not only raises F but low-ers A as nations realize the benefits from limiting terrorists’ resources and thecatastrophic consequences that inaction may have for all. As terrorists escalatethe carnage to capture the media’s attention, nations are increasingly drawnto coordinate counterterrorism activities when unified action is required. Fol-lowing 9/11’s unprecedented casualties, many more nations participated in

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freezing assets,7 but participation is by no means universal. Differentiatingthe right-hand side of (2) with respect to B shows that a decrease in the payoffassociated with unilaterally freezing assets inhibits cooperation by raising por q.8

This game scenario can be readily generalized to n homogeneous nations,where at least n nations must freeze assets if each participant is to receive apayoff of F. For less than n freeze participants, each adherent receives B forcooperating and the nonadherents get A. If nations are uncertain about theintentions of other nations, then freezing assets is a desired policy providedthat a nation believes that the n − 1 required additional participants will fol-low through with a collective probability greater than q. This then impliesthat each nation must be expected to cooperate by at least the n − 1st root ofq, which for even modest groups may require near certainty. This is not anencouraging finding. If, however, the required number of adherents for coor-dination gains can be limited, then this decreases the assurance probabilities.For an agreement to freeze assets, this is best accomplished by first unifyingsome of the major financial-center nations – i.e., the United States, the UnitedKingdom, Switzerland, Japan and Germany. A concern with this strategy isthat some near-catastrophic terrorist acts are not very costly – e.g., the 1993WTC bomb cost just $400 and caused $500 million in damages (Hoffman,1998) – so that near-universal freezes may be required.

In matrix b in Figure 3, an alternative scenario is displayed where notfreezing assets, when the other nation freezes, gives the second highest payoffto the noncooperator, so that F > E > A > B. This scenario implies that thenation that does not join the freeze can profit by providing a safe haven forterrorists’ funds. The nation may be motivated to do so if it does not view itsown people or property as likely targets of the terrorists. The two pure-strategyNash equilibriums are for a mutual freeze or no action along the diagonal of thematrix. For the mixed-strategy Nash equilibrium, the adherence probabilitiesare now:

p = q = (A − B)/[F − B + (A − E)], (3)

which are greater than those in (2), because (A− E) < 0. Hence, coordinatinga freeze becomes more difficult owing to profitable opportunities availableto less scrupulous nations that can greatly limit gains from action to freezeassets, eliminate safe havens, or abide by no-negotiation pledges (see, e.g.,Lee, 1988).

Policies that penalize noncompliance can reverse the ranking of A and E,so that A > E . As a consequence, adherence becomes easier to achieve. Thereare two practical problems: (i) to identify nations that accept terrorists’ fundsand (ii) to convince nations to punish nonadherents. Since nations hide their

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bad behavior, singling out nations for punishment is not so easy. Imposingsanctions is itself a prisoners’ dilemma game that presents its own collectiveaction concern.

In Figure 4, a final freeze scenario allows for asymmetry where nation 2has more potential nonadherence profits but fewer gains from acting alonethan its counterpart. That is, I assume that F > Ei > A > Bi , i = 1,2, where E2 > E1 and B1 > B2. The pure-strategy Nash equilibriumsare still the matching-behavior outcomes along the diagonal of the matrixin Figure 4. For the mixed-strategy equilibrium, the adherence probabilitiesare:

p = A − B2

F − B2 + (A − E2)>

A − B1

F − B1 + (A − E1)= q. (4)

To act, nation 2 needs greater assurance than nation 1 that the other nationwill freeze assets. Such asymmetry is likely to work against consummating afreeze.

When coordination is required for a counterterrorism measure, many fac-tors work against getting sufficient action. A crucial consideration is the min-imum number of nations required for coordinating antiterrorism activities.As this minimum increases, nations must have greater assurance that otherswill cooperate for them to follow suit. Any policy action that limits this min-imum bolsters cooperation. As the threat of terrorism escalates, coordinationof counterterrorism is encouraged because cooperative outcomes have greaterpayoffs and unilateral action has smaller payoffs. The application of technol-ogy to track money flows can identify duplicitous nations that hamper othernations’ actions by providing safe havens to terrorists’ assets. Retributionagainst these “spoiler” nations can foster more fruitful coordination by send-ing a clear signal that profiting from terrorism has consequences. Efforts bythe International Monetary Fund and World Bank to assist countries in track-ing asset transfers can lower the costs of unilateral action, thereby boostingefforts to freeze terrorists’ assets.

Figure 4. Asymmetric freezing assets scenario.

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6. Public Choice Dilemma

The recent terrorism literature has shown that there appears to be a positiveassociation between terrorism and democracy (Eubank & Weinberg, 1994,2001; Li & Schuab, 2004; Schmid, 1992). This association is traced to factorsin a liberal democracy that can provide a favorable environment for transna-tional terrorist activities. For example, freedom of the press allows terroriststo publicize their cause through news coverage of terrorist attacks. Media cov-erage of ghastly events also serves terrorists’ needs to create an atmosphereof fear where everyone feels at risk. File footage is reshown periodically onanniversaries of events and when related incidents occur, so that these eventsremain in the public consciousness. Restraints on governments’ powers limitthe ability of authorities to hold terrorist suspects or to gather intelligence.Obviously, 9/11 has eroded some of these restraints as civil society becamemore willing to trade away some civil liberties for greater security. Freedomof association also provides an environment conducive to terrorism. Moderndemocratic states are not only target-rich, but also present opportunities forfunding and military training. Information is also readily available on buildingbombs and guerrilla tactics in an open society. In contrast, an autocracy is aless supportive environment for terrorism. If a terrorist group in an autocracywants to publicize its cause, then it may stage incidents in democracies wherenews coverage is more complete and the environment is more supportive.Crossing borders is generally easier in a liberal democracy than in an autoc-racy which, in turn, encourages the export of terrorism and the prevalence oftransnational externalities.

This association between democracy and transnational terrorism presentsa real public choice dilemma. Usually, democratic ideals work in a coun-try’s favor – e.g., democratic countries do not tend to go to war with oneanother. There are a number of research issues that require further empir-ical analysis to understand the public choice implications of transnationalterrorism. First, the staging of terrorist events in liberal democracies requiresstudy. To date, there has been no careful and convincing study on whethertransnational terrorism is originating in or spilling over to democratic coun-tries. The level of this alleged externality needs to be investigated in orderto determine the appropriate policy response. For example, enhanced bordersecurity can address some spillover terrorism. Second, the influence of thetype of democracy on the level of terrorism requires analysis. Which kind ofdemocratic system – proportional representation or majoritarian system – ismore conducive to terrorism? Since proportional representation gives moreviews, even extreme ones, a presence in government, terrorism may be lessprevalent under proportional representation than under a majoritarian system.The impact of the type of democratic system on the level of terrorism has notbeen investigated.9 Third, the role of rent seeking as a motive for terrorism

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requires further analysis. A paper by Kirk (1983) argued that government sizeencourages more terrorism because of greater potential rents to capture. Hisanalysis probably does not apply in today’s world where fundamentalist-basedterrorism is the driving force, since these terrorists’ goals do not appear tobe distribution driven. Many fundamentalist groups – e.g., Al-Qaida – viewall nonbelievers as enemies and want an Islamic state (White, 2003). In thosecountries where there are rival terrorist groups, a rent-seeking explanation ofterrorism may be appropriate. Each terrorist group is in a contest with othergroups for the provision of a public good in the form of a political changethat favors the group’s constituency. Rent-seeking costs are the expense of theterrorist campaign that promotes the terrorists’ demands. Such costs representa lower bound on the expense that the campaign imposes on society, becausedamage to the latter must also be included.

7. Concluding Remarks

The paper applies elementary noncooperative game theory to explore the col-lective action dilemmas that confront nations as they address a global terroristthreat. Although incentives are conducive for terrorists to form networks andcooperate, incentives are less supportive for targeted nations to coordinatetheir counterterrorism policies. Both proactive and defensive measures oftenimply an underlying prisoners’ dilemma game in which insufficient actioncharacterizes offensive efforts and too much action characterizes defensiveresponses. For proactive measures, a prime-target country is anticipated toact. By concentrating their attacks on a couple of target countries, terroristsmotivate these countries to strike back and privilege all at-risk countries withtheir actions to weaken the terrorists. If countries realize that defensive mea-sures may merely divert attacks abroad where their people and property are stilltargeted, then there will be a smaller tendency to overspend on defensive mea-sures. For domestic terrorism, there is a better balance struck between proac-tive and defensive responses because a central government can internalize theexternalities among targets that plague responses at the transnational level.

Collective action concerns may be particularly troublesome for counterter-rorist actions requiring sufficient transnational coordination, where nonpartic-ipating countries can severely undermine the efforts of the cooperators. Suchcoordination concerns apply to efforts to freeze terrorists’ assets, eliminate ter-rorists’ safe havens, deny terrorists’ weapons, and maintain a no-negotiationpolicy. As the number of participants required for cooperative gains to berealized increases, the associated assurance probabilities also increase. Thus,in the case of freezing terrorists’ assets, a few nations that safeguard theseassets can provide terrorists with the means to engage in some large-scale at-tacks. This is especially true because deadly events may be relatively cheap tofinance. Sanctions for nonparticipants can improve coordination possibilities

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but raise a collective action problem of their own, since sanctions providepurely public benefits. By targeting countries and their interests at home andabroad, today’s terrorists worsen the coordination problem for at-risk coun-tries. As terrorists escalate the damage from their acts, they, however, increasethe likelihood of coordination success on the part of targeted countries. Fol-lowing 9/11, many more countries started to freeze terrorists’ assets.

Acknowledgments

The author is the Robert R. and Katheryn A. Dockson Professor of Interna-tional Relations and Economics. The author’s research was financed in partfrom the Dockson endowment. While assuming full responsibility for anyshortcomings, the author has benefited from comments by Hirofumi Shimizuand Kevin Siqueira on an earlier draft.

Notes

1. The Algerians immediately freed the 23 non-Israeli passengers. On 27 July 1968, theyreleased the Israeli women and children hostages (Mickolus, 1980, p. 94). The remaininghostages were held at an Algiers military base under the “protection” of the Algeriangovernment.

2. The figures in this paragraph come from US Department of State (2004, pp. 176–181).3. This asymmetry paraphrases what Irish Republican Army (IRA) terrorists said in a letter

after they learned that their 12 October 1984 bombing of the Grand Hotel in Brighton hadnarrowly missed killing Prime Minister Margaret Thatcher. Their letter said, “Today, wewere unlucky. But remember we have only to be lucky once. You will have to be luckyalways.” See Mickolus et al. (1989, vol. 2, p. 115).

4. If B > c, then the dominant strategy is for both nations to preempt – a scenario that wevirtually never see for multiple countries.

5. Before 9/11, airlines tried to save money in their employment of security personnel. Thedeployment of federally trained screeners removes this strategic option.

6. Another interpretation for mixing is that p and q denote the uncertain beliefs that the nationshave for the likelihood that the other country will act.

7. Since 9/11, $200 million of alleged terrorist assets have been frozen (White House, 2003).8. dq/d B = dp/d B = (A − F)/(F − B)2 < 0, so that a smaller B is associated with greater

adherence probabilities.9. Recently Reynal-Querol (2002) showed that the incidence of civil wars is lower with

proportional representation than with majoritarian systems. Her analysis can be applied tothe incidence of transnational terrorism.

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Enders, W., Sandler, T., & Cauley, J. (1990). UN conventions, technology, and retaliation inthe fight against terrorism: An economic evaluation. Terrorism and Political Violence, 2(1),83–105.

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Eubank, W. K., & Weinberg, L. (2001). Terrorism and democracy: Perpetrators and victims.Terrorism and Political Violence, 13(1), 155–164.

Hirshleifer, J. (1991). The paradox of power. Economics and Politics, 3(3), 177–200.Hoffman, B. (1998). Inside Terrorism. Columbia University Press: New York.Hoffman, B. (2003). Al Qaeda, trends in terrorism, and future potentialities: An assessment.

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time-series analysis. Journal of Conflict Resolution, 48(2), 230–258.Mickolus, E. F. (1980). Transnational Terrorism: A Chronology of Events 1968–1979.

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A Chronology of Events, 2 vols. Iowa State University: Ames.National Memorial Institute for the Prevention of Terrorism. (2004). Preventing Terrorism or

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391–398.Reynal-Querol, M. (2002). Political systems, stability and civil wars. Defence and Peace

Economics, 13(6), 463–483.Rosendorff, P., & Sandler, T. (2004). Too much of a good thing? The proactive response

dilemma. Journal of Conflict Resolution, 48(5), 657–671.Sandler, T. (2003). Collective action and transnational terrorism. World Economy, 26(6), 779–

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the control of transnational terrorism. In I. Kaul & P. Conceicao (Eds.), Public Finance ina Globalizing World: Innovations in Theory and Practice. Oxford University Press: NewYork, forthcoming.

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state.gov/s/ct/rls/rpt/24087.htm.

DISTRIBUTION OF TRANSNATIONAL TERRORISM AMONG COUNTRIES BY INCOME CLASS AND GEOGRAPHY AFTER 9/11

by

Walter Enders University of Alabama

and

Todd Sandler

University of Southern California

Author’s Note: This research was partially supported by the United States Department of Homeland Security through the Center for Risk and Economic Analysis of Terrorism Events (CREATE), grant number EMW-2004-GR-0112. However, any opinions, findings, and conclusions or recommendations are solely those of the authors and do not necessarily reflect the views of the Department of Homeland Security. The authors have profited from the comments of two anonymous reviewers. Walter Enders is the Bidgood Chair of Economics and Finance at the University of Alabama. Todd Sandler is the Robert R. and Katheryn A. Dockson Professor of International Relations and Economics at the University of Southern California. The data used in this paper are posted at http://www.isanet.org/data_archive.htm.

DISTRIBUTION OF TRANSNATIONAL TERRORISM AMONG COUNTRIES BY INCOME CLASS AND GEOGRAPHY AFTER 9/11

Abstract

This article applies an autoregressive intervention model for the 1968-2003 period to identify

either income-based or geographical transference of transnational terrorist events in reaction to

the rise of fundamentalist terrorism, the end to the Cold War, and 9/11. Our time-series study

investigates the changing pattern of transnational terrorism for all incidents and only those

involving U.S. people and property. Contrary to expectation, there is no evidence of an income-

based post-9/11 transfer of attacks to low-income countries except for attacks with U.S.

casualties, but there is a significant transference to the Middle East and Asia where U.S. interests

are, at times, attacked. We also find that the rise of fundamentalist terrorism has most impacted

those regions the Middle East and Asia with the largest Islamic population. The end to the

Cold War brought a terrorism peace dividend that varies by income and geography among

countries. Based on the empirical findings, we draw policy recommendations regarding

defensive counterterrorism measures.

DISTRIBUTION OF TRANSNATIONAL TERRORISM AMONG COUNTRIES BY INCOME CLASS AND GEOGRAPHY AFTER 9/11

The terrorist hijackings of September 11, 2001, (henceforth, 9/11) and their fiery aftermath

changed the way that the global community views its major security threats. There is now a

realization that a terrorist incident can result in large-scale casualties, huge property losses, and

long-lasting ramifications. Prior to 9/11, no terrorist event had caused more than $2.9 billion in

damages (Wolgast, 2002)1 or killed over 500 people (Quillen, 2002). The incidents on 9/11

murdered almost 3,000 and caused over $80 billion in losses (Kunreuther and Michel-Kerjan,

2004). In terrorists future attempts to outdo past atrocities, there is real anxiety among

authorities on the magnitude of the next large-scale attack. The March 11, 2004, commuter train

bombings in Madrid (henceforth, 3/11) underscore the vulnerabilities of all countries to terrorist

attacks. As antiterrorism efforts are bolstered, governments are beginning to recognize that there

is no foolproof defense that can eliminate the terrorist threat. Post-9/11 actions to augment

security in wealthy nations may have unintended negative consequences by inducing terrorists to

stage their attacks in countries less able to afford widespread defensive measures. Thus, the new

emphasis on homeland security in the United States and throughout the European Union (EU)

may merely displace terrorist attacks to softer venues where people and property from prime-

target countries are attacked abroad (Enders and Sandler, 1993, 1995; Sandler and Enders, 2004).

This transference of attacks may be income-based or geographically founded. When

transference is income based, attacks are anticipated to be displaced from high-income countries

(HICs) to low-income countries (LICs) as some HICs deploy enhanced security measures that

make attacks more difficult and costly for terrorists to accomplish. At a minimum, these

defenses imply that terrorists may be forced to choose targets of lower value in rich countries.

For example, current actions to secure the monuments, the U.S. Capitol building, the White

2

House, and other terrorist-prized targets mean that an attack in Washington DC would be

deflected to a lower-valued venue. If the transference is geographically based, then the

displacement may be from a rich region (e.g., Europe) to a poorer region (e.g., the Middle East

or Eurasia). A geographical shift may also be motivated by the ability of terrorists to blend in

and establish a support system, especially for religious fundamentalist terrorists. If terrorists

attack foreign interests nearer to home, then they do not have to cross borders that, in some

regions, are more safely guarded after 9/11. In the 1980s, there was a significant spillover of

Middle East terrorism throughout Europe e.g., there were 43 terrorist incidents of Middle

Eastern origin in Europe in 1987 (U.S. Department of State, 1988:16, 18). Given the increased

scrutiny attributed to Middle Easterners in Europe following 9/11, more incidents are anticipated

to be staged in the Middle East now.

After 9/11, casual empiricism gives an impression that terrorist events are being

displaced from rich to poor countries, perhaps in light of defensive measures in the former.

There have been many recent high-profile transnational terrorist attacks in low-income and

middle-income countries (MICs) e.g., in Morocco, Turkey, Indonesia, India, Malaysia, Kenya,

the Philippines, Pakistan, and Afghanistan. Casual empiricism may not, however, withstand

careful statistical scrutiny. The primary purpose of this paper is to empirically evaluate with

time-series methods (i.e., autoregressive intervention analysis) whether terrorists have shifted

their venue based on target countries income or regional location in reaction to the rise of

fundamentalist terrorism, the end to the Cold War, or 9/11. To accomplish this task, we partition

countries into income categories based on two alternative schemes. We also apply a standard

regional classification to pigeonhole countries geographically. Additionally, we analyze four

different time series of transnational terrorist events: all incidents, incidents with casualties,

incidents with a U.S. target, and casualty incidents with a U.S. target. A secondary purpose is to

3

draw policy conclusions from the empirical findings.

Our aim is not to establish that income or political systems (constraints) are explanatory

variables for transnational terrorism. Such variables are already related to transnational terrorism

in recent studies by Li and Schaub (2004), Li (2005), and others. Investigating the impact of

these economic and political variables on terrorism is appropriate for panel estimates where the

time period is sufficiently long to allow for their effect. We are, instead, concerned with the

changing venue patterns of terrorist attacks in response to shocks. Events following 9/11, such

as the invasion of Afghanistan and the ongoing war on terror, surely have motivated

grievances and attacks against the coalition of the willing. Moreover, upgrades in homeland

security may have changed terrorist venues.2

Among other things, we find that the rise of fundamentalist terrorism, starting in late

1979, concentrated the distribution of transnational terrorism over time in LICs and those regions

with a large Islamic population. At the time of 9/11, LICs had been experiencing the lions share

of transnational terrorism with relatively few incidents in HICs. After 9/11, there has been a

gradual escalation of attacks with some increase in incidents involving a U.S. target in countries

of all three income classes. These attacks have, however, not occurred on U.S. soil, so that U.S.

homeland security has secured America, but not necessarily Americans. We uncover no clear

evidence of a general transference of attacks from HICs to LICs following 9/11. This is due, in

part, to the low level of terrorism in HICs and the high level in LICs at the time of 9/11; thus,

even a small increase in HIC attacks will appear proportionately large. There is more convincing

evidence of a regional shift in the post-9/11 era with incidents being displaced from Europe and

Africa to the Middle East and Asia, especially when U.S. targets are involved.

Background and Theoretical Considerations

4

Terrorism is the premeditated use or threat of use of violence by individuals or subnational

groups to obtain a political or social objective through intimidation of a large audience beyond

that of the immediate victims. This standard definition rules out state terror, but does not

eliminate state-sponsored terrorism in which a country aids a terrorist group through logistical

support, training, a safe haven, financing, or other assistance (Mickolus, 1989). Terrorists

typically unleash their attacks against a general audience that does not directly make the

decisions that they want to affect. By making attacks appear to be random, terrorists intimidate a

wider audience and create a general anxiety in the targeted country. In response, the country

may expend huge amounts of resources to protect a wide range of vulnerabilities. As a society

becomes more aware of the terrorist threat, homeland security efforts may increase dramatically.

Terrorism falls into two categories: domestic and transnational. Domestic terrorism

involves only the host country so that the perpetrators, victims, financing, and logistical support

are all homegrown. More important, domestic incidents generate implications for just the host

country or its interests. In contrast, terrorist attacks that include perpetrators, victims, targets, or

interests from two or more countries constitute transnational terrorism. The 3/11 bombings are

transnational because they involved Moroccan terrorists on Spanish soil and killed or maimed

victims from a number of countries. The kidnappings of foreign workers in Iraq in 2004 are

transnational terrorist events intended to pressure foreign governments to pull out their troops,

workers, and diplomats. These acts are also meant to keep other governments from assisting the

U.S.-backed fledgling Iraqi government. Clearly, terrorist incidents whose ramifications

transcend the venue country are transnational.

We are particularly interested in investigating transnational terrorism before and after

9/11, insofar as this type of terrorism poses the greatest concern for the global community. At an

earlier time, we would have said that it presented the greatest security challenge to developed

5

countries, but with security upgrades in the United States and some other rich countries,

transnational terrorism is a potential exigency for all countries owing to attack transference. The

dispersed al-Qaida network of affiliated groups heightens the interest in transnational terrorism.

Actions by countries to implement defensive countermeasures are anticipated to influence the

distribution of transnational terrorist attacks across countries. Hence, our focus is solely on this

form of terrorism.

For our theoretical underpinnings, we rely on a choice-theoretic model of terrorist

behavior.3 A terrorist group or network chooses its target country or venue to maximize

expected benefits, U, subject to a resource constraint. In particular, the terrorist groups expected

benefits are derived from attacks against n alternative venues, denoted by Ti, 1,..., ,i n= so that

( )1 2, ,..., .nU U T T T= The terrorist group picks its target venues to

maximize ( )1 2, ,..., ,nU T T T subject to 1

,n

i ii

C T I=

=∑ (1)

where Ci is the per-attack expected costs of targeting country i, Ti is the number of attacks in i,

and I is the resource constraint of the terrorist group. Each Ci is determined by the complexity of

the attack and the countermeasures taken by the authorities. The solution to this problem is to

satisfy

1 1 2 2 ... n nU C U C U C= = = , (2)

subject to the resource constraint, where iU is the terrorists expected marginal benefits

( )iU T∂ ∂ of attacking country i. This solution indicates that anything that lowers (raises) a

single venues expected costs makes that venue more (less) attractive for terrorists to attack

relative to other venues. If the terrorists perceive the marginal benefits from attacking target i

(i.e., Ui) to increase because of new grievances against country i, then, other things constant, this

6

development augments incidents directed at i.

Based on equation (2), when two potential target venues offer the same expected benefits

for the terrorists (i.e., Ui = Uj), then they will pick the venue with the smaller expected costs (i.e.,

the smaller Ci or Cj). Actions by the authorities to harden target i may merely displace the attack

to another country whose Cj is now seen as smaller. The war on terror primarily influences the

terrorists resource constraint by reducing I and making all attacks less likely, or by changing the

relative costliness of attacking particular venues. Heavy-handed countermeasures may raise the

terrorists anticipated expected benefits, thereby making the proactive country a prized target.

When the attack venues imply the same expected costs (adjusted for risks), the terrorists will

choose the location with the greater expected benefits. Because terrorists must trade off

expected benefits and expected costs when deciding attack locations, action by a country to

secure homeland targets may fail to displace the attack abroad if the terrorists sufficiently value

the benefits to offset the greater expected costs. This is an essential insight in understanding the

pattern of attacks under investigation, because it implies that even massive increases in homeland

security need not deter nor deflect an attack at home when the terrorists sufficiently prize a target

i.e., view Ui as sufficiently high. Clearly, al-Qaida would dearly love to execute another attack

on U.S. soil even if it does not rival 9/11. Given these trade-offs of costs and benefits, the

distribution of terrorist attacks based on wealth or enhanced security is ultimately an empirical

question, dependent upon the terrorists perceived benefits and costs. Thus, redoubled efforts by

some rich countries to appear impregnable may merely increase the expected benefits of the

terrorists so that attacks may still occur in fortified countries. In contrast, support networks in

the terrorists home regions may reduce expected costs (Ci) enough or increase I sufficiently so

that some attacks hit foreign targets closer to the home of the terrorists following security

upgrades in the United States and elsewhere.

7

There are two significant developments prior to 9/11 that have influenced the pattern of

transnational terrorism and that must be taken into account in our post-9/11 investigation. The

first is the rise in fundamentalist-based terrorism. Hoffman (1998) places this rise at the fourth

quarter of 1979 (i.e., 1979:4) owing to the November 4, 1979, takeover of the U.S. embassy in

Tehran and the December 25, 1979, Soviet invasion of Afghanistan. Since 1980, the number of

religious-based terrorist groups has increased as a proportion of active terrorist groups: 2 of 64

in 1980; 11 of 48 in 1992; 16 of 49 in 1994; and 25 of 58 in 1995 (Hoffman, 1997:3). The

proportion of incidents with deaths or injuries increased by 17 percentage points after the onset

of fundamentalist terrorism (Enders and Sandler, 2000). Unlike the left-wing terrorists who were

the dominant influence until the 1990s, fundamentalist terrorists have resorted to suicide

missions, which are on average over thirteen times more deadly than other terrorist attacks (Pape,

2003).4 The rise of fundamentalist terrorism is anticipated to increase incidents with casualties

after 1979:4. This increase is anticipated to be unevenly distributed among countries, with the

greatest impact on LICs, where fundamentalist terrorists have greater support networks. When

geographical considerations are also taken into account, we expect that fundamentalist terrorism

will impact those regions i.e., the Middle East, Eurasia, and Asia with large Moslem

populations, since the marginal costs of terrorism there will be relatively less and resources more

plentiful.

The second pre-9/11 development is the end of the Cold War during the last quarter of

1991 with the demise of the Soviet Union and communist regimes in Eastern Europe. Their

demise removed some of the avid state-sponsors of terrorism (Wilkinson, 1992), because these

countries no longer had a reason to destabilize Western countries. This reduction in support

limits terrorist resources and, therefore, the number of attacks. In the late 1980s and early 1990s,

a number of European countries (e.g., France, Belgium, Germany, Spain, and the United

8

Kingdom) captured and brought to justice left-wing terrorists (Alexander and Pluchinsky, 1992;

Clutterbuck, 1992). In the early 1990s, there was also a collective initiative by the EU to take a

united front against terrorism (Chalk, 1994; Wilkinson, 1992). These events coming around the

end of 1991 have been shown to decrease the amount of transnational terrorism (Enders and

Sandler, 1999, 2000). Thus, any analysis of post-9/11 terrorism must account for this structural

shift at the start of the post-Cold War era.

Data

The data on transnational terrorist incidents are drawn from International Terrorism: Attributes

of Terrorist Events (ITERATE), which records the incident date, its location, number of deaths,

number of injured, and other variables (Mickolus et al., 2004). For location, ITERATE records

the starting country location of the terrorist attack only 47 out of 12,569 transnational incidents

had no start location listed and these 47 events are excluded from our statistical analysis.

Variable 28 of ITERATE indicates the type of U.S. target (i.e., commercial property, military

installation, diplomatic, U.S. government, or nonofficial), while variables 34 and 39 denote the

number of Americans wounded or killed, respectively. Thus, we can distinguish not only attacks

against U.S. interests but also attacks with U.S. casualties. ITERATE data are derived from the

worlds newsprint and electronic media with a heavy reliance until 1996 on the Foreign

Broadcast Information Service (FBIS) Daily Reports, which survey a couple hundred of the

worlds major newspapers and related sources. By splicing together previous ITERATE data

sets, ITERATE 5s common file contains over 40 key variables common to all transnational

incidents from 1968:1 to 2003:4. ITERATE excludes actions involving insurgencies, declared

wars, or an occupying force. Thus, roadside bombs against coalition forces in Iraq after the end

of the Iraq War in 2003 are not recorded as transnational terrorism, but the kidnappings of

9

foreign workers in Iraq are included. ITERATE coding conventions are nearly identical to those

of the U.S. Department of State.

In total, we extract four quarterly time series from ITERATE. We use a quarterly, rather

than a more disaggregated time interval, to minimize periods with zero or near-zero

observations, which would violate the underlying normality assumption upon which our

inferential techniques rest. The ALL incident time series includes the quarterly totals for all

types of terrorist incidents for the 1968:1-2003:4 sample period. A second time series is the

casualty series, which contains all incidents with either a death and/or injury. We include two

series involving all targeted countries because the rise of fundamentalist terrorism and the other

shocks analyzed may result in non-U.S. targets being attacked. For example, coalition-of-the-

willing countries are prone to al-Qaida attacks after 9/11. Moreover, fundamentalist terrorists

have grievances with a host of countries, including the United Kingdom, Spain, France, and

Israel. Approximately 60% of all transnational terrorist attacks is directed at non-U.S. targets.

Incidents with a U.S. target (i.e., a U.S. citizen or property) are a subset of the series with all

incidents, while casualty incidents with a U.S. target are a subset of either the casualty series or

the U.S. target series. These series are included to examine whether post-9/11 homeland security

upgrades in the United States may have shifted attacks against U.S. interests to other countries.

The two U.S. series can be thin in terms of zero or near-zero quarterly totals for some income

classes or geographical regions. This problem is then a concern that we address with appropriate

econometric procedures.

To examine the distribution of terrorism across countries income classes, we first use the

World Banks classification of countries into low, middle, and high per capita income nations.

Although income groupings are described in detail in each issue of the World Banks (various

years) World Development Report,5 we mention some of the key features of the classification

10

scheme. All World Bank member countries and others with populations in excess of 30,000 are

divided into three primary income groups LICs, MICs, and HICs. For 2000, LICs had a per

capita Gross National Income (GNI) of $755 or less, MICs had a per capita GNI greater than

$755 and less than or equal to $9,265, and HICs had a per capita GNI in excess of $9,265. These

dollar figures are adjusted annually to account for changes in a number of economic

circumstances including inflation, overall living standards, and exchange rates. Country codes

from ITERATE for location start of incidents allow us to associate terrorist events location to

the countrys income classification. Similarly, we can match terrorist events to other country

taxonomies described below.

In constructing our time series, we take account of the fact that individual nations may

switch among the three income groups. As a result of economic growth, the number of nations

included in the HIC group has generally increased, thereby working against a possible

transnational terrorism substitution from HICs to LICs. For instance, Algeria and Mexico moved

from the LIC group to the MIC group, whereas, Israel, Portugal, and Spain switched from the

MIC group to the HIC group owing to high per capita income growth. In the late 1980s, Poland

moved in the opposite direction from the class of MICs to LICs when it was a transition

economy, but returned to the MIC group in the mid-1990s.

When matching countries to terrorist attacks and income classes, we also had to adjust for

changes in the political map of Eastern Europe, Africa, and elsewhere over the entire sample

period. Prior to its division, ITERATE records terrorist incidents occurring in Czechoslovakia;

after its split, ITERATE separately keeps track of terrorist events in the Czech Republic and the

Slovak Republic. With respect to the Soviet Union, incidents before the breakup are attributed to

the U.S.S.R., while after the breakup they are assigned to the relevant new nations (e.g.,

Ukraine). The U.S.S.R. presents a potential concern because early issues of the World

11

Development Report recorded the per capita GNI of the U.S.S.R. as greater than that of Hong

Kong, Greece, or Spain. The accuracy of Soviet GNI data is doubtful, because it was artificially

inflated as a political tool in the Cold War. This does not present a real problem for our study,

because much of the focus is on the post-Cold War period. Moreover, throughout the sample

period, there were very few transnational terrorist incidents in the U.S.S.R. for example, just

four from 1980 to 1987.

For geographical groupings, we apply the regional classifications given in the U.S.

Department of State (2003) Patterns of Global Terrorism. These six regions are the Western

Hemisphere (North, Central, and South America), Africa (excluding North Africa), Asia (South

and East Asia, Australia, and New Zealand), Eurasia (Central Asia, Russia, and the Ukraine),

Europe (West and East Europe), and the Middle East (including North Africa). This partition of

countries puts most of the Islamic population into the Middle East, Eurasia, and Asia. The

geographical division does not correlate with the income taxonomy, so that geography is likely

to display different substitution possibilities before and after 9/11. The lack of correlation will

become apparent in the graphs displayed in the subsequent sections.

Distribution of Terrorist Incidents by Income Classes

Figure 1 displays four panels for the location of terrorist incidents by income groups for the

sample period, 1968:1-2003:4. In each panel, the quarterly number of incidents is measured on

the vertical axis, whose scale may differ between panels. Panel 1 depicts the quarterly total of all

incidents, while panels 2 to 4 show quarterly incident counts occurring in LICs, MICs, and HICs,

respectively. All four time paths indicate a decline around the start of 1992, during the start of

the post-Cold War era (Enders and Sandler, 2000). The panels also show an increase in incidents

following 9/11, with LICs and MICs displaying a more marked increase. In Figure 2, we display

12

the quarterly time series for terrorist incidents with one or more casualties for the entire sample

and the three income groups. For LICs, casualty incidents rose since the start of fundamentalist

terrorism in 1979:4 until 1992 when it started to decline. Following 9/11, there has been an

upward trend in casualty incidents, especially in LICs. The four panels of Figure 2 display that

LICs experienced by far the largest number of casualty incidents among the three income

classes.

[Figures 1 and 2 near here]

In Figure 3, the four quarterly time series are depicted by income group for terrorist

incidents against a U.S. target. Panel 2 shows that LICs generally suffered the largest number of

such attacks. There is also a somewhat more pronounced increase in these incidents in LICs

after 9/11 compared with the other income groups. When the time series for casualty incidents

against a U.S. target are plotted (not shown), there is also a marked upward trend of such attacks

in LICs.

[Figure 3 near here]

A useful way to simplify the long-run movements in these time series is to examine the

proportion of incidents staged in the LIC group. Figure 4 presents the proportion of each

incident type occurring in this income class. Because the proportions can be quite erratic, we

smoothe each series using a one-period lead and lag. If, for example, tx denotes the total

number of incidents of a particular type that occurs in period t, and ty represents the number of

incidents of that type that takes place in the LIC group in period t, the proportion of that incident

type in the LIC group ( )tp in period t is constructed as:

( ) ( )1 1 1 1 .t t t t t t tp y y y x x x+ − + −= + + + + (3)

In Figure 4, panels 1 to 3 indicate a clear upward trend in the proportion of all incidents,

13

casualty incidents, and incidents with a U.S. target taking place in the LIC group.6 Although

there are now more casualty incidents with a U.S. target in LICs compared with earlier periods,

there is no clear upward trend for this series since 1979 (see panel 4). An interesting feature of

all four proportion series is that all experienced a sharp decline around 1999 and a sharp rise

following 9/11. The magnitude of the rebound is, however, smaller than the 1999 decline; thus,

the proportion of terrorist incidents in LICs is greater in the late 1990s than after 9/11.

[Figure 4 near here]

Table 1 reports four descriptive statistics for the four quarterly time series for several

essential time periods. For example, the mean number of ALL incidents is 66.4 per quarter for

the time period between the end of the Cold War and 9/11 (1992:2-2001:2). Over the same time

period, the quarterly means for the LIC, MIC, and HIC groups are 42.9, 5.7, and 17.8 incidents,

respectively. We also list four descriptive statistics for each of the four time series in the nine

quarters prior to 9/11 and the nine quarters following 9/11. Table 1 also reports the proportion of

terrorist incidents occurring in LICs. Prior to 9/11, 74.3% of these incidents took place in LICs,

while following 9/11, only 57.0% occurred in LICs.

[Table 1 near here]

In contrast to the visual impressions of Figures 1 through 4, there appear to be only

modest differences in the pre-9/11 and post-9/11 series. The mean of the series including all

incidents rises from 42.3 to 46.6 incidents per quarter following 9/11; thus, the overall level of

terrorism rises by 10%. There is an interesting and unexpected change in the composition of

incidents by income categories. After 9/11, the mean number of incidents in LICs falls by 6.8

per quarter, while this mean in HICs rises by 7.3 per quarter. A more pronounced increase

characterizes incidents with casualties where the worlds mean rises from 12.9 incidents per

quarter before 9/11 to 20.6 incidents per quarter after 9/11. Although the overall level of

14

terrorism increases, the proportion of incidents with casualties in LICs falls from 72.2% to

67.9%. There is a 44% increase worldwide in the mean number of incidents with a U.S. target

(24.1/16.7 = 1.44) following 9/11, and more than a threefold increase in the mean number of

casualty incidents with a U.S. target (9.4 versus 2.6 incidents per quarter) following 9/11.

Because these incidents are not occurring in the United States, Americans may be safer at home

but not abroad in the aftermath of 9/11 and its security increases. About half of this increase

4.8 incidents per quarter occurred in LICs.

Statistical Analysis

Visual impressions and simple descriptive statistics do not replace formal inferential statistics.

Consider the increase in the number of casualty incidents in LICs that took place after 9/11.

Because this series is characterized by a number of increases and decreases, we must ascertain

whether this particular increase is statistically significant or just a random occurrence. To

determine whether the various incident series behaved differently following 9/11, we first

estimate each time series as an autoregressive (AR) process. Consider the AR(p) model:

1 2 3 41

,p

t i t i P L ti

y c a y FUND POST D Dα α α α ε−=

= + + + + + +∑ (4)

where p is the number of lags, ty is the number of incidents of a particular type in period t, c is a

constant, ia s and isα are undetermined coefficients, and ε is an error term. Equation (4) is a

standard autoregressive model augmented by four dummy variables. DP and DL are dummy

(intervention) variables representing potential impacts of 9/11. DP is a pulse dummy that equals

1 if t = 2001:3 and 0 otherwise. A pulse intervention variable is appropriate if the 9/11 attack

induced a temporary change in the ty series. The magnitude of 3α indicates the initial effect

15

of 9/11 on the time series, and the rate of decay of this impact, if any, is determined by the

characteristic roots of equation (4). To allow 9/11 to have had a permanent effect on yt, we

include a level dummy variable such that DL is 0 for t < 2001:3 and is 1 for 2001:3t ≥ . The

immediate impact of 9/11 on ty is given by 4α , and the long-run effect is given by

( )4 1 iaα −∑ . We also include dummy intervention variables to control for the rise of religious

fundamentalism (FUND) and the post-Cold War era (POST). As identified by Enders and

Sandler (2000), FUND is a dummy variable taking a value of 1 beginning in the last quarter of

1979, and POST is a dummy variable taking a value of 1 beginning in the last quarter of 1991.

For each series, the lag length is selected by the Schwartz Bayesian Criterion (SBC). We

perform the tests without including time as a regressor, because there is no evidence of a

deterministic trend in any of the incident series.

Because we use count data and some of the time series are thin, we also obtain the

maximum likelihood estimates for thin series using a Poisson distribution. This distribution is

often used to model discrete variables that possess a reasonable number of observations near the

lower zero bound. For a given set of regressors xt, the Poisson model assumes that yt is

distributed with a probability density function:

( ) ( )! .tt t t tf y x e yµ µ−= (5)

A Poisson distribution rules out negative realizations of yt. As is easily demonstrated, the

conditional mean t tE y x is .tµ We model this mean as:

( ) 1 2 3 41

exp ln ,p

t i t i t i P Li

c a y bI FUND POST D Dµ α α α α− −=

= + + + + + +

∑ (6)

where t iI − is an indicator function that equals 0 if 0t iy − > and 1 if 0.t iy − = The indicators

parameter is estimated using a grid search over the interval 0.1 0.9.b≤ ≤

16

Equations (4) and (6) are similar in that FUND, POST, DP, and DL can all affect the mean

of yt. Unlike equation (4), we permit the mean to be influenced by ln(yt-i) instead of the level of

yt-i. The rationale for this specification is to prevent the ty sequence from becoming

explosive. The logarithmic specification, however, mandates replacing zero values of yt-i with

some positive number b. Another way to understand the issue is to rewrite equation (6) in the

multiplicative form,

( ) [ ]1 2 3 41

exp .ip

a

t t i P Li

y c FUND POST D Dµ α α α α∗−

=

= • + + + +∏ (6′)

In equation (6′), 0t iy∗− = is an absorbing state. For ,i p≤ the expected value of ty is zero when

any value of t iy∗− is zero. Insofar as the ty cannot be negative, the probability of a positive value

of ty is then zero. To rule out such an undesirable implication of the model, a small positive

value (i.e., b) is added to zero values of t iy∗− by equation (6).

Although we do not provide a complete discussion of the alternative models, some

comparison of the ordinary least squares (OLS) and Poisson estimation methodologies is in

order. Given that equation (4) contains the appropriate specification of the mean, the coefficient

estimate using OLS can be consistent, but any confidence interval constructed using a t-

distribution may be severely distorted if the time series has zero or near-zero values. To assist

making appropriate inference, we report t-statistics based on robust standard errors. As shown in

equation (6) or (6′), the Poisson model is nonlinear so that the coefficients do not have a

straightforward interpretation. Moreover, the specification in equation (6) and the need to add b

to zero values of t iy∗− seem ad hoc. In a related point, the mean and variance of a Poisson-

distributed variable are identical. When the variance of ty is substantially greater than the mean,

some researchers replace the Poisson distribution with a negative binomial. As shown in Table

17

1, most of the series exhibit no evidence of excess volatility in terms of their variance.

Given the limitations of the Poisson model, we typically report the OLS estimates with

robust standard errors. When, however, a time series is especially thin, we report the Poisson

estimate. If there are important differences between the OLS and the Poisson estimates, we

report the results of both.

Results

For each sample of countries, the results of the estimations for the four different incident types

are displayed in Table 2 below the corresponding series name. Our four samples include all

countries (WORLD) and the countries in the three designated income classes of the World Bank

(various years). The entries for WORLD are the sums of the associated incidents occurring in

the countries within the three income classes. Column 2 indicates the estimation method;

column 3 reports the number of lags; column 4 displays the pre-intervention intercept, c; and

columns 5 through 8 list 1α through 4α estimates. Column 9 reports the estimated long-run

(LR) value of the effect of DL as ( )4 1 21 ... ,pa a aα − − − − and column 10 indicates the prob-

value of the F-test for the joint hypothesis that 3 4 0α α= = , i.e., for the null hypothesis that 9/11

did not have any significant impact on global terrorism patterns. Finally, column 11 displays the

prob-value of the Ljung-Box Q-statistic using 4 lags of the residuals. The coefficients t-

statistics, calculated using robust standard errors, are depicted in parentheses beneath each

estimated coefficient.

[Table 2 near here]

To explain Table 2s entries, we first consider the estimates for the worldwide sample for

the ALL incident series. Because this series is quite thick (see panel 1 in Figure 1 where no

18

quarterly total approaches zero), we report only the OLS results using a lag of one. The rise of

fundamentalism increases the series intercept by 25.68 incidents per quarter, while the end of

the Cold War (POST) decreases the intercept by 37.35 incidents per quarter. Both of the t-

statistics (2.98 and −3.49) exceed 1.96 in absolute value so that these two dummies are

statistically significant at the 5% level. The estimated coefficients on DP and DL are −30.13 and

−13.26, respectively, with t-statistics for 3α and 4α of −3.34 and −1.18. Moreover, the F-

statistic for the joint restriction that 3 4 0α α= = has a prob-value of 0.00; thus, we can conclude

that the decline in the number of incidents following 9/11 had a statistically significant

temporary, but not permanent component. Diagnostic checks indicate that the model is

adequate; for example, the reported prob-value for the Ljung-Box Q-statistic using 4 lags of the

residuals is 0.20.

For the time series with all incidents, the OLS estimates for the three income classes

indicate that FUND caused a significant increase in transnational terrorism of 27.56 incidents per

quarter for LICs, a significant decrease of 4.75 incidents per quarter for MICs, and no significant

change for HICs. Clearly, the influence of fundamentalist terrorism is income sensitive,

probably given the distribution of fundamentalist populations. All three income classes

experienced a significant decline in transnational terrorism in the post-Cold War period: 14.24

fewer incidents per quarter for LICs, 8.03 fewer incidents per quarter for MICs, and 13.80 fewer

incidents per quarter for HICs. There is no evidence of a substitution in overall transnational

terrorism from HICs to LICs following 9/11. In fact, the coefficients for both DP and DL are

negative and significant only for only LICs. Any long-run impact of the post-9/11 worldwide

decline in terrorist attacks was concentrated in LICs. The MIC sample experienced a temporary

fall in transnational terrorism, while the HIC sample did not register any significant effect as a

19

result of 9/11.7 The latter result indicates that any increased marginal costs from bolstered

homeland security in the HIC sample balanced any greater perceived marginal benefits that

terrorists derived from attacking these countries directly.

For the casualty series, there is little measurable influence of rise of fundamentalism or

the end of the Cold War on the income-based distribution of incidents. The sole exception is the

statistically significant decrease of 1.16 incidents per quarter in MICs as a result of the rise in

fundamentalist terrorism. A key finding is that there is no long-run impact of 9/11 on any of the

four samples. The two statistically significant coefficients of DP are −6.78 and 4.38 for LICs and

HICs, respectively. This result suggests an immediate and temporary switch in the composition

of casualty incidents from LICs to HICs, perhaps as groups sympathetic to al-Qaida tried to raise

anxiety in high-income countries in the wake of 9/11, as their perceived marginal benefits

increased in HIC venues.

Next, we turn to incidents with a U.S. target. For the OLS results, fundamentalist

terrorism had little influence except for a marginally significant increase in LICs, while the end

of the Cold War resulted in significant decreases for all four samples with the largest decrease

occurring in HICs. There was a significant temporary decline in terrorism following 9/11 of

17.44 incidents per quarter associated with the WORLD sample, where most of this decrease

(i.e., 12.54 fewer incidents per quarter) was concentrated in LICs. For the OLS estimates, DL is

only significant for the HIC sample. The Poisson estimates for the thin MICs and HICs series

reflect a small, but significant, positive coefficients for DL.

The casualty series with a U.S. target is particularly thin for the three income classes;

thus, the Poisson estimates are reported. For LICs, we also display the OLS estimates since the

OLS and Poisson results differ for DP and DL. The primary finding concerns the long-run impact

of 9/11. The OLS estimate of 4α for WORLD is 4.58 additional incidents per quarter with a t-

20

statistic of 2.26. The value of 4α for LICs is 3.45 additional incidents per quarter and the t-

statistic is 2.21. Most of the OLS-identified increase in attacks involving U.S. casualties was in

LICs, consistent with the greater concentration of U.S. targeted incidents in LICs owing to lower

anticipated marginal costs. The Poisson estimates of 4α are, however, positive and significant

for all income groups.

Alternative Search for Income-Based Substitution

To show the robustness of our income-based results, we apply an alternative partition of

countries into income classes that does not rely on the World Bank tripartite classification based

on cutoff per-capita GNI levels. We assign the 31 countries with the highest per capita GNI

according to the World Bank (2000) to the HIC group and all others to the LIC group. These 31

HICs include most member states of the Organization of Economic Cooperation and

Development (OECD) plus some other countries.8 Table 3 displays summary statistics for the

LICs, HICs, and LICs/WORLD based on the new partition for the four time series. Most

transnational terrorism had been staged in LICs during the 1990s. Prior to 9/11, HICs

experienced just 5.6 incidents per quarter on average, while LICs suffered 37.3 incidents per

quarter on average. During the nine quarters following 9/11, the quarterly mean rose in HICs

and fell slightly in LICs. Incidents with casualties are associated with an increase in their

quarterly means in both LICs and HICs after 9/11. A similar pattern holds for the two time

series involving a U.S. target, with a large apparent substitution to LICs for casualty incidents

with a U.S. target after 9/11. These impressions are now tested with the AR intervention model

represented in equations (4) and (6) above.

[Table 3 near here]

21

Table 4 indicates the empirical results. When countries are partitioned in this new

fashion, the rise of fundamentalism had virtually all of its impact in LICs for all incidents and

those involving casualties. The rise of fundamentalist terrorism is associated with a large and

statistically significant increase in transnational terrorism attacks in LICs of 24.38 incidents per

quarter. Casualty incidents rose by 3.24 per quarter in LICs. A similar finding holds for casualty

incidents with a U.S. target: The coefficient for fundamentalism is positive and significant for

the Poisson test, and positive and marginally insignificant for OLS. Thus, our new partition

shows that the impact of fundamentalism was entirely based in LICs. A different pattern

emerges with respect to the decline in transnational terrorism in the post-Cold War period. For

the ALL incident series, the decline was virtually evenly split between LICs and HICs. The only

significant POST decline for incidents with casualties occurred in HICs. Following the Cold

War, there was a significant decline in incidents with a U.S. target for both income classes, with

the biggest drop characterizing HICs. This was also the case for casualty incidents with a U.S.

target. Thus, the worlds richest countries experienced the largest decline in deadly transnational

terrorism following the end of the Cold War but prior to 9/11, as state-sponsorship declined and

terrorist resources fell.

[Table 4 near here]

A mixed picture emerges with respect to the influence of 9/11. Immediately following

9/11, the total number of incidents fell by 27.79 per quarter in LICs, but displayed no significant

change in HICs. Moreover, neither income class experienced a permanent impact in total

terrorism after 9/11 − i.e., the coefficient on DL is not significant. For incidents with casualties,

there was an immediate decrease of 8.45 incidents per quarter in LICs and an increase of 4.30

incidents per quarter in HICs , almost equal to the four hijackings on 9/11. There was again no

permanent 9/11 influence. Both series involving U.S. targets fell in LICs temporarily after 9/11.

22

However, incidents with a U.S. target increased permanently by 3.92 incidents per quarter in

HICs following 9/11. The Poisson result reinforces this finding. For casualty incidents with a

U.S. target, most of the worldwide increase of 4.59 incidents per quarter was in LICs where such

incidents rose by 3.56 incidents per quarter. Although there was also an increase in such

incidents in HICs, this increase was more modest, judging from the OLS results. Thus, there was

a greater concentration of deadly post-9/11 incidents involving a U.S. target in LICs, consistent

with the earlier findings and the view that homeland security upgrades in rich countries protected

Americans there. There is, however, an increased risk for American interests in LICs following

9/11 from transference of attacks.

The Distribution of Terrorism across Regions

The six panels of Figure 5 depict the time series with all incidents for the six designated regions.

Panels 1 and 2 show a sustained decrease in transnational terrorism beginning in the early 1990s

for the Western Hemisphere and Europe, respectively. In panel 3, the Middle East displays an

increase in transnational terrorism for the start of the 1990s, followed by a fall around 1993 and

then an increase around 9/11. A similar increase occurs for Asia following 9/11 in panel 4. In

panels 5 and 6, there is a jump in transnational terrorism in Africa and Eurasia at the start of the

1990s, followed by decreases and increases over the ensuing years. Some of the regional

incident patterns in Figure 5 (see, especially, Africa, Eurasia, and the Middle East) do not match

those in Figure 1 when countries are partitioned by income classes. Hence, the geographical

identification provides new insights on attack patterns.

[Figure 5 near here]

Figure 6 depicts the casualty series for the six geographical regions. The most striking

feature is the sharp upward trend in these terrorist incidents in the Middle East starting in 2000,

23

with a pronounced increase following 9/11. Much smaller increases characterize the other

regions. In Asia (panel 4), the increase in terrorist incidents after 9/11 is followed by a decrease.

Some of the series, especially that of Eurasia, may be too thin to conduct meaningful statistical

analysis.

[Figure 6 near here]

Table 5 reports that the descriptive statistics for three periods for the four incident series

and the six geographical regions.9 We focus our remarks on the time series that includes all

incidents. For the 1992:2-2001:2 period, Europes mean of 19.27 incidents per quarter exceeds

that of the other regions. The quarterly mean of terrorist incidents in the Western Hemisphere

(11.84), Africa (10.05), the Middle East (12.92), and Asia (9.76) are all quite similar; there are,

however, some contrasting regional changes for the two time intervals surrounding 9/11. In the

nine pre-9/11 quarters, the Western Hemisphere and Africa experienced an average of 12.33 and

9.44 incidents per quarter, respectively; in the nine post-9/11 quarters, the Western Hemisphere

and Africa experienced an average of 5.33 and 2.44 incidents per quarter, respectively. These

are rather drastic declines. In sharp contrast, the Middle East and Asia had incident means that

rose very sharply from 4.78 and 7.78 to 15 and 13 incidents per quarter, respectively, for the

same comparison intervals. The mean number of European incidents showed a modest rise from

6.33 to 10.78 incidents per quarter.

[Table 5 near here]

In the casualty series, the Middle East displayed the largest change on either side of 9/11

a rise of almost 8.5 incidents per quarter. In contrast, Africas casualty series fell by 2.78

incidents per quarter. For incidents with a U.S. target, the Western Hemisphere experienced a

reduction of 5.89 incidents per quarter when the periods on either side of 9/11 are compared.

Europe, the Middle East, and Asia, however, attracted more U.S.-targeted events following 9/11.

24

This same pattern held for the Middle East and Asia for casualty incidents with a U.S. target.

To formalize these impressions, we again conduct an AR intervention analysis for each

incident type in each region.10 The empirical results are summarized in Table 6. For all

incidents, the rise of fundamentalism was associated with a significant increase in terrorism in

Africa, Asia, and the Middle East, but not in the other three regions. The increase is greatest in

the Middle East. The post-Cold War period is associated with less transnational terrorism in the

Western Hemisphere, Europe, the Middle East, and Asia, which is due, in part, to the reduced

sponsorship by the Soviet-bloc countries and the demise of many left-wing European groups

(Enders and Sandler, 1999). In contrast, Eurasia had more terrorism during the post-Cold War

period, a result characteristic of fledgling democracies (Eubank and Weinberg, 1994). Africa,

the Middle East, and Asia experienced a significant immediate decline in terrorism following

9/11, as shown by the estimate of the DP coefficient. The Western Hemisphere, Eurasia, and

Africa had a significant long-term decrease in terrorism after 9/11. Asia showed a significant but

small increase. When these results are evaluated in conjunction with Table 5, there is strong

evidence that all regions experienced on balance a post-9/11 decline in terrorism due, in part, to

the war on terror and attacks against al-Qaida and associates.

[Table 6 near here]

The empirical results for the casualty series are similar to those for the ALL incident

series. The increase in fundamentalism was associated with a significant increase in casualty

incidents in Africa, the Middle East, and Asia. For the latter two regions, there are strong

fundamentalist populations and influences. The post-Cold War era experienced a significant fall

in casualty incidents in the Western Hemisphere and a significant rise in Eurasia. The various

results for Europe are ambiguous since the OLS and Poisson estimates have some marked

differences: e.g., the coefficient for the post-Cold War era (POST) is negative and insignificant

25

for OLS, but negative and significant for Poisson. The Western Hemisphere displays a positive

and significant temporary increase in casualty incidents during the post-9/11 period. The Middle

East and Asia experienced a temporary drop in these events after 9/11. The OLS estimates show

that no region displayed a permanent and significant change (at the 5% level) in casualty

incidents following 9/11. The decline for Europe is only significant for the Poisson estimation.

Overall, there is less evidence of a permanent 9/11-induced fall of casualty events compared with

ALL events. This finding is consistent with transnational terrorist incidents remaining deadly in

the post-Cold War era.

Interestingly, the rise of fundamentalism is not associated with a significant effect on the

number of incidents against U.S. interests in any region but Eurasia, where there is a negative

and significant impact. The positive influence of fundamentalist terrorism in Asia is almost

significant at the 5% level. The end of the Cold War or POST resulted in region-specific

differences: There is a negative and significant impact in the Western Hemisphere, Europe, the

Middle East, and Asia. Again, these findings can be partly explained by reduced state-

sponsorship of terrorism and the demise of many left-wing groups in Europe. In contrast, the

end of the Cold War is tied to a rise in incidents involving U.S. targets in Eurasia and Africa,

where there was greater political instability in the 1990s. The pulse dummy for 9/11 indicates a

negative and significant fall in U.S.-targeted events in Europe, the Middle East, and Asia.

During the post-9/11 period, there are marginally significant permanent declines in incidents

involving U.S. targets in the Western Hemisphere and Africa. There is, however, a significant

positive increase in the coefficient for DL in the Middle East. This result is strongly suggestive

of a transfer of U.S.-targeted events from North America and other venues to targets in the

Middle East, in keeping with the terrorists responding to augmentations in U.S. homeland

security.

26

Finally, we turn to the regional effects tied to casualty incidents with a U.S. target. In

Table 6, the rise in fundamentalism is not associated with any significant changes in these

incidents. In contrast, POST leads to significant drops in these events in the Western

Hemisphere and Europe. The so-called peace dividend derived from the end of the Cold War

involved not only reduced military spending but also a decrease in terrorism directed at U.S.

interests owing to less state-sponsorship. There is, however, a significant increase in such events

in Africa following the end of the Cold War. The 9/11 pulse coefficient reflects a temporary but

significant rise in casualty incidents with a U.S. target in the Western Hemisphere and a

significant decrease in the Middle East and Asia after 9/11. More important, the level impact of

9/11 is quite different: Both the Middle East and Asia experienced a significant increase in these

events, while Africa experienced a marginally significant decrease. For the Middle East and

Asia, we again see a geographical switch of venue following 9/11 possibly coinciding with

increases in security in the wealthy countries and the associated increases in the costs of carrying

out an attack Ci.

Concluding Remarks

We apply time-series methods to identify shifting patterns of transnational terrorism across

countries income classes and geographical distribution in response to three defining events.

Intuition and eyeballing of data may give different impressions than careful statistical analysis

that controls for important interventions such as the rise of fundamentalism, the end of the Cold

War, and 9/11. Although intuition suggests a substitution of terrorist events from rich to poor

countries in response to 9/11-motivated increases in homeland security in some rich countries

(especially the United States and the EU) and the terrorists hunt for soft targets, we find no

convincing evidence of this shift except for incidents with U.S. casualties. Our failure may be

27

due to offsetting factors (i.e., increased marginal costs and higher marginal benefit of terrorist

incidents) or the rather low beginning GNI per capita level for designating HICs and MICs. To

address the latter concern, we reclassify HICs as those with the 31 highest per capita GNIs and

look for a transference of terrorist events after 9/11 from HICs to LICs. Again, we find no

evidence of an income-based transfer in the anticipated direction except for incidents with U.S.

casualties, so that our results are robust to an alternative income taxonomy.

When countries are classified into six regional groups, there is evidence of shifting

venues based on geography. For terrorist incidents with a U.S. target, a clear transference away

from the Western Hemisphere and Africa to the Middle East and Asia is uncovered. In addition,

the augmenting influence of the rise of fundamentalism on transnational terrorists was greatest in

the Middle East and Asia, where there are large Islamic populations. The end to the Cold War

and the breakup of the Soviet Union reduced transnational terrorism in most regions except

Eurasia, where it has increased with augmented political instability. The effects of

fundamentalism and the end of the Cold War on terrorism differed markedly between income-

based and geographically based partitions of countries.

While Americans are safer at home owing to enhanced homeland security, the

vulnerability of U.S. citizens and property abroad has increased following 9/11. This

vulnerability probably also applies to other prime-target countries, particularly those identified as

assisting the U.S. agenda in the Middle East. The U.S. policy to assist LICs that request help11

does not go far enough given the changing post-9/11 pattern of the transnational terrorism aimed

at U.S. targets. Soft targets can exist anywhere and our analysis identifies increased post-9/11

attacks not only in HICs but also in the Middle East and Asia. Thus, U.S. assistance must

account for changing patterns of attacks against U.S. and other interests. Our study shows that

this pattern may go against intuition owing to opposing considerations and be more

28

geographically based. For example, post-9/11 attacks in Saudi Arabia have involved a wealthy

Middle East country. Todays fundamentalist terrorism is shifting to the Middle East and Asia,

where large support populations exist and terrorists do not have to transcend fortified borders to

attack U.S. and Western interests. Thus, regions that once experienced greater spillover

terrorism from the Middle East and Africa (e.g., Europe in the 1980s) may want to reallocate

some homeland security spending to these regions to protect their interests.

Our time-series analysis identifies where the United States and the international

community need to direct their security efforts in light of recent events. In a globalized world

with transnational terrorism, countries must realize that terrorists will react to homeland security

upgrades by identifying weaker links abroad. The ability to shore up the weakest links

worldwide requires collective action beyond efforts observed to date. Such actions are prone to

free riding as countries wait for the prime-target countries to act. Past events the rise of

fundamentalist terrorism and the end to the Cold War demonstrate that transnational terrorism

patterns can change rather drastically. Both events have had a greater influence on patterns than

9/11. Moreover, this change in terrorism patterns may be geographically, rather than income

driven. There is clearly a need to keep track of such changes if defenses are to be appropriately

deployed.

29

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Li, Quan, and Drew Schaub (2004) Economic Globalization and Transnational Terrorism.

Journal of Conflict Resolution 48:230−258.

Mickolus, Edward F. (1989) What Constitutes State Support to Terrorists? Terrorism and

Political Violence 1:287−293.

Mickolus, Edward F., Todd Sandler, Jean M. Murdock, and Peter Flemming (2004) International

Terrorism: Attributes of Terrorist Events, 1968-2003 (ITERATE 5). Dunn Loring, VA:

Vinyard Software.

Pape, Robert A. (2003) The Strategic Logic of Suicide Terrorism. American Political Science

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Quillen, Chris (2002) A Historical Analysis of Mass Casualty Bombers. Studies in Conflict &

Terrorism 25:279−292.

Sandler, Todd, and Walter Enders (2004) An Economic Perspective on Transnational Terrorism.

European Journal of Political Economy 20:301−316.

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Sandler, Todd, John Tschirhart, and Jon Cauley (1983) A Theoretical Analysis of Transnational

Terrorism. American Political Science Review 77:36−54.

U.S. Department of State (1988, 2003) Patterns of Global Terrorism. Washington, DC: U.S.

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Wolgast, Michael (2002) Global Terrorism and the Insurance Industry: New Challenges and

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Wirtschaftsforschung) Workshop, The Economic Consequences of Global Terrorism,

June 14−15, Berlin.

World Bank (1978, 1980, 1990, 1995, 2000) World Development Report. New York:

Oxford University Press.

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Notes

1. The April 10, 1992, bombing of the London financial district by the Irish Republican

Army caused $2.9 billion of losses, making it the most costly terrorist incident prior to 9/11.

2. In the United States, homeland security involves securing targets at home (Enders and

Sandler, 2006: Chapter 10). Upgrades to U.S. embassies and military installations abroad started

in 1976 and 1985, well before 9/11 (Enders and Sandler, 1993). For the United States, except for

a few years, there is no homeland security expenditure data; thus, we cannot explicitly add this

variable. We can, however, infer that rich countries are more able to afford homeland security.

Moreover, some wealthy nations (e.g., Israel, Spain, the United Kingdom, and the United States)

are motivated to augment security because their interests are prime targets of terrorists.

3. Pioneering studies include Landes (1978), Sandler, Tschirhart, and Cauley (1983),

and Atkinson, Sandler, and Tschirhart (1987).

4. The average terrorist incident kills one person, while a suicide mission murders

thirteen.

5. We used the 1978, 1980, 1990, 1995, and 2000 volumes of the World Development

Report to track changes in the countries income classifications.

6. We use smoothed proportions in Figure 4 only; the actual proportions are utilized in

our statistical analysis.

7. We also ran a three-variable vector-autoregressive (VAR) model with separate

estimating equations for LICs, MICs, and HICs. For each equation, current variables of

incidents in each income class are regressed against past values of incidents in each of the three

income classes and the four intervention dummies. The results for the ALL series is virtually

identical to the single-equation estimates. These results are available from either author upon

request.

33

8. The 31 countries are: Luxembourg, Norway, the United States, Switzerland,

Denmark, Iceland, Austria, the Netherlands, Canada, Belgium, Hong Kong, Japan, Ireland,

Germany, France, Australia, the United Arab Emirates, the United Kingdom, Finland, Italy,

Sweden, Singapore, Spain, Israel, Macao, New Zealand, Kuwait, Malta, Cyprus, Portugal, and

Greece.

9. Figures 5 and 6 display the pattern of the time series for the entire period and show

whether a series is thin in terms of zero values. Table 5 gives a more focused characterization of

the series for the post-Cold War and 9/11 periods.

10. A spatial econometric specification requires a nonlinear estimator that conflicts with

our linear time-series approach. Spatial estimation is reserved for another paper.

11. This assistance is one of the four pillars of U.S. antiterrorism policy (U.S. Department

of State, 2003).

Figure 1: Location of Incidents by Income GroupPanel 1: All Incidents

inci

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Panel 3: MIC Incidents

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Panel 2: LIC Incidents

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Panel 4: HIC Incidents

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Figure 2: Location of Casualty Incidents by Income GroupPanel 1: All Casualty Incidents

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Panel 3: MIC Casualty Incidents

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Panel 2: LIC Casualty Incidents

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Panel 4: HIC Casualty Incidents

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Figure 3: Incidents with a U.S. Target by Income GroupPanel 1: All Incidents with a U.S. Target

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Panel 3: MIC Incidents with a U.S. Target

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Panel 2: LIC Incidents with a U.S. Target

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Panel 4: HIC Incidents with a U.S. Target

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Figure 4: Proportion of Incident Types in the LIC GroupPanel 1: Proportion of Incidents in the LIC Group

1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 20010.1

0.2

0.3

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Panel 3: Proportion of Incidents with a U.S. Target

1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 20010.1

0.2

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Panel 2: Proportion of Casualty Incidents

1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 20010.0

0.2

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Panel 4: Proportion of Casualty Incidents with a U.S. Target

1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 20010.00

0.25

0.50

0.75

1.00

Figure 5: Incidents by RegionPanel 1: Western Hemisphere

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Panel 4: Asia

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Panel 6: Eurasia

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Figure 6: Casualty Incidents by RegionPanel 1: Western Hemisphere

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Panel 4: Asia

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5.0

7.5

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Panel 2: Europe

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Panle 5: Africa

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Panel 3: Middle East

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TABLE 1. Summary Statistics of the Various Incident Types by Income Group

Series Start End Mean Variance Min Max Mean Variance Min Max

ALL Incident Types Incidents with Casualties WORLD 1992:2 2001:2 66.4 44.0 10 242 22.7 14.3 4 57

1999:2 2001:2 42.3 22.2 10 82 12.9 7.3 4 262001:4 2003:4 46.6 29.4 17 105 20.6 12.8 7 43

LICs 1992:2 2001:2 42.9 24.7 6 125 16.5 11.3 2 501999:2 2001:2 33.1 20.4 6 72 9.9 6.8 2 232001:4 2003:4 26.3 16.8 8 58 14.0 9.5 4 34

MICs 1992:2 2001:2 5.7 3.9 0 16 2.3 2.2 0 91999:2 2001:2 3.7 1.1 2 5 1.8 1.5 0 52001:4 2003:4 7.3 8.7 0 23 2.8 3.0 0 8

HICs 1992:2 2001:2 17.8 28.7 2 171 4.0 4.6 0 211999:2 2001:2 5.6 2.3 2 9 1.2 1.1 0 32001:4 2003:4 12.9 8.1 5 26 3.8 2.0 0 7

LICs/WORLD 1992:2 2001:2 67.5% 0.145 0.262 0.878 71.8% 0.122 0.385 0.9131999:2 2001:2 74.3% 0.095 0.600 0.878 72.2% 0.134 0.500 0.8852001:4 2003:4 57.0% 0.117 0.394 0.758 67.9% 0.112 0.500 0.857

Incidents with a U.S. Target Casualty Incidents with a U.S. Target

WORLD 1992:2 2001:2 16.2 10.4 3 38 3.9 3.3 0 171999:2 2001:2 16.7 12.9 3 38 2.6 1.2 0 42001:4 2003:4 24.1 17.1 8 59 9.4 6.5 1 20

LICs 1992:2 2001:2 12.3 9.6 2 35 2.9 3.0 0 161999:2 2001:2 13.9 12.8 3 33 1.9 1.3 0 42001:4 2003:4 13.6 9.4 4 33 6.7 4.7 1 14

MICs 1992:2 2001:2 1.6 1.9 0 10 0.4 0.7 0 31999:2 2001:2 1.0 0.9 0 2 0.4 0.5 0 12001:4 2003:4 4.3 5.4 0 16 1.0 1.9 0 6

HICs 1992:2 2001:2 2.3 2.2 0 8 0.6 0.8 0 31999:2 2001:2 1.8 2.5 0 7 0.2 0.4 0 12001:4 2003:4 6.2 4.9 0 16 1.8 1.2 0 4

LICs/WORLD 1992:2 2001:2 73.6% 0.183 0.250 1.000 71.6% 0.243 0.000 1.0001999:2 2001:2 78.7% 0.210 0.333 1.000 69.8% 0.209 0.500 1.0002001:4 2003:4 57.1% 0.133 0.366 0.778 71.1% 0.119 0.333 1.000

Notes: LICs denotes low-income countries; MICs indicates middle-income countries; and HICs depicts high-income countries. Min is the smallest quarterly total, and Max is the largest quarterly total.

TABLE 2. OLS and Poisson Estimates of Intervention Variables Region Method Lags c FUND POST DP DL LR F Q(4)

ALL Incident Types WORLD OLS 1 61.29 25.68 -37.35 -30.13 -13.26 -17.71 0.00 0.20 (5.66) (2.98) (-3.49) (-3.34) (-1.18) LICs OLS 1 21.61 27.56 -14.24 -21.26 -12.48 -15.24 0.00 0.31 (5.68) (4.68) (-2.58) (-4.10) (-1.85) MICs OLS 1 18.15 -4.75 -8.03 -5.91 1.35 1.49 0.00 0.29 (6.93) (-2.08) (-4.61) (-2.22) (0.50) HICs OLS 2 19.32 2.99 -13.80 -2.22 -1.36 -2.56 0.45 0.89 (4.88) (0.84) (-2.33) (-0.83) (-0.29)

Incidents with Casualties WORLD OLS 2 6.63 2.59 -2.73 -3.41 2.79 9.37 0.53 0.52 (3.72) (1.17) (-1.16) (-1.09) (0.78) LICs OLS 2 2.44 2.97 -0.80 -6.78 2.47 8.28 0.00 0.71 (2.79) (1.66) (-0.48) (-3.02) (0.96) MICs OLS 1 3.46 -1.16 -0.77 -1.38 0.54 0.79 0.02 0.92 (6.27) (-2.28) (-1.66) (-1.58) (0.57) HICs OLS 3 2.67 0.11 -1.58 4.38 -0.06 -0.19 0.00 0.52 (3.25) (0.10) (-1.27) (5.44) (-0.06)

Incidents with a U.S. Target WORLD OLS 1 29.86 0.10 -15.96 -17.44 7.01 8.18 0.00 0.76 (6.19) (0.02) (-4.15) (-3.34) (1.30) LICs OLS 1 10.30 4.09 -5.04 -12.54 1.50 1.98 0.00 0.30 (4.69) (1.95) (-2.24) (-4.19) (0.46) MICs OLS 2 6.59 -3.00 -2.62 -3.16 1.69 2.78 0.00 0.26 (4.38) (-1.95) (-2.38) (-1.70) (0.90) Poisson 1 1.92 -0.45 -0.96 -32.77 0.86 0.00 (23.70) (-5.88) (-6.62) (0.00) (4.21) HICs OLS 1 10.68 -0.45 -7.83 -1.28 3.89 3.85 0.00 0.37 (6.56) (-0.28) (-5.92) (-0.79) (2.42) Poisson 1 2.35 -0.04 -1.44 -0.21 0.96 0.00 (32.09) (-0.67) (-11.46) (-0.45) (5.53)

Casualty Incidents with a U.S. Target WORLD OLS 2 4.62 0.83 -2.48 -3.09 4.58 6.08 0.00 0.89 (5.51) (1.10) (-2.90) (-1.54) (2.26) LICs OLS 1 2.49 1.72 -1.58 -6.31 3.45 3.89 0.00 0.25 (6.64) (3.53) (-2.63) (-4.17) (2.21) Poisson 1 0.96 0.45 -0.38 -34.35 0.75 0.00 (10.32) (3.92) (-3.24) (0.00) (4.68) MICs Poisson 1 0.53 -0.67 -0.70 -34.01 0.86 0.12 (4.67) (-3.42) (-2.36) (0.00) (2.07) HICs Poisson 1 0.40 0.10 -0.99 1.16 1.04 0.00

(3.31) (0.58) (-3.99) (2.18) (3.07) Notes: Column 2 refers to the estimation method; column 3 indicates the number of lags; column 4 is the pre-intervention intercept; and columns 5-8 indicate coefficient estimates. FUND denotes the rise in fundamentalist terrorism; POST indicates the end of the Cold War; DP is a pulse dummy for 9/11; DL is a level dummy for 9/11; LR is the long-run effect of 9/11; F is the F-statistic, and Q(4) is Ljung-Box Q-statistic using 4 lags.

TABLE 3. Summary Statistics of the Various Incident Types by Income Group for Alternative Classification

Series Start End Mean Variance Min Max Mean Variance Min Max

ALL Incident Types Incidents with Casualties LICs 1992:2 2001:2 49.0 25.7 8 130 18.8 11.5 3 53 1999:2 2001:2 37.3 21.6 8 79 11.8 7.0 4 25 2001:4 2003:4 34.1 23.4 10 80 16.8 11.9 5 40HICs 1992:2 2001:2 17.7 27.5 2 163 3.9 4.7 0 21 1999:2 2001:2 5.6 2.3 2 9 1.2 1.1 0 3 2001:4 2003:4 12.8 7.9 5 25 3.8 2.0 0 7LICs/WORLD 1992:2 2001:2 77.7% 0.142 0.329 0.929 85.2% 0.115 0.563 1.000 1999:2 2001:2 85.2% 0.053 0.763 0.929 90.6% 0.090 0.769 1.000 2001:4 2003:4 70.8% 0.114 0.526 0.846 79.1% 0.124 0.625 1.000 Incidents with a U.S. Target Casualty Incidents with a U.S. Target

LICs 1992:2 2001:2 14.2 10.1 3 37 3.4 3.2 0 16 1999:2 2001:2 15.0 12.5 3 33 2.4 1.2 0 4 2001:4 2003:4 18.2 13.8 4 49 7.7 5.7 1 14HICs 1992:2 2001:2 2.1 2.0 0 7 0.5 0.8 0 3 1999:2 2001:2 1.8 2.5 0 7 0.2 0.4 0 1 2001:4 2003:4 6.2 4.9 0 16 1.8 1.2 0 6LICs/WORLD 1992:2 2001:2 84.6% 0.150 0.417 1.000 84.9% 0.231 0.000 1.000 1999:2 2001:2 87.8% 0.193 0.417 1.000 90.6% 0.186 0.500 1.000 2001:4 2003:4 73.4% 0.152 0.500 1.000 79.6% 0.121 0.667 1.000Notes: HICs depicts the 31 countries with highest per-capita GNI in 2000, while LICs denotes all other countries. See Table 1 for the WORLD statistics.

TABLE 4. OLS and Poisson Estimates of Intervention Variables for Alternative Income Classification Region Method Lags c FUND POST DP DL LR F Q(4)

ALL Incident Types LICs OLS 1 34.54 24.38 -16.90 -27.79 -11.92 -13.89 0.00 0.59 (6.24) (3.84) (-2.77) (-3.89) (-1.41) HICs OLS 2 22.13 2.87 -16.99 -1.99 -1.16 -2.27 0.54 0.97 (4.91) (0.77) (-2.71) (-0.76) (-0.26)

Incidents with Casualties

LICs OLS 2 3.51 3.24 -0.74 -8.45 2.76 8.26 0.00 0.84 (3.15) (1.69) (-0.43) (-3.10) (0.86) HICs OLS 2 4.42 0.03 -2.88 4.30 -0.25 -0.64 0.00 0.31 (4.63) (0.03) (-2.19) (5.68) (-0.26)

Incidents with a U.S. Target

LICs OLS 1 16.15 0.87 -6.33 -16.59 3.66 4.88 0.00 0.32 (4.73) (0.29) (-2.31) (-3.84) (0.80) HICs OLS 1 12.97 -1.01 -9.84 -1.06 3.92 4.03 0.00 0.28 (6.54) (-0.55) (-6.37) (-0.67) (2.46) Poisson 1 2.44 -0.07 -1.59 -0.13 0.97 0.00 (26.19) (-1.28) (-11.56) (-0.27) (5.42)

Casualty Incidents with a US Target

LICs OLS 2 2.75 0.96 -1.31 -6.62 3.56 5.11 0.00 0.82 (4.79) (1.60) (-1.90) (-4.03) (2.09) Poisson 1 1.24 0.28 -0.35 -33.52 0.75 0.00 (14.60) (2.85) (-3.22) (0.00) (4.99) HICs Poisson 1 0.75 -0.10 -1.20 1.23 1.09 0.00

(7.26) (-0.67) (-4.58) (2.29) (3.11) Notes: See Table 2 for the OLS results for the WORLD sample. Column 2 refers to the estimation method; column 3 indicates the number of lags; column 4 is pre-intervention intercept; and columns 5-8 indicate coefficient estimates. FUND denotes the rise of fundamentalist terrorism; POST indicates the end of the Cold War; DP is a pulse dummy for 9/11; DL is a level dummy for 9/11; LR is the long-run effect of 9/11; F is the F-statistic, and Q(4) is Ljung-Box Q-statistic using 4 lags.

TABLE 5. Summary Statistics of the Various Incident Types by Region

Note: West. Hem. denotes Western Hemisphere, and Mid. East indicates Middle East. Min is the smallest quarterly total, and Max is the largest quarterly total.

Series Start End Mean Variance Min Max Mean Variance Min Max ALL Incident Types Incidents with Casualties West. Hem. 1992:2 2001:2 11.84 8.41 1 32 1.97 1.71 0 6 1999:2 2001:2 12.33 12.19 1 29 0.67 0.71 0 2 2001:4 2003:4 5.33 4.80 0 17 1.00 1.00 0 3 Europe 1992:2 2001:2 19.27 27.57 1 163 4.81 4.69 0 22 1999:2 2001:2 6.33 2.60 2 10 2.22 1.39 0 4 2001:4 2003:4 10.78 9.19 4 30 1.44 1.59 0 4 Eurasia 1992:2 2001:2 3.00 2.17 0 9 1.51 1.82 0 8 1999:2 2001:2 2.33 2.00 0 6 0.56 1.01 0 3 2001:4 2003:4 1.00 0.71 0 2 0.44 0.73 0 2 Africa 1992:2 2001:2 10.05 9.46 1 42 4.78 5.31 0 26 1999:2 2001:2 9.44 6.42 1 18 4.22 3.73 0 13 2001:4 2003:4 2.44 2.46 0 7 1.44 2.30 0 7 Mid. East 1992:2 2001:2 12.92 9.84 1 44 5.84 5.86 0 23 1999:2 2001:2 4.78 3.99 1 13 1.89 1.83 0 6 2001:4 2003:4 15.00 9.95 4 32 10.33 8.00 2 26 Asia 1992:2 2001:2 9.76 8.48 0 44 3.86 3.81 0 20 1999:2 2001:2 7.78 6.22 1 21 3.44 2.65 0 8

2001:4 2003:4 13.00 10.91 4 40 6.44 3.28 2 12 Incidents with a U.S. Target Casualty Incidents with a U.S. Target West. Hem. 1992:2 2001:2 6.30 6.90 0 25 0.76 1.04 0 5 1999:2 2001:2 9.22 10.91 1 25 0.44 0.53 0 1 2001:4 2003:4 3.33 3.46 0 12 0.78 0.83 0 2 Europe 1992:2 2001:2 1.59 1.26 0 4 0.35 0.48 0 1 1999:2 2001:2 1.78 1.48 0 4 0.44 0.53 0 1 2001:4 2003:4 4.67 5.00 0 13 0.22 0.44 0 1 Eurasia 1992:2 2001:2 0.49 0.65 0 2 0.16 0.44 0 2 1999:2 2001:2 0.67 0.71 0 2 0.22 0.67 0 2 2001:4 2003:4 0.44 0.73 0 2 0.22 0.67 0 2 Africa 1992:2 2001:2 2.68 3.58 0 17 1.30 2.82 0 16 1999:2 2001:2 1.78 1.64 0 4 0.44 0.53 0 1 2001:4 2003:4 1.00 1.00 0 3 0.11 0.33 0 1 Mid. East 1992:2 2001:2 2.86 2.35 0 8 0.62 0.83 0 3 1999:2 2001:2 1.33 1.58 0 5 0.33 0.50 0 1 2001:4 2003:4 7.56 4.82 2 11 4.78 4.09 0 11 Asia 1992:2 2001:2 2.41 2.58 0 11 0.76 1.06 0 3 1999:2 2001:2 2.00 1.73 0 5 0.78 1.97 0 2 2001:4 2003:4 7.56 8.40 1 29 3.11 2.32 1 7

TABLE 6. OLS and Poisson Estimates of Intervention Variables by Geographic Region Region Method Lags c FUND POST DP DL LR F Q(4)

ALL Incident Types West. Hem. OLS 1 22.57 0.22 -13.25 0.51 -5.51 -7.16 0.01 0.81 (7.40) (0.08) (-4.86) (0.33) (-2.58) Europe OLS 2 18.44 5.62 -14.54 -5.40 -3.15 -5.75 0.02 0.87 (5.45) (1.47) (-2.56) (-1.75) (-0.65) Eurasia Poisson 1 -0.71 0.41 1.17 -33.63 -0.74 0.12 (-2.56) (1.25) (4.35) (0.00) (-2.06) Africa OLS 2 1.97 2.33 1.89 -2.09 -4.53 -7.25 0.00 0.68 (3.44) (2.65) (1.25) (-2.89) (-2.46) Mid. East OLS 1 6.91 9.10 -7.35 -11.00 2.71 3.95 0.00 0.48 (4.40) (3.85) (-2.91) (-3.65) (0.89) Asia Poisson 1 1.62 0.28 -0.22 -1.63 0.24 0.01 (23.42) (4.03) (-3.39) (-2.28) (2.22)

Incidents with Casualties

West. Hem. OLS 2 2.50 0.63 -2.25 3.64 -0.52 -1.14 0.00 0.85 (4.55) (0.75) (-2.74) (8.77) (-1.06) Europe OLS 3 2.70 0.26 -1.66 0.22 -0.53 -1.80 0.78 0.98 (3.53) (0.25) (-1.39) (0.42) (-0.70) Poisson 1 1.32 0.17 -0.42 1.18 -0.64 0.06 (13.62) (2.32) (-4.65) (1.55) (-2.20) Eurasia Poisson 1 -3.35 1.29 2.50 -33.03 -0.91 0.23 (-3.28) (1.15) (4.54) (0.00) (-1.71) Africa OLS 2 0.92 0.99 1.10 -1.13 -1.97 -3.08 0.00 0.58 (3.18) (2.17) (1.29) (-1.59) (-1.83) Mid. East OLS 1 2.07 1.88 -1.03 -6.64 3.75 7.28 0.00 0.21 (3.66) (2.38) (-1.02) (-3.17) (1.69) Asia OLS 1 1.16 1.53 0.12 -3.37 2.01 2.77 0.00 0.31 (3.71) (2.73) (0.19) (-3.03) (1.57)

Incidents with a U.S. Target West. Hem. OLS 1 14.08 -2.18 -6.23 0.87 -2.79 -3.20 0.13 0.22 (6.49) (-1.11) (-3.29) (0.79) (-1.87) Europe OLS 1 8.80 -0.13 -7.32 -4.35 2.73 3.14 0.00 0.93 (6.55) (-0.07) (-4.15) (-2.85) (1.76) Eurasia Poisson 1 -1.00 -2.57 3.01 -31.42 -0.02 1.00 (-2.76) (-2.47) (2.90) (0.00) (-0.03) Africa OLS 5 1.01 -0.21 1.41 -0.37 -1.28 -1.53 0.01 0.99 (3.45) (-0.82) (2.22) (-0.77) (-1.82) Mid. East OLS 1 3.04 0.38 -1.33 -5.25 3.91 5.29 0.00 0.78 (5.46) (0.57) (-2.21) (-3.52) (2.63) Asia OLS 1 2.92 2.26 -2.97 -7.26 4.66 5.17 0.00 0.69

(4.14) (1.94) (-2.97) (-2.68) (1.69)

Casualty Incidents with a U.S. Target West. Hem. OLS 2 1.21 0.30 -1.14 3.70 -0.07 -0.14 0.00 0.41 (4.09) (0.71) (-2.72) (11.00) (-0.18) Europe OLS 1 1.34 0.42 -1.41 -0.23 -0.12 -0.12 0.00 0.70 (5.89) (1.40) (-4.87) (-1.64) (-0.78)

Eurasia Poisson 1 -56.74 0.00 29.30 -32.61 0.32 0.93 (-138.98) (0.00) (0.00) (0.00) (0.39) Africa Poisson 1 -0.90 -0.07 1.35 -30.76 -1.10 0.19 (-2.99) (-0.17) (4.17) (0.00) (-1.83) Mid. East OLS 2 0.52 -0.07 -0.17 -2.40 2.56 5.79 0.06 0.56 (1.86) (-0.23) (-0.72) (-2.28) (2.36) Asia OLS 1 0.83 0.40 -0.46 -3.12 2.36 2.35 0.00 0.91

(4.76) (1.65) (-1.94) (-4.25) (3.06) Notes: Column 2 refers to the estimation method; column 3 indicates the number of lags; column 4 is the pre-intervention intercept; and columns 5-8 indicate coefficient estimates. FUND denotes the rise in fundamentalist terrorism; POST indicates the end of the Cold War; DP is a pulse dummy for 9/11; DL is a level dummy for 9/11; LR is the long-run effect of 9/11; F is the F-statistic, and Q(4) is Ljung-Box Q-statistic using 4 lags.

Global terrorism: deterrence versus preemption

by

Todd Sandler School of Social Sciences

University of Texas at Dallas tsandler@usc.edu

and

Kevin Siqueira

School of Social Sciences University of Texas at Dallas

siqueria@clarkson.edu 1-315-268-6609

Final Revision: January 2006

Abstract This paper analyzes two anti-terrorism policies when a targeted nations people and property are

in jeopardy at home and abroad. A countrys deterrence decision involves both external benefits

and costs as the terrorist threat is deflected, while its preemption decision typically gives external

benefits when the threat is reduced for all potential targets. With damages limited to home

interests, a country will overdeter, while, for globalized terror, a country will underdeter.

Preemption is usually undersupplied. Leader-follower behavior is apt to lessen inefficiency for

deterrence, but worsens inefficiency for preemption as compared with simultaneous-choice

equilibrium allocations. Targeted nations can never achieve the proper counterterrorism policy

through leadership. JEL Codes: H40, D62

Keywords: transnational externalities, simultaneous choices, leader-follower, terrorism, deterrence, preemption.

Global terrorism: deterrence versus preemption

1. Introduction

Since the Israeli-Arab conflicts of the late 1960s and beyond, transnational terrorism (i.e.,

terrorist attacks involving victims, perpetrators, or audiences from two or more countries) have

posed worldwide security concerns (Hoffman 1998) that are highlighted by the London subway

bombing on 7 July 2005, the Madrid commuter train bombing on 11 March 2004, the Bali

nightclub bombing on 12 October 2002, and the four hijackings on 11 September 2001

(henceforth, 9/11). Decentralized counterterrorism measures by autonomous national

governments to deter attacks by hardening targets at home or to preempt future terrorist actions

by annihilating the terrorists, their supporters, and resources result in transnational externalities

with diverse outcomes. Although one may jump to the conclusion that underprovision of effort

is likely to characterize such measures owing to an underlying provision of an international

public good (e.g., Lee 1988; Lee and Sandler 1989; Rosendorff and Sandler 2004), the situation

is more complex so that intuition may be misleading. The nature of externalities stemming from

counterterrorism depends on the governments payoff functions and how they account for

repercussions at home and abroad. That is, homeland security may protect not only citizens but

also foreign visitors, while such measures may jeopardize other countries assets by deflecting a

potential attack abroad. Recent empirical investigations demonstrate that defensive actions taken

by some targeted countries have transferred the attacks abroad (Enders and Sandler 1993, 2004,

2006a, b).

The purpose of this paper is to gain an understanding of countermeasure externalities

because, despite some examples of cooperation to freeze assets or to share information,

homeland security budgets and preemptive responses are still decided independently by nations

that cherish their autonomy (Sandler and Enders 2004). Consequently we may either end up in

2

an unsafe world where too little of an international public good is provided, or else in an

excessively defended one where too much is invested to shift attacks abroad. When decisions

are simultaneous, deterrence may be too much or too little compared with the social optimum,

depending on the relative magnitude of opposing deterrence-induced externalities. Preemption,

in contrast, will typically be undersupplied as compared with the social optimum. The extent of

overdeterrence or underdeterrence generally diminishes when a leader-follower equilibrium is

compared with that of simultaneous moves. Although all targeted nations benefit from a leaders

deterrence decisions, a nation is relatively better off moving second. We are interested in such

leader-follower responses because spectacular attacks at home may necessitate that a targeted

country (e.g., the United States following 9/11 or England following the subway bombings)

assume the initiative. Under these circumstances, we investigate how such positions influence

the internalization of counterterrorism externalities. Leadership typically exacerbates the

inefficient level of preemption as decisive action by one targeted country can result in a reduced

level of overall preemption when compared with the equilibrium allocation of simultaneous

actions. Deterrence often represents strategic complements where actions by targeted countries

move in unison, while preemption represents strategic substitutes where actions by targeted

countries move in opposite directions.

2. Toy game representations

Terrorism is the premeditated use, or threat of use, of extra-normal violence by individuals or

subnational organizations to obtain a political objective through intimidation or fear directed at

an audience beyond the immediate victim. Generally, a terrorist act is transnational when its

ramifications transcend the host country where the act is staged. Policies directed at thwarting

such incidents are prone to generate uncompensated interdependencies among at-risk countries,

3

because actions to address the exigency may either ameliorate the risks to all or deflect the attack

elsewhere. Astute terrorists will not only exploit the failure of governments to cooperate by

attacking the weakest link (e.g., the least-secure airport), but will also exacerbate this

noncooperative inefficiency by playing alternative targets off against one another. Globalization

heightens the risk of transnational terrorism owing to the greater mobility of terrorists, better

communication networks among terrorists, enhanced means to publicize terrorist causes, and the

greater dispersion of countries assets and people.

If one were to display the deterrence and preemption games as 2 × 2 normal-form

matrices, both games are apt to be a Prisoners Dilemma (PD) for the targeted nations (Arce and

Sandler 2005). This follows because the deterrence game is analogous to an arms race when

external costs dominate, with each country best off when it deters and the other does not. For

preemption, a PD is also likely owing to the public good nature of such action, where each nation

is best off when it can free ride on the other nations action. To illustrate, consider figure 1. In

panel a, a 2 × 2 generic deterrence game is depicted where nation 1 is the row player and nation

2 is the column player. This representation is reflective of other defensive countermeasures.

Deterrence by just nation i gives it a benefit of b at a cost of C, in which b > C so that a country

is motivated for self-defense. Moreover, passive country j endures a cost of Cj as it draws more

attacks, since it becomes a relatively softer target in light of is defensive measures. No action

by either nation gives no net gain, while mutual action provides each nation a negative payoff of

b − (C + Ci), for i = 1, 2, as private and external costs overwhelm private gains. Obviously, the

dominant strategy of this PD is to deter and a Nash equilibrium of mutual deterrence with

negative payoffs results.

[Figure 1 near here]

Alternatively, panel b of figure 1 displays the generic preemption game, where each of

4

two targeted nations can preempt or maintain the status quo. If, say, nation 1 preempts while

nation 2 does not, then nation 1 gains a net benefit of B − c as it deducts its private preemption

costs of c from the public benefit of B that it receives along with nation 2. Thus, nation 2 obtains

a free-rider benefit of B in the upper right-hand cell. A reversal of roles reverses payoffs. If both

countries preempt, then each gains 2B from the cumulative action at an individual cost of c, so

that net gains are 2B − c for both. Payoffs are zero from all-around inaction. The public good

dilemma is aptly captured by assuming that 2B > c > B so that acting alone is not desirable but

mutual activity is desirable. Again, a PD applies. Each countrys dominant strategy is now to do

nothing and the Nash equilibrium is mutual inaction.

The potential identity of the underlying 2 × 2 matrices may lead one to conclude that

these countermeasures require the same policy corrections. As our continuous-choice analysis

demonstrates, this conclusion could not be further from the truth policy implications differ

greatly for these terrorism-thwarting decisions. As the game is generalized, differences arise that

not only apply to a simultaneous-move representation, but also to a leader-follower

representation.

3. The deterrence decision

To highlight the similarities and differences between the deterrence and preemption decisions for

two countries confronting a transnational terrorist threat, we construct a single game model that

can be adapted by some parameters to represent either counterterrorism instrument. In so doing,

we limit notation. We first focus on deterrence efforts to harden potential targets.

The model involves two governments (countries) that are targeted by the same terrorist

group or network. Targeted governments are denoted by i = 1, 2. In any given period, the

terrorists can stage their attack in just a single country, known as the host country. For example,

5

al-Qaida may engage in simultaneous attacks but typically in the same country during the same

period. This assumption agrees with how most groups operate owing to limited resources. Each

country is vulnerable at home and abroad, insofar as an attack anywhere may involve residents or

foreigners. Government i first chooses its policy instrument or effort to raise the probability of a

terrorist failure at home, denoted by θi . Thus, 1 θi− represents the probability of a terrorist

success in country i. Government i decides its expenditure level on deterrence ( )θ ,iG where

( )θ 0iG′ > and ( )θ 0iG′′ > . We treat the terrorist threat as exogenous and focus on the strategic

interactions between the targeted governments. The probability that government i is attacked is

given by ( )π θ ,θ ,i i j which for deterrence satisfy 0i i∂π ∂θ < and 2 2π θ 0,i i∂ ∂ > so that

defensive measures limit the likelihood of a home attack with diminishing returns to effort.

However, greater deterrence by country j augments the probability of an attack on country i, but

at a decreasing rate: π θ 0i j∂ ∂ > and 2 2π θ 0.i j∂ ∂ < Finally, country js deterrence will reduce

(increase) the marginal impact of country is action to limit the probability of being attacked

when js efforts are greater (less) than that of is efforts so that 2π θ θ 0i i j∂ ∂ ∂ ! as θ θ .i j"

When each countrys efforts are equal, the value of the cross partials is zero. The assumptions

on π hold for i, j = 1, 2 and .i j≠ In todays world of fundamentalist terrorists, there is always

a likelihood of attack even when both countries are heavily defended. The model, however,

captures the real-world observation that terrorists favor softer targets (Enders and Sandler 1993).

Unless otherwise indicated, we assume symmetry such that ( ) ( )π θ ,θ π θ ,θ .i i j j j i=

The game has four alternative outcomes: the attack succeeds or fails in country i = 1, 2.

In addition to the deterrence costs that each country pays in any of these eventualities, each

country incurs costs from the attack at home or abroad as its people or property may be in harms

6

way. For simplicity, we have made payoffs symmetric, so that the costs of a failed (successful)

attack in a host country are A ( ) ,H where H A> as failure limits damage to the venue country.

We use lower-case analogous symbols, a and h, for the costs to country i from a terrorist attack

failure (success) abroad, where h > a.

3.1. Government costs functions

Country is expected damage from a home attack is ( )θ ,il while is expected damage from an

attack on its interests abroad is ( )θ .jv This is captured in (1)-(2):

( ) ( )θ θ 1 θi i il A H= + − (1)

and

( ) ( )θ θ 1 θ .j j jv a h= + − (2)

Given the assumptions on the cost parameters, l(θi) decreases as θi increases and v(θj) decreases

as θj increases, because expected damages fall as terrorist failure is more imminent. Given (1)-

(2), the expected costs of terrorism for government i is:

( ) ( ) ( ) ( )θ π θ π θ ,i i i i j jC G l v= + +θ (3)

where θ ( )θ ,θi j= and an interchange of the is and js would give country js costs. Country is

expected costs derive from three considerations: deterrence expenditure, attacks at home, and

attacks on is interests abroad.

The simultaneous-move equilibrium follows when country i chooses θi to minimize its

expected costs, subject to the constancy of θj, while country j chooses θj, subject to the constancy

of θi. For either country, the first-order condition requires that

7

( ) ( ) ( ) ( ) 0, , 1, 2, and .ji ii i i i j

i i i

CG l l v i j i j

∂π∂ ∂π′ ′= θ + π θ + θ + θ = = ≠∂θ ∂θ ∂θ

(4)

On the right-hand side of (4), the first and fourth terms represent the costs of increasing θi

(coming from greater deterrence expense and the expected damage of deflecting an attack abroad

to is own interests), while the second and third terms represent the benefits of increasing θi

(arising from the reduced expected costs and the smaller likelihood associated with home

attacks).1 Second-order conditions require that 2 2 0,i iC∂ ∂θ > which we assume holds.2 Given

the presence of externalities, independent behavior by the governments are unlikely to give a

cost minimum for society at large, where CT = Ci + Cj is minimized, in which

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) .Ti j i i i j j jC G G l v l v = θ + θ + π θ + θ + π θ + θ θ θ (5)

Minimization of CT yields a Pareto optimum whose equilibrium choice variables are denoted by

( )* *, i j= θ θ*θ in contrast to the simultaneous-action noncooperative solution indicated by

( )N N, i j= θ θNθ , which satisfies (4). The Pareto first-order conditions for minimizing CT are:

( ) ( ) ( ) ( ) ( ) ( ) ( ) 0,T

jii i i i i i j j

i i i

CG l v l v l v

∂π∂π∂ ′ ′ ′= θ + π θ + θ + θ + θ + θ + θ = ∂θ ∂θ ∂θ (6)

and a similar expression for ,TjC∂ ∂θ where the is and js are switched as compared with (6).3

The nature of the opposing externalities is clear when the noncooperative first-order

conditions are compared with those for the cooperative solution. Evaluation of the first-order

conditions for the cooperative problem at the simultaneous-move Nash equilibrium yields:

( ) ( ) ( )N N N jii i i j

i i

v v l∂π∂π′π θ + θ + θ

∂θ ∂θ 0, for i, j = 1, 2, and i ≠ j. (7)

The first term on the left-hand side of (7) is a marginal external benefit, conferred by government

is deterrence on protecting js citizens when they are in country i. Similarly, the second left-

≥<

8

hand expression in (7) is a marginal external benefit conferred by is deterrence on country js

interests by reducing terrorist attacks in i. In contrast, the third left-hand term in (7) is a marginal

external cost that arises as is deterrence increases the likelihood of an attack in j, where js

interests are in harms way. Given the presence of opposing externalities, the net marginal

externality in (7) cannot be signed without further structure. Marginal external benefits result in

too little deterrence, whereas marginal external costs result in too much deterrence when the

simultaneous-move equilibrium levels of deterrence are compared with social-optimizing levels.

For the simultaneous deterrence decision, the slope of the governments best-response

(BR) path, which indicates the best choice of θi for alternative values of θj, proves instructive.

This slope is derived by implicitly differentiating i iC∂ ∂θ in (4) with respect to θj to give:

( ) ( ) ( ) ( )22

2

2

j ji ii j i j

j i i j i ji

ij

i

l v l vBR

C

∂π ∂ π∂π ∂ π′ ′− θ − θ − θ − θ∂θ ∂θ ∂θ ∂θ ∂θ ∂θ∂ =

∂∂θ∂θ

, (8)

for i, j = 1, 2, and i ≠ j. The denominator of (8) is positive since the second-order conditions are

satisfied by assumption, so that the sign of this slope hinges on the numerator. At the symmetric

equilibrium, the numerator is positive and therefore the sign of the slope of these best-response

paths are both positive.4 As such, the countries efforts at deterrence represent strategic

complements (see Bulow, Geanakoplos, and Klemperer 1985).

4. Fully symmetric simultaneous-move case: alternative terrorist scenarios

To get some definitive results that possess some real-world analogues, we make some specific

assumptions. The outcomes for our specialized scenario provide insights for less stark examples

that may include aspects of both scenarios to varying degrees.

9

4.1. No collateral damage

In the first two scenarios, we assume that attacks are host-country specific with no collateral

damage on foreign interests, so that a = h = 0 and, therefore, ( ) ( ) 0i iv v′θ = θ = for i = 1, 2,

owing to symmetry. The evaluation of CT at the symmetric Nash equilibrium allocation implies:

( ) ( ) ( )N 0,Ti i j iC l∂ ∂θ = θ ∂π ∂θ >Nθ i, j = 1, 2, and i ≠ j. (9)

Eq. (9) indicates that a country overdeters as compared with the Pareto-optimal level, because

the external costs imposed on the other country by deflecting the attack there are not taken into

account. Consequently, a deterrence race applies as each nation tries to transfer the terrorist

threat abroad where it has no interests.

Thus, the reaction of the United States to 9/11 or England to the London subway

bombings may be excessive. The seemingly uncontrollable homeland security spending in the

United States, when state and local spending is included, has this hallmark. Terrorists hurt their

targeted countries budgets in ways that transcend the carnage and destruction. Overdeterrence

bolsters these economic consequences of terrorism. Even when there is some collateral damage,

host-country losses motivate overdeterrence.

The best-response curves are displayed in figure 2 (ignoring point S) where θj is on the

vertical axis and θi is on the horizontal axis. These best-response paths connect the optimums of

the isocost curves (suppressed except for the dashed curve) for each country. These isocost

curves are generally hill-shaped for government i (see the dashed curve) and an inverted C-

shaped for government j. Country is welfare improves on lower isocost curves, while country

js welfare improves on left-shifted isocost curves (closer to the vertical axis). This follows

because each country then experiences a smaller deterrence level abroad for any level of its own

10

deterrence, thereby making it relatively safer at home. In figure 2, the intersection of the two

reaction paths at N denotes the simultaneous-move equilibrium, where country is isocost curve

has a zero slope and js isocost curve has a vertical slope. The symmetric Pareto optimum is

some point, P, along the 45° line that is closer to the origin than point N. This is a case of

strategic complements where the deterrence choice of potential targets moves together.

[Figure 2 near here]

4.2. Globalized terror scenario

Our second polar case is globalized terror where a countrys risk is equivalent at home and

abroad, so that A = a and H = h. This implies that a countrys expected attack costs are such that

( ) ( )i jl vθ = θ at the symmetric equilibrium where .i jθ = θ = θ Now, an evaluation of CT at the

simultaneous-move equilibrium gives:5

( ) ( )N N 0,Ti iC v′∂ ∂θ = π θ <θ i = 1, 2. (10)

Thus, the external benefits that a countrys deterrence efforts provide to foreigners are not taken

into account and this leads to underdeterrence i.e., θ* > θN, where subscripts are suppressed.

Although this scenario is extreme to focus our thinking, it provides insight for other

cases. In nonsymmetric cases for which a countrys citizens are at greater risks abroad owing to

excellent protection at home (e.g., the United States after 9/11), foreign-generated external

benefits and, hence, foreign underdeterrence are anticipated to dominate. As such, the downside

to successful efforts at home to deflect attacks is that a countrys citizens are then more

vulnerable abroad, where the country has little influence owing to sovereignty issues. Recent

statistical analyses have uncovered a shift in transnational terrorist incidents from Western

venues to the Middle East and Asia, where post-9/11 upgrades have not been instituted (Enders

and Sandler 2006a). This shift is particularly strong for attacks against US interests. If the

11

terrorists purposely limit the collateral damage to the host country from their attacks against, say,

Americans, then the terrorists can maximize the host country’s underdeterrence. This appears to

have been the Greek scenario with respect to its ineffective efforts to curb 17-November terrorist

activities for 22 years until a terrorist accidentally blew himself up during the summer of 2002

(Lee 1988; Wilkinson 2001). The US assistance to foreign governments one of the four

pillars of US antiterrorist policy (US Department of State 2002) is a sensible action to

address this foreign underdeterrence, but, of course, the United States can fortify only a limited

number of potential target nations. If, however, the asymmetry involves dominant costs at home

(A > a, H > h), then overdeterrence may characterize a less extreme degree of globalized

terrorism. Thus, the richness of the deterrence game is brought out.

For the fully symmetric globalized scenario, the slope of the best-response curve is

positive for both countries. Once again, we have strategic complements for the deterrence game,

but the isocost curves are now U-shaped and C-shaped for country i and j, respectively.

Moreover, the Pareto optimum (not displayed for this case) is on the 45û line above the

simultaneous-move equilibrium N in figure 2. The discussion above establishes:

Proposition 1. In the case of no collateral damage, each noncooperative target government

overdeters relative to the Pareto-optimal level; in the case of globalized terror, each

noncooperative target government undeters relative to the Pareto-optimal level.

5. Preemption game

In the preemption game, the targeted government (i = 1, 2) must independently decide whether to

launch an attack against a terrorist group or its sponsor. Although the preemption game bears

great similarities to the deterrence game, the former displays some subtle but important

12

differences. First, preemption confers public benefits on targeted countries, while deterrence

confers public costs and benefits on targeted countries. Second, a corner solution may

characterize preemption as only one government (i.e., the prime target) takes action. In contrast,

all targeted governments will take deterrent measures so that a corner solution is not

economically relevant. Third, with preemption, a fanatical terrorist group may be kept from

attacking if the governments actions sufficiently deplete a groups capabilities. Other

differences will be noted in the ensuing analysis.

We utilize the same notation as before, but ( )iG θ now denotes preemption costs. All of

the other parameters e.g., ( ) ( ),i il vθ θ , A, H, a, and h have analogous interpretations as those

in the deterrence game. The essential difference in parameters involves the probability that

country i will be attacked, as given by ( ).iπ θ An increase in is preemption reduces this

probability not only for country i but also for j − i.e., 0i i∂π ∂θ < and 0j i∂π ∂θ < − with

diminishing returns to effort. This second inequality is a key difference between preemption and

deterrence. A second associated difference is the unambiguous sign of the cross partial i.e.,

2 0i i j∂ π ∂θ ∂θ > − which indicates that js preemption reduces the marginal impact of is

preemptive efforts owing to diminishing returns. Collective preemption may be sufficient to

eliminate all attacks, where 0 1 21π = − π −π is the governments perceived likelihood of no

attack.6

The first-order conditions characterizing the Nash equilibrium of the preemption game

played between two targeted countries are identical in form to that in (4), and are not displayed

here. Now, ( )iG′ θ denotes the marginal preemption costs and the remaining three terms

represent marginal benefits either conferred at home or abroad. Unlike deterrence with opposing

13

externalities, preemption reduces vulnerabilities in all potential target countries by curbing

terrorists capabilities. Because all externalities are positive, best-response paths and outcomes

are easier to sign.

In figure 3, government is isocost curves are U-shaped (see IiIi), while government js

isocost curves (see IjIj) are translated through 90û. For i, higher isocost curves indicate a greater

well-being, since each level of is preemption is associated with a higher preemption by the other

country. Similarly, isocost curves to the right represent greater well-being for country j. Based

on the assumptions, the thickened best-response curves (BRi and BRj) are negatively sloped,

indicative of the public good nature of preemption. BRi joins the zero slopes of the isocost

contours for i, while BRj joins the vertical slopes of the isocost contours for j. These negatively

sloped best-response paths are also consistent with the preemption decisions of the governments

being strategic substitutes. The simultaneous-move equilibrium occurs at N.

[Figure 3 near here]

5.1. Noncooperative versus cooperative behavior: alternative scenarios

By evaluating the first-order conditions for minimizing CT at the symmetric, Nash equilibrium

allocation of the simultaneous-move preemption game, we find that ( )TiC∂ ∂θNθ is negative in

any scenario. This comparison leads to the following result:

Proposition 2. For all cases, the simultaneous-move equilibrium allocation results in a smaller

level of preemption by both targeted governments, compared with the Pareto optimum.

Proof: See Appendix

Both polar scenarios now lead to the same outcome. The extent of underpreemption will be

14

greater in the globalized terror instance because there are a couple sources of external benefits in

contrast to the single source for no collateral damage. Less extreme cases would also result in

too little preemption. The situation is displayed in figure 3, where the cross-hatched region,

defined by the governments isocost curves through N, denotes Pareto-improvement allocations

for preemption. The symmetric Pareto optimum, P, is located somewhere in this region on the

45û line.

These results generalize to n target countries. In an asymmetric world where some

countrys interests are the preferred targets of the terrorists, the country is motivated to preempt

despite the free ride given to others. For example, US interests are the target of 40% of the

transnational terrorist attacks; its war on terror embodies its preemptive effort (Sandler and

Enders 2004).

6. Stackelberg leader-follower in the deterrence game

Although a leader-follower representation is often of interest because there is an issue of

coordination, signaling, or commitment, we choose to use this framework to ascertain if there is

a possibility for the externalities to be internalized by one nation moving first. There has been

little evidence either before or after 9/11 that nations coordinate their deterrence or preemption

decisions (Sandler 2003). In a world where some countries interests are the preferred target of

terrorists, these countries will heavily invest in intelligence and antiterrorist measures. With

their greater risks, such targeted countries may have little political choice but to assume a

leadership role by deciding their deterrence prior to other targeted countries. Since 9/11, the

United States has been more aggressive than other countries in bolstering antiterrorist measures,

as reflected in the tens of billions of dollars of extra security spending. Currently, the United

States is considering installing defensive measures against surface-to-air missiles on commercial

15

planes. Thus, we first investigate the allocative implications if a past attack forces a government

to assume a leadership position in terms of defensive measures.

Country i is assumed to be the leader and country j the follower. As the leader, i

minimizes its costs, taking into account the impact that its deterrence decision will have on js

choice of deterrence. That is, country i will choose θi to minimize its deterrence costs, while

treating θj as dependent on its θi according to js best-response path, so that θj = BRj(θi). The

leaders cost function is:

( ) ( ) ( ) ( ) ( ) ( ), , , .i i j i i i i j i i j i j i j iC BR G BR l BR v BR θ θ = θ + π θ θ θ + π θ θ θ (11)

Differentiating (11) with respect to θi, we derive the leaders first-order condition,

( ) ( ) ( ) ( ) ( ) ( ) ( )S

0,j j ji i ii i i i j i j j j

i i i j j i

BRCl l v l v vG

∂π ∂π ∂∂ ∂π ∂π′ ′= θ + π θ + θ + θ + θ + θ + θ π =∂θ ∂θ ∂θ ∂θ ∂θ ∂θ

′

(12)

where the superscript S on Ci denotes Stackelberg or leader-follower equilibrium allocation. In

(12), the first bracketed expression consists of the same terms as in the simultaneous-move first-

order conditions, while the second bracketed expression, which is multiplied by the slope of

country js reaction path, distinguishes the leaders behavior from that in a noncooperative (N)

simultaneous-move game. That is, when (12) is evaluated at ( )N N, ,i j= θ θNθ the first bracketed

term equals zero, leaving the second composite expression as the determinant of the relationship

of the leader-follower equilibrium allocation to that in the Nash simultaneous-move game. The

terms in the second bracketed expression are the marginal external benefits and costs that j

imposes on i from not cooperating [see (7)]. Even if the slope of the best-response path is

positive, the net influence of this expression cannot be evaluated unless additional structure is

placed on the problem.

16

6.1. Alternative scenarios: simultaneous-move versus Stackelberg equilibrium allocation

If there is no collateral damage beyond the host countrys interests, so that the v expressions are

zero, then the evaluation of the leaders Stackelberg first-order condition at the symmetric

simultaneous-move equilibrium gives:

( ) ( )S

N 0.i ji

ii j i

C BRl

∂ ∂∂π= θ > ∂θ ∂θ ∂θ

Nθ (13)

This sign follows because 0i j∂π ∂θ > (from deflecting the attack abroad) and the positive slope

of js reaction path. This inequality indicates that the leader internalizes some of the marginal

external costs from deflecting the attack. This partial internalization arises as the leader accounts

for the strategic complementarity, in which overdeterrence on its part leads the follower to

overdeter in response. To reduce the reciprocal external costs, the leader curtails its deterrence,

an action that induces a similar response by the follower. As a consequence, N Sθ θ! where

( )S S, i j= θ θSθ . Leader-follower behavior limits overdeterrence when the Stackelberg outcome is

compared with the simultaneous-move equilibrium. This can be seen in figure 2, presented

earlier, where leader is dashed isocost curve is tangent to js best-response curve at the leader-

follower equilibrium S.7 The isocost curves associated with S imply that both countries are better

off than at N owing to the curtailment of the deterrence race. Because the followers isocost

curve necessarily shifts left by more than the leaders isocost curve shifts down, there is a

second-mover advantage that a prime-target country relinquishes out of political necessity to act

first. The 9/11 attacks have imposed a strategic disadvantage on the United States by making it

assume a deterrence leadership role; nevertheless, the United States makes some gain by seizing

the initiative.

In the globalized scenario, a similar internalization occurs. An evaluation of the leaders

17

Stackelberg first-order conditions at the symmetric simultaneous-move equilibrium allocation

implies that the leader internalizes some of the marginal external benefits that stem from the

strategic complementarity. In particular, the leader increases its level of deterrence, because

such efforts induce a greater deterrence by the follower, which safeguards the leaders interests

on the latters soil. As compared with the underdeterrence associated with simultaneous moves,

both the leaders and followers deterrence levels are greater, so that S Nθ θ! . In figure 2, the

leader-follower solution is up along BRj to the right of N at S′ where one of the leaders U-shaped

isocost curves (not shown) is tangent to js best-response path. Once again, both governments

gain from leadership by one of the targeted countries, but the follower has a second-mover

advantage. In summary, we have:

Proposition 3. For either no collateral damage or globalized terrorism, the equilibrium allocation

in the leader-follower game results in deterrence levels that are closer to the social optimum,

compared with those of the simultaneous-move outcome. The follower, however, gains relative

to the leader.

6.2. Leader-follower and preemption

Given the unidirectional externalities in the preemption situation, the evaluation of the impact of

leader-follower behavior is simple to ascertain. An evaluation of the leader-follower first-order

condition at the simultaneous-move equilibrium of the preemption game gives:

Proposition 4. The leader decreases its preemption efforts relative to the simultaneous-move

equilibrium. Moreover, total preemption for the leader-follower allocation is less than that for a

18

unique (interior) simultaneous-move equilibrium.

Proof: See Appendix

At an interior solution, the leader reduces its preemption because it foresees that this reduction

will induce the follower to provide more. This action improves the leaders well-being at the

expense of the follower. Unlike deterrence, taking the initiative is not Pareto improving.

In figure 3 (displayed earlier), the leader-follower equilibrium at S will be northwest

along the followers best-response path. The aggregate leader-follower level of preemption must

decrease as compared with the unique simultaneous-move equilibrium N, given that the slope of

BRj is greater than 1. All terrorist scenarios no collateral damage, globalized terror, or some

combination give this outcome. If there is a corner solution where BRi is everywhere above

BRj, then the leader-follower solution is at the θi intercept of the BRi reaction path where i does

all of the preemption and j free rides. In this case, leadership has no influence on the outcome.

With an attack like 9/11, the host countrys best-response curve may shift sufficiently to the

northeast that a corner solution results where one or two most impacted countries do virtually all

of the preempting e.g., post-9/11 actions of the United States and the United Kingdom in

Afghanistan.

7. Policy implications and concluding remarks

Although deterrence and preemption games are almost identical in structure, they possess some

essential differences that influence the conduct of sensible and effective counterterrorism policy.

For the deterrence game, the mix of home and abroad risks imply both external benefits and

costs, which, in turn, can yield a wide variety of outcomes. Thus, noncooperating nations may

overdeter if host-country risks outweigh threats to a countrys citizens while abroad. If,

19

however, terrorism is globalized, placing citizens equally in harms way everywhere, then

underdeterrence is the outcome. Because only external benefits are typically generated for

preemption, too little action is the norm so that policy must bolster this measure.

In the absence of a corner solution, less global preemption will result from leadership so

that the Bush doctrine of 2002 will limit the overall level of preemption, opposite to the

doctrines intention. This result follows because preemption is purely public to potential targets

of transnational terrorism, thus allowing the leader to reduce its efforts by more than the follower

increases its efforts. After 9/11, there were some countries most notably, the United Kingdom

that followed the US invasion of Afghanistan, so that a corner solution did not apply. For these

follower countries, US leadership is anticipated to have increased their participation level,

consistent with the administrations wishes. Prime-target countries confront a real policy

dilemma because preemption leadership shows its citizens that it is decisive, but at the risk of

reducing overall efforts. As such, political realities lead to the wrong policy choice. When,

however, deterrence decisions are considered, leadership is apt to limit the inefficiency

whether there is underdeterrence or overdeterrence. Thus, leadership is apt to be helpful for

deterrence but not for preemption. This policy insight does not fully concur with the Bush

administrations current actions.

As fundamentalist terrorist drive for ever-greater atrocities, they motivate leadership in a

small set of prime-target nations e.g., the United States, the United Kingdom, Israel, and Spain.

What our analysis highlights is that leadership, without true cooperation, is a two-edged sword

for the practice of counterterrorism: leadership curbs inappropriate deterrence levels but

exacerbates inappropriate preemption levels. Given the diverse strategic character of deterrence

and preemption decisions, nations can never get the mix correct through leadership, induced by

large-scale terrorist attacks. The only solution is the creation of a cooperative network of nations

20

with integrated counterterrorist measures. We are nowhere near this goal (Enders and Sandler

2006b).

Our models abstract by assuming just two targeted nations. This abstraction is

appropriate because an individual nation views its actions vis-à-vis the collective target of the

rest of the world. In the case of the United States, the rest of the world (in terms of targeted

countries) is a collective player roughly of similar size. For a small country, the rest of the world

overshadows it, so that a corner solution where it does no preemption of transnational terrorism

is likely. In our future work, we are examining the mix between deterrence and preemption.

This mix greatly complicates the analysis, which is best understood by first having these policies

examined in isolation, as done here.

21

Appendix

Proof of Proposition 2.

We evaluate the first-order conditions for minimizing CT at the symmetric Nash equilibrium of

the simultaneous-move preemption game. This gives

( ) ( ) ( ) ( )N N N 0T

jii i i i

i i i

Cv v l

∂ ∂π∂π′= π θ + θ + θ <∂θ ∂θ ∂θ

Nθ for i, j = 1, 2, and .i j≠ (A1)

For the no collateral damage case where 0v v′= = and for the globalized terror case where

( ) ( ) ,v l⋅ = ⋅ there is too little preemption at the Nash equilibrium allocation compared with the

Pareto optimum, so that all terms to the left of inequality are negative.

Proof of Proposition 4.

To compare the interior of Stackelberg equilibrium allocation to that of the simultaneous-move

preemption game, we evaluate the first-order conditions charactering leader-follower behavior at

Nθ :

( ) ( ) ( ) ( )S

N N N 0.i j ji

i j j ji j j i

C BRl v v

∂ ∂π ∂∂π ′= θ + π θ + θ > ∂θ ∂θ ∂θ ∂θ

Nθ (A2)

In (A2), all terms in the brackets are negative and the slope of the followers best-response path

is also negative; hence, the product of these expressions is positive for all scenarios. The sign in

(A2) indicates that the leader will preempt to a smaller extent than at the simultaneous-move

equilibrium. The follower will then increase its preemption, but since the slope of BRj is less

than one in absolute value to ensure uniqueness and existence of equilibrium (Cornes, Hartley,

and Sandler 1999), the overall value of preemption falls relative to the simultaneous-choice

equilibrium.

22

References

Arce, Daniel G., and Todd Sandler (2005) Counterterrorism: a game-theoretic analysis,

Journal of Conflict Resolution 49, 183−200

Bulow, Jeremy I., John D. Geanakoplos, and Paul D. Klemperer (1985) Multimarket oligopoly:

strategic substitutes and complements, Journal of Political Economy 93, 488−511

Cornes, Richard, Roger Hartley, and Todd Sandler (1999) Equilibrium existence and uniqueness

in public goods models: an elementary proof via contraction, Journal of Public

Economic Theory 1, 499−509

Eaton, B. Curtis (2004) The elementary economics of social dilemmas, Canadian Journal of

Economics 37, 805−29

Enders, Walter, and Todd Sandler (1993) Effectiveness of anti-terrorism policies: vector-

autoregression-intervention analysis, American Political Science Review 87, 829−44

−−−−−− (2004) What do we know about the substitution effect in transnational terrorism?, in

Researching Terrorism: Trends, Achievements, and Failures, ed. A. Silke (Ilford, UK:

Frank Cass)

−−−−−− (2006a) Distribution of transnational terrorism among countries by income classes and

geography after 9/11,International Studies Quarterly 50, forthcoming

−−−−−− (2006b) The Political Economy of Terrorism (Cambridge: Cambridge University Press)

Hirshleifer, Jack (1989) Conflict and rent-seeking success functions: ratio vs. difference models

of relative success, Public Choice 63, 101−12

−−−−−− (2000) The macrotechnology of conflict, Journal of Conflict Resolution 44, 773−92.

Hoffman, Bruce (1998) Inside Terrorism (New York: Columbia University Press)

Lee, Dwight R. (1988) Free riding and paid riding in the fight against terrorism, American

Economic Review Papers and Proceedings 78, 22−6

23

Lee, Dwight R., and Todd Sandler (1989) On the optimal retaliation against terrorists: the paid-

rider option, Public Choice 62, 141−52

Rosendorff, B. Peter, and Todd Sandler (2004) Too much of a good thing? The proactive

response dilemma, Journal of Conflict Resolution 48, 657−71

Sandler, Todd (2003) Collective action and transnational terrorism, World Economy 26,

779−802

Sandler, Todd, and Walter Enders (2004) An economic perspective on transnational terrorism,

European Journal of Political Economy 20, 301−16

United States Department of State (2002) Patterns of Global Terrorism (Washington, DC: US

Department of State)

Wilkinson, Paul (2001) Terrorism versus Democracy: The Liberal State Response (London:

Frank Cass)

24

Footnotes

Sandler is an Endowed Professor of Economics and International Political Economy, and

Siqueira is an Associate Professor. This research was partially supported by the United States

Department of Homeland Security (DHS) through the Center for Risk and Economic Analysis of

Terrorism Events (CREATE) at the University of Southern California, grant number EMW-

2004-GR-0112. Any opinions, findings, and conclusions or recommendations are solely those of

the authors and do not necessarily reflect the DHS. The authors gratefully acknowledge helpful

comments provided by Miguel Costa-Gomes and Gianni De Fraja following presentation of an

earlier version of this paper at the University of York, UK. Helpful comments were also

provided by a referee.

1. Although a corner solution is technically interesting, it is not economically

meaningful. Terrorism-prone countries do not choose zero deterrence levels; every country with

airports have installed metal detectors.

2. The second-order condition requires that

( ) ( ) ( ) ( )22 2

2 2 22 0.ji i i

i i i ji i i i

CG l l v

∂ π∂ ∂π ∂ π′′ ′= θ + θ + θ + θ >∂θ ∂θ ∂θ ∂θ

This condition will hold if the probability function consistent with our assumption on iπ is of the

following specific form:

π ,ji

i j

θ=θ + θ

, 1, 2,i j = and .i j≠

A countrys perceived likelihood of a terrorist attack hinges on the other targets relative

deterrent measures. This attack probability function is similar but different than contest success

functions in the conflict literature, where success hinges on the ratio of own effort to total effort

(Hirshleifer 1989, 2000).

25

3. We assume that the second-order condition for the cooperative minimization problem

is satisfied. A sufficient condition for this to hold is that the principal minors of the Hessian

matrix are strictly positive:

2

20

T

i

C

θ∂ >∂

and

22 2 2

2 20

T T T

i j i j

C C C

θ θ θ θ ∂ ∂ ∂− > ∂ ∂ ∂ ∂

.

For the specific probability function assumed in footnote 2, this condition holds.

4. In (8), the first two terms in the numerator are positive, while the last two terms will

be of differing signs. The sum of these last two terms will, however, be zero when i jθ = θ

because cross partials are then zero.

5. This follows since .i i j i∂π ∂θ = −∂π ∂θ

6. The following specific forms for the attack probabilities would give such results:

0

0 0

,ji

i j i j

θπ =

θ + θ + θ + θ for , 1, 2,i j = i j≠

and

00 0

.i j

i j i j

θ + θπ =

θ + θ + θ + θ

In these equations, 0iθ and 0jθ are proxies for some kind of obstacle that protects country i and j,

respectively. An increase in 0iθ reduces the likelihood of i being attacked, but increases the

likelihood that country j is targeted. The need for a different underlying specific probability

function is another difference between the two models.

7. Our problems are similar to some of the social dilemmas analyzed in the excellent

article by Eaton (2004). Some important differences exist because deterrence has opposing

externalities.

(C + Ci > b > C), i = 1, 2 a. 2 × 2 Generic deterrence game

(2B > c > B) b. 2 × 2 Generic preemption game

Figure 1. Preemption and deterrence games in normal form

nation 2 Status quo Deter

Status quo

0, 0

−C1, b − C

nation 1

Deter

b − C, − C2

b − C − C1, b − C − C2

nation 2 Preempt Status quo

Preempt

2B − c, 2B − c

B − c, B

nation 1

Status quo

B, B − c

0, 0

45o

θj

θi

P

N

BRi

BRj

0

Figure 2. Best-response paths for symmetric deterrence game

SS '

45o

0

BRi

BRj

PS

N

Figure 3. Symmetric preemption best-response paths

N

ii

N

j

jIj

Ij

IiIi

θ θ

θ

θ

Terrorist backlash, terrorism mitigation, and policy delegation

Kevin Siqueira*

and

Todd Sandler School of Economic, Political and Policy Sciences

University of Texas at Dallas 2601 N Floyd Road

Richardson, TX 75083 USA 1-972-883-6725

fax: 1-972-883-6297

January 2007

Abstract This paper presents a three-stage proactive game involving terrorists, elected policymakers, and

voters. In each of two targeted countries, a representative voter chooses an elected policymaker,

charged with deciding proactive countermeasures to ameliorate a transnational terrorist threat.

Two primary considerations drive the voters’ strategic choice: free riding on the other countries’

countermeasures and limiting a reprisal terrorist attack. The resulting low proactive

countermeasures benefit the terrorists, whose attacks successfully exploit voters’ strategic

actions. This finding stems from a delegation problem where leadership by voters has a

detrimental consequence on the well-being of targeted countries. Domestic politics add another

layer of concern when addressing a common terrorist threat.

JEL classification: H41, D72, H56, D74 Keywords: Terrorism; Delegation problem; Counterterrorism; Public Goods; Three-stage game email address: siqueira@utdallas.edu (K. Siqueira), tsandler@utdallas.edu (T. Sandler) Corresponding Author: Sandler *Siqueira is an Associate Professor of Economics. Sandler is the Vibhooti Shukla Professor of Economics and Political Economy. We have profited from the comments of two anonymous references. This research was partially supported by the U.S. Department of Homeland Security through the Center for Risk and Economic Analysis of Terrorism Events (CREATE) at the University of Southern California, grant number N00014-05-0630. However, any opinions, findings, and conclusions or recommendations are solely those of the authors and do not necessarily reflect the views of the Department of Homeland Security.

Terror backlash, terrorism mitigation, and policy delegation 1. Introduction

The unprecedented and destructive terrorist attacks on September 11, 2001 (hereafter 9/11) not

only had economic ramifications but also political consequences, felt across the globe. Estimates

of economic losses run from $80 to $90 billion, not including increased expenditures on

homeland security and other indirect costs that followed in the wake of these attacks (Kunreuther

and Michel-Kerjan, 2004; Kunreuther et al., 2003). To maintain political support from the

American public, the Bush administration had to demonstrate its ability to take decisive actions

to protect US people and property from future attacks. These measures took two tracks:

defensive responses in the form of greatly expanded homeland security and offensive responses

in the form of the Afghan invasion on October 7, 2001. The latter was intended to destroy al-

Qaida’s assets and send a clear message that such terrorist attacks will elicit a massive and

prolonged retaliatory blow against the terrorists, their associates (i.e., Abu Sayyaf in the

Philippines), and their supporters (i.e., the Taliban who had provided a safe haven).

As a targeted government takes stringent proactive measures against terrorists and their

sponsors, the government must also worry about a potential backlash that these efforts might

trigger at home by another terrorist group that objects to Draconian countermeasures. For

example, Spain’s support of the US-led “war on terror,” including its participation in

Afghanistan and Iraq, resulted in the March 11, 2004 (hereafter 3/11) Madrid commuter train

bombings, which killed 191 and injured 1,200. Spanish voter’s viewed the ruling Partido

Popular party’s strong stance against al-Qaida as having brought this backlash attack to the

homeland – a belief bolstered by the statements by the perpetrators. The government’s

culpability was exacerbated by its false accusation of Euskadi ta Askatasuna (ETA). Similarly,

Britain’s close alliance with US post-9/11 proactive efforts likely resulted in the London subway

2

and bus bombings on July 7, 2005 and a subsequent failed attack four weeks later. As with

Spain, proactive measures against al-Qaida caused another sympathetic group to retaliate on the

retaliator’s home turf. A series of terrorist attacks in Saudi Arabia during 2004-2005 appears

motivated by its cooperation in US-led antiterrorism efforts against al-Qaida. After 9/11, Abu

Sayyaf’s attacks in the Philippines followed a similar backlash motivation.

Thus, a strong proactive response presents a dilemma for politicians and the electorate in

a liberal democracy. If a targeted government pursues rigorous antiterrorist policies that curtail

the general threat at home and abroad, these efforts may trigger a backlash that leads to a direct

attack at home.1 This is illustrated by Osama bin Laden threatened attacks on American soil in

retaliation for US actions in early 2006 to kill al-Qaida leaders (e.g., Ayman al Zawahiri).

However, a failure to address the general threat of terrorism also leaves the country vulnerable to

attacks at home and abroad. Hence, any response – retaliation or inaction – has negative

consequences that must be balanced. This dilemma is further complicated in the case of a

common transnational terrorist threat confronting two or more countries, insofar as each

country’s action has strategic implications on the other countries’ response.

The purpose of this article is to investigate proactive counterterrorism measures when

voters delegate such policy choices to elected officials in two countries facing a common

terrorist threat.2 The underlying game involves terrorists, elected officials, and voters. Unlike

the literature, our representation accounts for the strategic aspects of domestic politics, associated

with offensive countermeasures against a transnational terrorist threat. Previous analyses

focused on just two-player games with the targeted countries’ policymakers as the strategic

players.3 The inclusion of voters allows us not only to investigate the delegation problem, where

voters rely on elected officials to represent their preferences, but also to account for the

grievance aspect of proactive policies.4 We establish that voters are inclined to restrict offensive

3

operations. In particular, voters may strategically elect a government that places a low priority

on meeting the general terrorism threat so as to minimize backlash attacks while obtaining a free

ride on the efforts of another targeted nation. This strategizing on the part of voters results in a

Pareto-inferior level of proactive countermeasures than in the absence of delegation. Thus,

terrorist attacks can make targeted countries work against one another by inducing constituencies

to elect candidates who are soft on terrorism. If, however, the terrorists were only to target a

single country, then this adverse delegation problem is absent, because there is no other target to

provide a terrorist counteroffensive or to draw an attack. Our analysis shows that confronting a

common transnational terrorist threat is especially difficult in democracies.

The remainder of the paper contains four sections. Section 2 provides background and a

justification for the game’s structure. In Section 3, stage 2 and 3 of the three-stage game are

analyzed. Section 4 solves the all-important first stage where farsighted voters assume a

leadership role over the officials whom they elect. Section 5 indicates concluding remarks and

policy implications.

2. The underlying game: background and justification

To capture domestic politics and policy choice, we focus on the problem of delegation where

voters choose elected officials or policymakers in two terrorism-threatened democratic countries.

These policymakers must then decide proactive measures to mitigate future attacks from a

common terrorist threat from group A. Today, group A could be al-Qaida, while, in the 1980s, it

would have been the Abu Nidal Organization (ANO) or Islamic Jihad. Proactive responses –

e.g., infiltrating a terrorist group, attacking terrorist training camps, or assassinating or capturing

terrorists – represent a privately provided pure public good problem, because such actions come

at a private cost to the provider nation and generate nonexcludable and nonrival benefits to all at-

4

risk countries. We also recognize that enhanced offensive actions also increase the likelihood of

being attacked by another group, denoted by group B, that objects to the counteroffensive. For

example, Israeli retaliatory actions against the Palestine Liberation Organization (PLO) and

Black September at home and abroad led to more militant groups – e.g., the Popular Front for the

Liberation of Palestine (PFLP) and ANO – that frequently staged attacks to protest Israeli

actions. Hamas is a particularly apropos example of group B, since it retaliates against Israeli

responses and does so within Israel. Recent Israeli crackdowns on Fatah and Hezbollah incited

Hamas attacks.

Since 9/11, countries in the US-led coalition (e.g., Great Britain, Spain, Australia, the

Philippines, and Turkey) endured attacks at home from terrorists aligned or sympathetic to al-

Qaida. The loosely tied al-Qaida network nicely fits the scenario of our model where pressures

on al-Qaida can erupt in another group launching an attack on the country’s home soil. The

country that draws the attack is often the one that is perceived to have acted more heavy-

handedly than other countries,5 which fits the London bombings in the summer of 2005. Our

game representation captures several aspects of the proactive dilemma associated with

transnational terrorism: namely, the free-riding incentive, the backlash risk, and the delegation

problem. The latter arises because voters have an incentive to strategically elect a government

that puts less weight on the general terrorism threat in the hopes of shifting abroad more of the

offensive response, thereby putting more backlash risk on the other country. As such, an

electorate can influence the game subsequently played by the countries’ policymakers as they

enact counterterrorism measures. If, for example, voters are more concerned about the

retaliatory attacks than about the general threat, then they will choose a dovish policymaker.

This strategic vote can result in less action by both countries and a greater general terrorism

threat.6 Consequently, voters may be worse off than had they not acted strategically.

5

2.1. The players and the timing of the game

The game involves three different sets of players: voters, policymakers, and terrorists. Although

terrorists do not act strategically in our model and respond only to the actions taken by the two

countries, each terrorist group represents a particular type of threat to each country. Terrorist

group A poses a general threat to two countries whose people and properties can be targeted at

home and abroad. In addition, terrorist group B hits a proactive country at home with a

retaliatory attack, meant to display its displeasure and grievance at the county whose

countermeasures are viewed as more stringent. In each targeted country, a second set of players

consists of elected policymakers who decide countermeasures against group A in order to

minimize the expected damages from possible terrorist attacks in addition to minimizing the cost

of implementing the associated policy. The third set of players is the countries’ voters who share

the same objectives as elected policymakers. In each country, we assume that voters and

policymakers only differ in the weight that they place on the threat of experiencing a backlash

attack at home, stemming from their actions to curb the general terrorism threat. To simplify and

abstract from the complex political process associated with two democratic countries, we focus

on a representative voter from a majority group that dominates the process and is decisive in

determining the election of political candidates and, thus, policy alternatives.

The timing of the game is as follows: In stage 1, the voters in each targeted country

simultaneously elect a policymaker who then decides a proactive response to group A in stage 2.

This response is decided in a noncooperative fashion even though both governments are

confronted by a common threat. Given the reluctance of most governments to coordinate their

security policies, this is an appropriate assumption. We assume that voters and governments

know the terrorists’ preferences but are unsure about their propensity to engage in terrorist acts.

6

In stage 3, terrorist group A decides the nature of its campaign against the two countries. As a

potential reaction to government countermeasures, terrorist group B surfaces and attacks the

heavier-handed country. We employ the subgame perfection solution concept and thus solve the

game backwards starting with the terrorist campaigns in stage 3, moving to the choices of the

policymakers in stage 2, and ending with the voters’ election of the policymakers in stage 1.

3. Stage 2 and 3 of the game: counterterrorism and terrorism

As motivated by our discussion in Section 2, we first examine the general threat posed by group

A in stage 3 as it decides whether to conduct its terror campaign against countries 1 and 2, based

on the countermeasures ( ), 1,2i iθ = taken by the two countries. To capture the public good

nature of government actions at curbing the terrorist threat, we let ( )1 2g θ θ+ represent the

probability of a terrorist campaign failure and ( )1 21 g θ θ− + denote the probability of a terrorist

campaign success. The probability of failure function is strictly increasing and concave in the

cumulative countermeasures of the targeted governments, so that 0g′ > and 0.g′′ < The

campaign can result in failure (a “miss”) with payoff m or a success (a “hit”) with payoff h. Any

expected gains from A’s campaign must be at least as large as the benefit, b, of delaying the

campaign and pursuing the best alternative nonterrorist activity. Thus, the terrorist group will

engage in its campaign against both countries provided that the following inequality holds:

( ) ( )1 ,g m g h bγΘ + − Θ + ≥⎡ ⎤⎣ ⎦ (1)

where 1 2 ,θ θΘ = + ,h m> and γ represents A’s predisposition to waging its terror campaign.

For simplicity, γ is assumed to be uniformly distributed on the interval [ ], .α α− Because group

A’s predisposition is unknown to voters and their elected officials, A’s campaign likelihood, p, is

7

viewed as a random event. Given our assumptions, the voters’ and officials’ perceived

probability of a terror campaign is given by,7

( ) ( ) [ ] 1 2

1 1, 1 1 ( ) ,

2p b g m g hθ θ

α⎛ ⎞= − − Θ − − Θ⎜ ⎟⎝ ⎠

(2)

which is itself dependent on the two governments’ countermeasures. Performing comparative

statics on (2), we obtain,

( )1 2

0,2

p p gm h

θ θ α′∂ ∂= = − <

∂ ∂ (3)

so that the probability that group A engages in a terror campaign decreases as either country

exerts more antiterrorist efforts. These marginal probabilities are themselves increasing in the

actions of either country:

( )2 2 2 2

2 21 2 1 2 2 1

0.2

p p p p gm h

θ θ θ θ θ θ α′′∂ ∂ ∂ ∂= = = = − >

∂ ∂ ∂ ∂ ∂ ∂ (4)

Next, we turn to group B which, as discussed earlier, attacks as a protest to the

countermeasures levied by one of the countries on group A. The voters and policymakers

evaluate the threat that their country could be attacked by B to be a function of the relative

differences between the effort levels expended by the two countries in countering the general

terrorist threat. Each government or its designated policymaker assumes that country 1 will be

attacked if 1 2 ,θ η θ+ ≥ where 0η > represents B’s bias against government 1. This bias could be

the result of B’s accumulated past grievances built up over the years. This random variable is

assumed to be uniformly distributed on the interval [ ], .ψ ψ− Given the timing of the game, η is

unknown to the voters and policymakers in stage 1 and 2 when they make their decisions. We,

thus, let the perceived probability, 1,π that B attacks country 1 to be given by:

( ) ( )1 1 2 2 1, .π θ θ ρ η θ θ= ≥ − Since the distribution of η is uniform, we have:8

8

( ) ( )1 1 2 2 1

1 1, 1 ,

2π θ θ θ θ

ψ⎡ ⎤= − −⎢ ⎥⎣ ⎦

(5)

so that 2 11π π= − is the probability that B retaliates against country 2. From (5), we have:

1 2 1 2

1 2 2 1

10.

2

π π π πθ θ θ θ ψ

∂ ∂ ∂ ∂= = − = − = >∂ ∂ ∂ ∂

(6)

Thus, country i’s risk from a backlash attack increases with its own countermeasures and

decreases with those of the other country. All second-order partials are zero since the first-order

partials are independent of the iθ s.

Terrorist group B may arise out of an ethnic, religious, or political community, common

to both countries – e.g., the suicide bombers in London on July 7, 2005 were Islamic

fundamentalists with beliefs aligned with al-Qaida. Russian offensives against terrorists and

insurgents in Chechnya resulted in Chechen terrorists staging missions in Russia, including the

bombings of two Moscow apartment buildings (September 9 and 13, 1999) and the barricade and

hostage seizure of a Moscow theater (October 23, 2002). In addition, the terrorists behind the

3/11 Madrid train bombings shared religious and ethnic affinities with al-Qaida. Increases in

security against terrorism are apt to be directed in part against those interests identified with a

particular terrorist threat at home and abroad. This may then result in grievances among

sympathetic elements at home that erupt into a new group demonstrating its displeasure,

especially when the country’s measures appear particularly harsh relative to the other targeted

country.

3.1. Elected policymakers’ counterterrorism response: stage 2

We now fold the game back to stage 2 where an elected policymaker in each of the two targeted

countries decides the proactive response, while taking its counterpart’s response as given. To

9

represent the policymakers’ objective function, we must first indicate country i’s damage and

likelihood in four scenarios, given the presence of a general terrorist threat from group A and

localized threat from group B. iiD represents the damage to country i when group A directs

attacks at i’s interests at home and abroad, while group B stages protest attacks at home. The

likelihood of this scenario is ,ipπ where p and iπ have been previously defined. If, however,

group A attacks i’s interests at home and abroad, but B retaliates against j (i.e., the other country),

then ijD denotes the damage to i and occurs with probability ( )1 .ip π− Given that the first

scenario involves additional attacks than the second scenario, it is reasonable to assume

.ii ijD D> The third and fourth scenario involve no general threat from group A to country i. In

the third scenario, country i endures attacks from group B at home, resulting in damage iid with

probability (1 ) .ip π− Clearly, ii iiD d> since iiD also involves losses from attacks by group A at

home and abroad. Finally, the fourth case involves country i experiencing no attacks from either

terrorist group so that damage, ,ijd is zero with a probability of ( )( ) 91 1 .ip π− − Similarly, we

can define four scenarios for country j where , ,jj ji jj jjD D D d> > and 0.jid =

In each targeted country, the elected policymaker chooses its proactive response

( ), 1, 2 ,i iθ = taking its counterpart’s policy as given while anticipating the consequences of its

choice on the probabilities that it is attacked by group A or B or both. The policymaker’s

objective is to minimize the sum of its expected damages from the four scenarios and the costs of

its countermeasures, ( ).iC θ The cost function is assumed to be strictly increasing and convex in

.iθ As a special feature of the expected damages from attacks, a weight of igα is applied by the

elected policymaker to iiD , which reflects damages from attacks by groups A and B on i’s soil.

10

The weight is also applied to .iid This weight captures a policymaker’s aversion to policy-

induced terrorist attacks on home soil. As such, the proactive choice in country i is also

influenced by ,igα which varies along the unit interval, [ ]0,1 . An elected policymaker in stage 2

chooses ,iθ taking jθ as given, to

minimize ( ) ( ) ( )1 1 ,ig ig igi ii i ij i ii iZ p D p D p d Cπ α π π α θ= + − + − + (7)

where the arguments of p and iπ are suppressed. The associated first-order condition, after

rearrangement, is:

( ) (1 ) ( ) (1 ) 0.ig ig igii ii ii i ij ii ij ii

i i

pD d D p D D p d C

ππ α π α αθ θ

∂∂ ′⎡ ⎤ ⎡ ⎤− + − + − + − + =⎣ ⎦ ⎣ ⎦∂ ∂ (8)

The second-order condition associated with (7) is assumed to hold.10

Given that the sign of the first expression in brackets in (8) is positive, the first composite

expression in (8) is negative (recall that 0ip θ∂ ∂ < ) and captures i’s added benefits from

reducing the likelihood that group A will initiate its terror campaign owing to greater proactive

measures. The sign of the second expression in (8) is ambiguous and hinges, in large parts, on

igα or the potential distaste placed by the policymaker on a backlash attack launched by group B

to protest actions taken against group A. If this weight is close to zero so that backlash losses are

greatly discounted, then the second expression in (8) may be negative and represents an

additional marginal benefit from proactive measures. In this scenario, the policymaker places

more weight on shifting the retaliatory attack abroad than on the damage sustained at home. Of

course, C′ denotes the marginal provision cost of the proactive measure. A second relevant

scenario involves igα with values near one. When this occurs, the sign of the second bracketed

expression will be unequivocally positive if ,igii ijD Dα > since the iid term is positive.11 This

scenario means that the second expression in (8) represents an additional (proactive) marginal

11

cost coming from the backlash consequence. Scenario 1 with two marginal benefit terms and

single marginal cost expression implies greater offensive action than scenario 2 with its single

marginal benefit term and two marginal cost expressions. Sufficient weight placed on backlash

curtails a proactive response beyond the standard free-rider response associated with a

transnational terrorism threat (Sandler and Siqueira, 2006). In either scenario, marginal benefits

are equated to marginal costs for an interior solution to (8).

3.2. Nash equilibrium at stage 2

We now turn to the mathematical and geometrical representation of the Nash equilibrium for the

elected policymaker of the two targeted countries that confront the same general terrorism threat

and potential backlash consequences. The simultaneous solution of (8) for each policymaker

denotes the equilibrium counterterrorism policies of elected officials in stage 2. This solution

and comparative statics are described shortly, but first we display the solution graphically.

Equation (8) implicitly defines the best-response functions ( )iBR for policymaker i

( )1,2; i i j= ≠ where ( ), .igi i jBRθ θ α= This function relates i’s optimal choice of iθ to

alternative choices of jθ by country j, along with the weight attached to backlash damage. Other

parameters of the best-response function are suppressed for simplicity. Using the implicit

function theorem, we derive the slope of i’s best-response function to be:

( ) ( )2

2

2

1

0.

igi ii ii i ij

i jiig

j

i

pD d D

BR

Z

π α πθ θ

θθ

∂ ⎡ ⎤− − + −⎣ ⎦∂ ∂∂ = <∂∂∂

(9)

The sign of (9) is unequivocal because the cross-partial derivative and the bracketed

expression are both positive, so that the numerator must be negative. Moreover, the second-

12

order condition ensures that the denominator is positive. By (9), the reaction path of

policymaker i is thus negatively sloped: as he or she expends less counterterrorism effort, his or

her counterpart in j expends more effort. This negative slope can be traced to free riding and an

intent to draw fewer retaliatory attacks. By analogous reasoning, j’s reaction path is also

negatively sloped. Hence, proactive countermeasures are viewed as strategic substitutes.

[Figure 1 near here]

In Figure 1, the reaction paths (ignore the dashed reaction path) are displayed with 1θ on

the horizontal axis and 2θ on the vertical axis. The Nash equilibrium is at N, where the reaction

paths intersect. 1BR is steeper than a downward-sloping line with slope −1, while 2BR is flatter

than a downward-sloping line with slope −1 in order to ensure stability and uniqueness (Cornes

et al., 1999; Cornes and Sandler, 1996). In Figure 1, a line with slope −1 through N will intersect

the horizontal axis at the aggregate Nash equilibrium level of proactive measures for the two

policymakers combined; i.e., *1 2 .N Nθ θΘ = +

Next we display the influence of the policymaker’s weight ,igα attached to retaliatory

attacks, on his choice of .iθ Differentiating (8) with respect to this weight gives:

( )

2

2

,i i i

ii ii i ip ii

i iiigig

i

D d pd

BR

Z

π θ θπ πε ε

θ θα

θ

−⎛ ⎞ ∂⎡ ⎤− +⎜ ⎟⎣ ⎦ ∂∂ ⎝ ⎠=∂∂ −∂

(10)

where ( )( )/ /i i i i i iπ θε π θ θ π≡ ∂ ∂ and ( ) ( )/ /

ip i ip pθε θ θ≡ − ∂ ∂ are elasticity expressions. In

particular, i iπ θε captures i’s probability elasticity of suffering a backlash attack in response to its

countermeasures, while ipθε indicates the probability elasticity of preventing group A’s attacks at

home or abroad. Henceforth, the first elasticity is called the backlash elasticity, and the second

13

elasticity is termed the prevention elasticity. If i i ipπ θ θε ε≥ , then the expression in (10) is negative

owing to the numerator being positive and the denominator being negative. Thus, a greater

backlash elasticity relative to the prevention elasticity means that the best-response curve shifts

down and to the left in response to a large backlash weight (see dashed curve 1BR′ in Figure 1).

As a result, there is less total expended proactive measures at the new Nash equilibrium, N ′ ,

even though policymaker 2 increases such efforts in response to policymaker 1’s reduced efforts

– i.e., *′Θ < Θ in Figure 1. If, however, i i ipπ θ θε ε< , then the sign of (10) can be negative, zero,

or positive depending on whether the left-hand multiplicative expression in the numerator is less

than, equal to, or greater than (in absolute value) the right-hand expression. When the latter

holds, which we henceforth assume,12 the policymaker’s best-response curve shifts up in Figure

1 (not shown) and more total counterterrorism effort results. This case follows when the damage

from solely retaliatory attacks at home, ,iid is small and the backlash elasticity is also small, so

that i’s policymaker is not intimidated by group B.

3.3 Stage 2: further implications

To determine the equilibrium responses to changes in 1gα and 2gα at stage 2, we implicitly solve

the elected policymaker’s first-order conditions and obtain *( , )ig jgi iθ θ α α= , i, j = 1, 2 and .i j≠

Next, we incorporate these expressions into the two first-order conditions in (8) and totally

differentiate the resulting equation with respect to the two alphas to display the comparative

static reactions to changes in the weights given by the policymakers. We rearrange the

differentiated expressions and apply Cramer’s Rule to obtain the following proposition:

Proposition 1:

14

(i) If i i ipπ θ θε ε≥ , then * 0ig

id dθ α < and * 0igjd dθ α > .

(ii) If i i ipπ θ θε ε< and if

i iπ θε or iid is small enough, then * 0igid dθ α > and

* 0igjd dθ α < .

Proof: See Appendix 1.

Case (i) indicates that if the backlash elasticity is at least as great as the prevention elasticity,

then policymaker i’s countermeasures will fall as he puts more weight on the retaliatory threat.

As such, the shift displayed with curve 1BR′ in Figure 1 applies. Policymaker i places a heavier

burden on country j (i.e., * 0igjd dθ α > ), and both countries are more vulnerable to the general

threat as overall proactive measures drops. Proactive efforts are undersupplied owing to free-

riding and backlash concerns. When, however, case (ii) applies, policymakers’ proactive

responses move in opposite directions as igα changes. If, for example, less weight is placed on

backlash damages, then policymaker i exerts less countermeasures at combating the general

terrorism threat while policymaker j expends more effort.

4. Strategic voting in stage 1

We now fold the game back to stage 1 where each country’s voters can act strategically and elect

a policymaker, who can conceivably improve the voters’ well-being, perhaps at the expense of

the voters in the other targeted country. Two basic concerns are at play: the desire to free ride

on the proactive response of others and the wish not to draw a retaliatory attack by avenging

group B.13 Strategic voting can result in a worse outcome than without such voting.

Given some specified electoral process, voters in each country are viewed as electing a

policymaker (or government), while taking the election results in the other country as given.

Although the set of voters can differ over the single-dimensional parameter, ivα , representing

15

voter iv’s weight on damages from a retaliatory attack by terrorists, we assume that one group of

voters is decisive in each country. Moreover, the group’s preferences can be characterized by a

representative voter in each country.14 Since voters move first and are assumed to be forward

looking, voters must address a strategic delegation problem insofar as the elected policymaker,

not the voter, picks the proactive response according to his or her own preferences. If the

electorate looks ahead and takes this factor into account, they may choose a policymaker whose

igα will likely differ from the voter’s own weight. We now investigate the implication of this

difference.

Given our assumptions, the policymaker elected in each country is the one most preferred

by the representative voter from the majority group. Let this voter’s preference be characterized

by the backlash weight .imα In stage 1, the representative voter in country i chooses igα of the

elected policymaker to

*minimize (1 ) (1 ) ( )im im imi ii i ij i ii iZ p D p D p d Cπ α π π α θ= + − + − + , (11)

where ,p ,iπ and *iθ are all functions of igα and .jgα Analogous to the policymaker objective,

the objective in (11) is a sum of the damages in the various scenarios and the cost of proactive

measures. The sole difference is the weight that the representative voter (and its majority group)

attaches to the possibility of enduring a backlash attack. When determining which policymaker

to elect, each representative voter takes into account the impact of his choice on the policy that

will be played in the subsequent stage of the game. In so doing, each representative voter acts as

a Stackelberg leader vis-à-vis the elected policymaker (the follower) of both countries, who

displays Nash-Cournot behavior toward one another. Minimizing (11) with respect to ,igα and

using policymaker i’s first-order condition from (8) and the equilibrium best responses to

changes in ,igα we obtain the following expression (see Appendix 2 for details):

16

( ) ( )

i i i

ii ii i im igip ii jj

i i

D d pdπ θ θ

π πε ε α αθ θ

−⎧ ⎫∂⎡ ⎤− + Φ − =⎨ ⎬⎣ ⎦ ∂⎩ ⎭

( ) ( ) ( ) ( )1 1 ,im im imii ii ii i ij ii ij ii ji

j j

pD d D p D D p d

ππ α π α αθ θ

⎧ ⎫∂∂⎪ ⎪⎡ ⎤⎡ ⎤− + − + − + − Φ⎨ ⎬⎣ ⎦ ⎣ ⎦∂ ∂⎪ ⎪⎩ ⎭ (12)

where 0jjΦ > and 0jiΦ > are defined in Appendix 1. The remaining terms in (12) have been

defined previously, where 0jp θ∂ ∂ < and 0.i jπ θ∂ ∂ <

A sufficient condition for the right-hand expression within i of (12) to be negative is

that ,imii ijD Dα ≥ so that the representative voter’s weighted damages from attacks by groups A

and B on i’s interests exceed the damages from just attacks by group A on i’s interests. Although

stronger than needed, this assumption is likely to hold provided that the representative voter

views retaliatory attacks at home with sufficient disdain not to reverse the ii ijD D≥ inequality.

We are left with the following proposition:

Proposition 2: Assuming ,im

ii ijD Dα ≥ there are two scenarios depending on the relative

elasticities to the alternative threats:

(i) If ,i i ipπ θ θε ε≥ then .ig imα α>

(ii) If i i ipπ θ θε ε< and if

i iπ θε or iid are sufficiently small, then .im igα α>

Proof: See Appendix 3.

If the elasticity to experiencing a backlash attack is greater or equal to the elasticity to the

general threat of terrorism, then the representative voter will elect a government that puts more

weight on the threat of a backlash than he or she does. This results in each government exerting

less effort to combat the terrorist threat than had voters’ not acted strategically. Country i’s

17

voters are motivated by free riding on the proactive response of j and a desire not to draw a

retaliatory response from group B. This agrees with Spain’s election following 3/11 and the

withdrawal of forces by some other countries with troops in Iraq and Afghanistan once the threat

of a backlash attack grew. If both countries’ representative voters satisfy case (i), then a

Prisoners’ Dilemma delegation game follows with both countries reducing proactive efforts

beyond the suboptimal level implied by stage 2.15 In Figure 2, this shows up with the

policymakers’ best-reaction paths shifting down from the continuous paths to the dashed paths.

As such, the Nash equilibrium goes from N to ,N where individual and aggregate proactive

levels fall. Unfortunately, the representative voters’ strategic actions result in reduced welfare

levels to both – i.e., the iso-utility curves associated with N (not displayed) imply lower welfare

levels than those through N as the general threat of terrorism increases at home and abroad.

[Figure 2 near here]

In case (ii), it still remains possible that less effort toward combating the general threat of

terrorism will follow when the representative voter tries strategically to gain a greater free ride

from the other country’s proactive response by choosing a policymaker who downplays the

backlash concern. That is, the representative voter chooses a policymaker whose backlash

weight is less than .imα In case (ii), the representative voter knows that the elasticity of

prevention exceeds the backlash elasticity, where i iπ θε or iid is small. Because of the lack of

responsiveness to backlash or the small damages associated with iid , a policymaker has a greater

inclination to address the general terrorism threat without fear of reprisal. As such, a

policymaker that puts more weight on backlash damages will expend more proactive effort in

this case. By choosing a policymaker who cares little about the backlash, the representative

voter installs a policymaker less inclined to act in the hopes of getting a larger free ride from the

18

other targeted country. This kind of strategic thinking on the part of both countries’ voters will

again result in the downward shifts of the reaction paths in Figure 2. The attempt to profit on the

other country’s efforts yields an undersupply of proactive measures that jeopardizes both

countries and reduces welfare in a Prisoners’ Dilemma type of scenario. For both cases, voters’

strategic action results in the Nash equilibrium shifting in the southwestern direction where the

aggregate proactive response falls.

5. Concluding remarks and policy implications

This paper presents a three-stage game with three sets of participants: terrorists, elected

policymakers, and voters. The model accounts for the strategic interaction between voters and

their delegated policymakers, charged with deciding proactive countermeasures to limit a

transnational terrorist threat confronting two countries. As such, this paper is the first to

investigate domestic politics in a strategic framework as it applies to counterterrorism. The

analysis shows that strategic foresight by the voter leads to an undersupply of proactive

measures. This reduced effort is motivated by two desires: free riding on the other country’s

countermeasures and limiting any reprisal terrorist attacks. The voter elects a policymaker who

will subsequently exploit his or her counterpart by curbing proactive measures. Similar actions

abroad will result in an equilibrium where welfare is reduced – i.e., the strategic move is self-

defeating.

This result indicates that the need for international cooperation when addressing a

common terrorist threat (e.g., al-Qaida, Jemaah Islamiyah, and Abu Nidal Organization) could be

even more important than shown in past studies, which do not consider domestic politics

(Sandler and Siqueira, 2006). This extra difficulty stems from a delegation problem, associated

with the voters’ reliance on an elected policymaker. This then provides yet another factor why

19

liberal democracies confront a real dilemma when addressing terrorism (Wilkinson, 1986).

Nations must devise some mechanism for orchestrating an international proactive response to a

common terrorism threat. To date, the best example of this is the Afghanistan response. But

even there, most of the effort fell on the US and UK shoulders with token help by Canada,

Australia, and Denmark (The Economist, 2006). Reprisal attacks on British, Australian, South

Korean, and Spanish interests were intended by terrorists to limit or eliminate these countries’

participation – a strategy that worked in the case of Spain and South Korea. Terrorists remain

better than governments in acting as a united force.

As a future direction, the influence of strategic voting on cooperative solutions can be

investigated. The delegation problem may still work against cooperation if voters elect

policymakers with greater backlash concerns or free-riding interests. The analysis here can also

be applied to defensive measures deployed by commonly targeted nations. Even without

cooperation, strategic voting may ameliorate the oversupply of defensive actions in an attempt to

transfer the attack to a softer target abroad. Since such measures are strategic complements,

strategic voting, and the leadership that it implies, may elect officials who are less concerned

with transferring the attack, particularly when the country has interests at home and abroad.

20

Appendix 1: Derivation of Proposition 1 Following the procedures outlined in the text, we obtain:

*

,i jjiig

d

d

θα

−Ω Φ=

Δ , 1,2i j = , ,i j≠ (A1)

*

,j i ji

ig

d

d

θα

Ω Φ=

Δ , 1,2i j = , i j≠ , (A2)

where

11 12

21 22

,Φ Φ

Δ ≡Φ Φ

( )

,i i i

ii ii i ii p ii

i i

D d pdπ θ θ

π πε εθ θ

− ∂⎡ ⎤Ω ≡ − +⎣ ⎦ ∂ 1,2,i =

( ) ( ) ( )2

21 2 ,jjg jg

jj j jj jj j ji jj jj jij j j

p pD d D D d D C

ππ α π α

θ θ θ∂∂ ∂⎡ ⎤ ⎡ ⎤ ′′Φ ≡ − + − + − − +⎣ ⎦ ⎣ ⎦∂ ∂ ∂

, 1, 2,i j = ,i j≠

( ) ( )2

1 ,jgji j jj jj j ji

j i

pD d Dπ α π

θ θ∂ ⎡ ⎤Φ ≡ − + −⎣ ⎦∂ ∂

, 1,2i j = , i j≠ .

Given 0jjΦ > , 0jiΦ > , and the fact that stability requires 11 22 12 21Δ ≡ Φ Φ − Φ Φ > 0, the signs of

(A1) and (A2) depend on the sign of iΩ .

Thus if ,i i ipπ θ θε ε≥ then 0iΩ > so that * 0ig

id dθ α < and * 0igjd dθ α > . For the

remaining case, iΩ can be rewritten as

( ) ( ) ,i i i i i

ii p ii ii ii

i

p D d dπ θ θ π θπε ε εθ

⎡ ⎤Ω ≡ − − +⎣ ⎦

owing to the definition of .i iπ θε If , therefore

i i ipπ θ θε ε< and i iπ θε or iid is sufficiently small, then

0iΩ < and we obtain: * 0igid dθ α > and * 0ig

jd dθ α < .

21

Appendix 2: Derivation of equation (12)

Minimizing (11) with respect to ,igα we obtain:

* ** *j jim im im imi i i i

i ii i ii ii iiig ig ig igi j i j

p pD D p D p D

θ θθ π θ ππ α π α α αθ α θ α θ α θ α

∂ ∂∂ ∂ ∂ ∂∂ ∂+ + +∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂

( ) ( )* ** *

1 1j ji i i ii ij i ij ij ijig ig ig ig

i j i j

p pD D p D p D

θ θθ π θ ππ πθ α θ α θ α θ α

∂ ∂∂ ∂ ∂ ∂∂ ∂+ − + − − −∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂

( ) ( )* ** *

1 1j jim im im imi i i ii ii i ii ii iiig ig ig ig

i j i j

p pd d p d p d

θ θθ π θ ππ α π α α αθ α θ α θ α θ α

∂ ∂∂ ∂ ∂ ∂∂ ∂− − + − + −∂ ∂ ∂ ∂ ∂ ∂ ∂ ∂

*

0iig

Cθα

∂′+ =∂

. (A3)

Rearranging, we obtain:

( )1im im imi ii ii i ij i ii ii ij

i i i i i

p p pD D d p D p D

π ππ α π π α αθ θ θ θ θ

⎧ ∂ ∂∂ ∂ ∂+ − − + −⎨∂ ∂ ∂ ∂ ∂⎩

( )*

1 imi iii ig

i

p d Cπ θαθ α

⎫∂ ∂′+ − + =⎬∂ ∂⎭

( )1im im imi ii ii i ij i ii ii ij

j j j j j

p p pD D d p D p D

π ππ α π π α αθ θ θ θ θ

⎧ ∂ ∂∂ ∂ ∂⎪− + − − + −⎨∂ ∂ ∂ ∂ ∂⎪⎩

( )*

1 jimiii ig

j

p dθπ α

θ α⎫ ∂∂ ⎪+ − ⎬∂ ∂⎪⎭

. (A4)

Using the policymaker’s first-order condition in (8) to substitute out for C′ in (A4) and

rearranging slightly, we have:

( ) ( )1 1im im im imi i ii ii i ij i ii ii ij ii

i i i i i i

p p pD D d p D p D p d

π π ππ α π π α α αθ θ θ θ θ θ

⎧ ∂ ∂ ∂∂ ∂ ∂+ − − + − + −⎨∂ ∂ ∂ ∂ ∂ ∂⎩

( ) ( )*

1 1ig ig ig igi i i ii ii i ij i ii ii ij ii ig

i i i i i i

p p pD D d p D p D p d

π π π θπ α π π α α αθ θ θ θ θ θ α

⎫∂ ∂ ∂ ∂∂ ∂ ∂− − − + − + − − ⎬∂ ∂ ∂ ∂ ∂ ∂ ∂⎭

( ) ( )*jim im im im imi

i ii ij ii ij ii ij ii ii igj j

pD D d D p D D d d

θππ α α α α αθ θ α

⎧ ⎫ ∂∂∂⎪ ⎪⎡ ⎤ ⎡ ⎤= − − − + + − − +⎨ ⎬⎣ ⎦ ⎣ ⎦∂ ∂ ∂⎪ ⎪⎩ ⎭. (A5)

Focusing only on the left-hand side (A5), we cancel and arrange terms to yield:

22

( ) ( ) ( )*

( ) (1 ) .im ig im ig im ig im igi i ii ii i ii ii ii ig

i i i i

p pD d p D p d

π π θπ α α π α α α α α αθ θ θ θ α

⎧ ⎫∂ ∂ ∂∂ ∂− − − + − + − −⎨ ⎬∂ ∂ ∂ ∂ ∂⎩ ⎭ Further rearranging slightly gives:

( ) ( ) ( )*

im igi i ii ii ii ii ii ii ig

i i i

pD d p D d d

π π θπ α αθ θ θ α

⎧ ⎫∂ ∂ ∂∂ − + − + −⎨ ⎬∂ ∂ ∂ ∂⎩ ⎭.

After some slight manipulations, the above expression becomes:

( ) ( )

*ii ii i im igi i i i i

ii igi i i i i

D d ppd

p

πθ π θ π θ α αθ θ π θ θ α

⎧ ⎫−⎡ ⎤∂ ∂ ∂∂⎪ ⎪+ + −⎨ ⎬⎢ ⎥∂ ∂ ∂ ∂⎪ ⎪⎣ ⎦⎩ ⎭.

Using the two definitions for elasticity and putting the above expression together with the right-

hand side of equation (A5), we have:

( ) ( )

*

i i i

ii ii i im igi ip ii ig

i i

D d pdπ θ θ

π π θε ε α αθ θ α

−⎧ ⎫∂ ∂⎡ ⎤− + − =⎨ ⎬⎣ ⎦ ∂ ∂⎩ ⎭

( ) ( ) ( ) ( )1 1 jim im imii ii ii i ij ii ij ii ig

j j

pD d D p D D p d

θππ α π α αθ θ α

⎧ ⎫ ∂∂∂⎪ ⎪⎡ ⎤⎡ ⎤− − + − + − + −⎨ ⎬⎣ ⎦ ⎣ ⎦∂ ∂ ∂⎪ ⎪⎩ ⎭. (A6)

Using (A1) and (A2), and canceling terms, the above expression becomes (12) in the text.

Appendix 3: Derivation of Proposition 2 By assumption, im

ii ijD Dα ≥ . From our results in Appendix 1, we know that 0jjΦ > and

0jiΦ > . Furthermore, given i i ipπ θ θε ε≥ for case (i), we can sign (12) in the following way:

( )( ) ( )im igα α+ + − = − + .

The parenthesis terms in the above expression represent the terms jjΦ and jiΦ in (12). From the

above equation, we can conclude that .im igα α< Alternatively, for case (ii) where i i ipπ θ θε ε<

and i iπ θε or iid is small, we can sign (12) as follows:

23

( )( ) ( ) ,im igα α− + − = − +

from which we can conclude that .im igα α>

24

Footnotes

1. To simplify the analysis and discussion, we only allow for such attacks at home. We can,

however, extend the analysis to permit backlash incidents at home and abroad. For example,

Israeli actions against the Palestine Liberation Organization led, in part, to a more militant

breakaway Abu Nidal Organization that attacked “Zionist” targets at home and abroad. The

Jemaah Islamiyah car bombing of the Australian embassy in Jakarta, Indonesia, however, fits the

assumption of the model, because a country’s embassy is considered to be home soil. Australia

was targeted in the bombing that killed 9 and injured over 150, owing to its support of US-led

operations against al-Qaida.

2. From 1968 until the early 1980s, this common threat either came from the Palestinian

groups or the leftists. Since 1979, this threat came increasingly from Islamic fundamentalist

terrorists. The model can be expanded to allow there to be more than two threatened countries.

This extension would greatly increase the notation without additional insight.

3. For example, see Arce and Sandler (2005), Sandler and Lapan (1988), and Sandler and

Siqueira (2006). For domestic terrorism, the two active players are the terrorists and the

policymaker (Anderton and Carter, 2005; Frey and Leuchinger, 2003).

4. Only Rosendorff and Sandler (2004) in a recruitment context examined grievances

stemming from proactive measures. These authors did not include voters.

5. The risk of a counterattack may be tied to vulnerability – soft-target status. Our analysis

implicitly assumes equal defensive measures, so that relative vulnerability is not a consideration.

Earlier papers have investigated soft-target vulnerability (Heal and Kunreuther, 2005).

6. Because voters choose policymakers that later implement policy, strategic voting is

analogous to strategic delegation. In a related paper, Persson and Tabellini (1992) considered

strategic delegation in the context of tax competition and European integration. In a

25

noncooperative game, these authors showed that voters possessed incentives to delegate fiscal

`policy to policymakers who were different than them in terms of endowments. In the symmetric

political equilibrium, voters of both countries delegated policymaking to a government that was

more prone to taxation than both median voters. Also, see Besley and Coate (2003) and Dur and

Roelfsema (2005) on different delegation problems.

7. Equation (2) follows from writing the probability density function as ( ) ,p p γ= ≥ Γ

where ( ) ( )1b g m g h⎡ ⎤Γ = − Θ − − Θ⎣ ⎦ is based on (1). Thus ( )1 ,p P γ= − ≤ Γ where the

cumulative density function ( )P i equals: ( )1

.2 2

ds

α α α α

Γ

−

Γ= +− −∫

8. To derive (5), we note that ( )1 2 11 ,Pπ η θ θ= − ≤ − where ( )P i equals:

( )2 1

2 11.

2 2

dsθ θ

ψ

θ θψ ψ ψ

−

−

−= +− −∫

9. For simplicity, we assume that the backlash attack by group B must be in country i to

cause losses to i. We can easily allow B’s attacks to harm i’s interests at home and abroad. The

model will be the same provided that the Ds and ds are ordered as in the text. This will hold if

there is a “host country disadvantage” – i.e., losses to i are greater from B hitting i’s interests at

home than abroad.

10. The second-order condition is given by

( ) ( ) ( )2 2

2 21 2 0.

igig igi

i ii ii i ij ii ii iji i i i

Z p pD d D D d D C

ππ α π αθ θ θ θ

∂∂ ∂ ∂ ′′⎡ ⎤ ⎡ ⎤= − + − + − − + >⎣ ⎦ ⎣ ⎦∂ ∂ ∂ ∂

11. Even if ,igii ijD Dα < the expression can still be positive if the iid expression is

sufficiently large.

12. We employ this assumption on two grounds. First, it provides a more distinct case to

26

earlier situations where reaction paths shift down. Second, this assumption allows us later to

utilize a direct connection between voter preferences over damages and government policy for

particular scenarios that simplifies discussion without unduly sacrificing generality by

maintaining two alternative scenarios.

13. A good example of this reaction is the terrorists’ response to the US retaliatory raid on

Libya on April 15, 1986 for its alleged involvement in the La Belle discotheque bombing in

Berlin earlier in April. Following the US raid, terrorism directed at US interests at home and

abroad increased greatly (Enders and Sandler, 1993, 2006).

14. Such a group may prove decisive, given its skills at organizing and mobilizing its

members. Historical and demographic factors may also play a role in maintaining this group’s

predominant electoral role. For more specific models concerning voting and elections, see

Persson and Tabellini (2000).

15. Free-riding incentives in stage 2 lead to suboptimal offensive countermeasures, since

neither policymaker accounts for reduced damages to the other country from his or her efforts

(Sandler and Siqueira, 2006).

27

References Anderton, C.H., Carter, J.R., 2005. On rational choice theory and the study of terrorism. Defence

and Peace Economics 16, 275–282.

Arce, D.G., Sandler, T., 2005. Counterterrorism: a game-theoretic analysis. Journal of Conflict

Resolution 49, 183–200.

Besley, T., Coate, S., 2003. Centralized and decentralized provision of local public goods: a

political economy approach. Journal of Public Economics 87, 2611–2637.

Cornes, R., Hartley, R., Sandler, T., 1999. Equilibrium existence and uniqueness in public goods

models: an elementary proof via contraction. Journal of Public Economic Theory 1, 499

–509.

Cornes, R., Sandler, T., 1996. The Theory of Externalities, Public Goods, and Club Goods, 2nd

ed. Cambridge University Press, Cambridge.

Dur, R., Roelfsema, H., 2005. Why does centralisation fail to internalise policy externalities?

Public Choice 122, 395–416.

The Economist, 2006. Afghanistan: heading south. The Economist 378(8463), 12.

Enders, W., Sandler, T., 1993. The effectiveness of anti-terrorism policies: a vector-

autoregression-intervention analysis. American Political Science Review 87, 829–844.

Enders, W., Sandler, T., 2006. The Political Economy of Terrorism. Cambridge University

Press, Cambridge.

Faria, J. R., Arce, D.G., 2005. Terror support and recruitment. Defence and Peace Economics

16, 263–273.

Frey, B.S., Luechinger, S., 2003. How to fight terrorism: alternative to deterrence. Defence and

Peace Economics 14, 237–249.

Heal, G., Kunreuther, H., 2005. IDS model of airline security. Journal of Conflict Resolution

28

49, 201–217.

Kunreuther, H., Michel-Kerjan, E., 2004. Policy watch: challenge for terrorism risk insurance in

the United States. Journal of Economic Perspectives 18, 201–214.

Kunreuther, H., Michel-Kerjan, E., Porter, B., 2003. Assessing, managing and financing extreme

events: dealing with terrorism. Working Paper 10179. National Bureau of Economic

Research, Cambridge, MA.

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Review of Economic Studies 59, 689–701.

Persson, T., Tabellini, G., 2000. Political Economics. MIT Press, Cambridge, MA.

Rosendorff, B. P., Sandler, T., 2004. Too much of a good thing? The proactive response

dilemma. Journal of Conflict Resolution 48, 657–671.

Sandler, T., Lapan, H.E., 1988. The calculus of dissent: an analysis of terrorists’ choice of

Targets. Synthèsis 76, 245–261.

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Journal of Economics 39, 1370–1387.

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B.J.Pol.S. 37, 573–586 Copyright © 2007 Cambridge University Press

doi:10.1017/S0007123407000324 Printed in the United Kingdom

Terrorist Signalling and the Value of Intelligence

DANIEL G. ARCE A N D TODD SANDLER*

This article presents a model of terrorist attacks as signals where the government is uncertain as to whetherit is facing a group that is politically motivated or militant. Pooling equilibriums result with two types ofex post regret: P-regret, where the government concedes to political types that would not subsequently attack;and M-regret, where the government does not concede to militant types that subsequently attack at greaterlevels. Avoidance of such regret defines a measure of the value of intelligence. Counter-terrorism policy canthen be characterized in terms of whether a government should focus on increased intelligence versus increasedsecurity (hardening targets). The recommended use of asset freezing is also evaluated in terms of the resourcesrequired by terrorists to achieve the various equilibriums. Finally, this article supports the empirical findingof intertemporal substitution of resources by terrorists, concerned with the level of government response totheir attacks.

Terrorism is the premeditated use, or threat of use, of violence by individuals or subnationalgroups to obtain a political or social objective through intimidation of a target audience,beyond that of the immediate victims. Terrorists try to impose sufficient costs on a targetconstituency so that its government is pressured into conceding to the terrorists’ demands,when concessions are viewed as less costly than enduring future attacks. The immediateresponse to an attack is for the government to address the initial consequences, includingclean-up and additional security measures. Thereafter, the government assesses the likelysubsequent threat that the group poses in terms of its resources and proclivity for futureattacks. Politically orientated groups are ultimately interested in change and will eventuallychannel resources into political activities. In contrast, militant groups are more vengefuland will focus on attacks until concessions are granted.

Consider, for example, the Spanish government, which has had an armed struggle since1968 with the Basque-separatist group Euskadi ta Askatasuna (ETA). Spain also sufferedfrom the Madrid train station bombings on 11 March 2004 by Islamic terrorists seekinga withdrawal of Spanish troops from Iraq and Afghanistan. ETA can be characterized asa politically motivated group because the demands of its larger constituency may be metthrough the granting of more regional autonomy and self-determination (for example,responsibility for social services, taxation and policing). On occasion, ETA has agreed toa cease-fire. Moreover, ETA has been discriminate in its targeting, avoiding attacks withmass casualties. The Islamic terrorists in the Madrid bombing were more militant, intenton escalating attacks if their demands were not immediately met. They threatened toturn Spain into an ‘inferno’ should the withdrawal of Spanish troops from Iraq not takeplace.1 Three days after the Madrid bombings, Spanish voters reversed their apparentcourse to re-elect the government of the popular party Aznar and elected the socialist

* School of Economic, Political and Policy Sciences, University of Texas at Dallas. This article has benefitedfrom the comments by three anonymous referees and the Editor Hugh Ward; the authors are solely responsiblefor the article’s content.

1 MSNBC.com, ‘Group Threatens to Turn Spain into Inferno: Islamic Group Issues Warning after AllegedPlotters Kill Selves’, 5 April 2004, accessed 3 June 2005.

574 A R C E A N D S A N D L E R

Zapatero government, which had campaigned under the promise to withdraw Spanishtroops in Iraq unless they came under United Nations’ control.

In assessing the signalling content of an attack, the government must determine anappropriate response that hinges on its beliefs about the militancy of the terrorists. Thisdecision is made under conditions of incomplete information, because the government isunlikely to be completely informed whether the terrorists’ preferences are militant orpolitical. This lack of information may stem from many causes. For example, multipleterrorist groups may be claiming responsibility for a series of attacks. Moreover, terroristgroups may have both political and militant elements that vie for dominance, so that thecontrolling wing may change and not be apparent at any point in time. This change in grouporientation may arise when government concessions appease the moderates, therebyleaving the more extreme elements to carry on the terrorist campaign.2 Followingconcessions of partial autonomy made to ETA in 1978, extremist elements in ETA wageda much more deadly campaign into the 1990s. Additionally, new and splinter groups maycome on the scene. Splintering was especially true of the Palestine Liberation Organization(PLO), which gave rise to more militant groups such as Black September, Popular Frontfor the Liberation of Palestine, Abu Nidal Organization and others. During a group’s initialattacks, the target government does not know the group’s resolve or militancy. In still otherinstances, no group may claim responsibility, leaving the government unenlightened as tothe perpetrator or its orientation.

The effect of incomplete information is twofold. First, there is a reputation incentive forpolitically motivated terrorists (P-types) to mimic militants (M-types) with a spectacularattack if it will quickly lead to concessions. Secondly, an incentive may exist for M-typesto mimic P-types so that the government will be less compelled to harden targets, whichwould diminish the likelihood (or increase the cost) of the logistical success of futureterrorist activity. This then feeds into a notion of intelligence consistent with that givenin Cilluffo et al. by involving an understanding of the motivations, thoughts and futureplans of one’s enemies.3 Multi-disciplinary intelligence, including insights into thecultures and mindsets of terrorist organizations, is crucial for counter-terrorism policy. Inparticular, there is the possibility of ex post regret where a government concedes topolitically motivated terrorists to whom it would not have conceded under completeinformation. This type of regret may arise because the magnitude of the attacks leads thegovernment to conclude falsely that it is facing militants who will escalate attacks if theirdemands are not met. Alternatively, a government may hold firm and face a second typeof ex post regret when it is subsequently attacked by militant terrorists whom thegovernment would have accommodated under complete information. Examples of the firsttype of ex post regret include concessions to groups such as the PLO, African NationalCongress (ANC), Irish Republican Army (IRA) and ETA, which each have a history ofusing diplomacy as well as sustaining a military wing, whose influence is not wellunderstood.4 Examples of the second type of regret include the Algerian revolt (1954–62)and Israel’s conflict with Hezbollah and Hamas, where the government did not seek a

2 Ethan Bueno de Mesquita, ‘Conciliation, Counterterrorism, and Patterns of Terrorist Violence’, InternationalOrganization, 59 (2005), 145–76; Todd Sandler and Daniel Arce, ‘Terrorism and Game Theory’, Simulation andGaming, 34 (2003), 319–37.

3 Frank L. Cilluffo, Ronald A. Marks and George C. Salmoiraghi, ‘The Use and Limits of US Intelligence’,Washington Quarterly, 25 (2002), 61–74.

4 Per Baltzer Overgaard, ‘The Scale of Terrorist Attacks as a Signal of Resources’, Journal of ConflictResolution, 38 (1994), 452–78.

Terrorist Signalling and the Value of Intelligence 575

political solution and attacks subsequently escalated. We will discuss these cases in furtherdetail in the body of the article. There is, thus, a value of intelligence that corresponds toeliminating or diminishing the likelihood of ex post regret.5 Similarly, Hoffman has arguedthat because religious-based terrorists are generally more violent than secular ones, thereexists a need for intelligence to identify terrorists’ type/preferences.6

A suicide mission is a tactic of some militant groups to signal their resolve.7 Suchmissions indicate that the group will gladly sacrifice even its human resources to raise thecarnage of the campaign. This graphic signal was first employed by Hezbollah in itssuccessful efforts to rid Lebanon of Israeli forces and then foreign peacekeepers in 1982and 1983, respectively. Noteworthy suicide attacks included the 23 October 1983 suicidetruck bombing of the US Marines barracks and the near-simultaneous suicide car bombingof the French paratroopers’ apartment building. The effectiveness of these attacks inremoving the peacekeepers led other militant groups – such as, Hamas, the PalestineIslamic Jihad (PIJ), the Al-Aqsa Martyrs Brigade and the Liberation Tigers Tamil Eelam(Tamil Tigers) – to adopt suicide missions. In some instances, these suicide campaignsresulted in concessions (for example, political concessions to Tamil Tigers) after an initialregret, once the extent of future attacks became understood by the targeted government.

In this article we examine a signalling model of terrorist attacks in which the governmenthas incomplete information about terrorists’ types. Past signalling models focused onattacks as signals of terrorist resource levels, where terrorists are (initially) able to stagean attack of sufficient magnitude to induce concessions, irrespective of whether they havehigh or low resources. Specifically, Lapan and Sandler examined the case where terroristsare militant and expend all remaining resources on attacks if concessions are not granted.8

By contrast, Overgaard analysed politically motivated groups that allocate all remainingresources to (non-violent) political purposes if no accommodations are made.9

Our analysis is centred on the creation of a unifying model that simultaneously allowsfor both militant and political terrorist types. This facilitates a comparison of the value ofintelligence for each case. No generality beyond the nexus of intelligence and uncertaintyabout terrorists’ types/preferences is claimed. In addition, our model permits a fundamentalextension whereby the government institutes defensive measures when attacks surpass athreshold, so that the value of intelligence depends not only on whether concessions occur,as is the case in the prior literature, but also on counter-terrorism policy. Specifically, thevalue of intelligence is broadened to include not only ex post regret following concessions,but also ex post regret following an escalation of terrorism in the absence of anaccommodation. We characterize when a government should focus on increased

5 The literature on the value of intelligence for terrorism has focused on the prevention of specific events, suchas 9/11 or terrorists’ use of weapons of mass destruction – see, e.g., Kevin Michael Derksen, ‘Commentary: TheLogistics of Actionable Intelligence leading to 9/11’, Studies in Conflict and Terrorism, 28 (2005), 253–68; FrancisH. Marlo, ‘WMD Terrorism and US Intelligence Collection’, Terrorism and Political Violence, 11 (1999), 53–71.In so doing, earlier articles indicated what type of intelligence (e.g., signal interception, human, or imagery) hasthe greatest effectiveness at each stage of a terrorist event. Unlike our exercise, the literature has not characterizedthe value of intelligence in terms of a signalling game of incomplete information, where the government isill-informed about the nature of the terrorist group.

6 Bruce Hoffman, Inside Terrorism (New York: Columbia University Press, 1998), pp. 185–205.7 Bruce Hoffman and Gordon H. McCormick, ‘Terrorism, Signaling, and Suicide Attacks’, Studies in Conflict

and Terrorism, 27 (2004), 243–81.8 Harvey E. Lapan and Todd Sandler, ‘Terrorism and Signalling’, European Journal of Political Economy,

9 (1993), 383–97.9 Overgaard, ‘The Scale of Terrorist Attacks as a Signal of Resources’.

576 A R C E A N D S A N D L E R

intelligence versus increased security (hardening targets) to mitigate this possibility.Finally, the resulting equilibriums exhibit intertemporal substitution of terrorist resourceswhere a militant group may restrain attacks for strategic advantage, thereby exhibitingvarying patterns of terrorism, consistent with low-terrorism and high-terrorism periods ashave been empirically identified.10 The effects of proactive measures to freeze terroristassets are also examined in this context.

The remainder of the article contains three sections. The next section presents a unifyingsignalling model where governments are uninformed about terrorist types. In the ensuingsection, we indicate the value of intelligence. The final section contains concludingremarks.

TERRORIST SIGNALLING: A UNIFYING MODEL

In this section, we introduce a signalling model where the government has incompleteinformation about the type (preferences) of terrorists that it confronts. Information isasymmetric because terrorists can observe the outcomes of elections, implementation ofproactive policies and the hardening of potential targets. As is standard, we consider atwo-period model with dichotomous type set: M, P. Terrorists are M-types if they aremilitant; that is, they receive a benefit equal to the discounted sum of their attacks in thefirst and second period when the government holds firm. This is the case if terroristsperceive a positive value from attacking an obstinate government, or if they test agovernment’s never-to-concede pledge by unleashing their military wing. In addition,fundamentalist terrorists often view violence as sanctified, so that they are less constrainedin their carnage. Militant fundamentalists use violence to punish non-believers and seekmaximum casualties even when attacks will not result in concessions. Similarly, Dorandiscussed militant (Arabic/Islamic) terrorists in terms of their predilection for escalation.11

To summarize, militants are willing to escalate their attacks as a form of brinkmanship thatchallenges the interests of the opposing power to provoke the threat of intervention, if notactual intervention. For these militant terrorists, there exists a gap between the long-termgoals set by their (religious/ideological) convictions and their immediate goals,constrained by unlikely successful political action. The terrorists’ short-term goals aretherefore aimed at foiling the targeted government, through escalated attacks, rather thanthe attainment of their long-term goals. For this reason, some argued that terrorist groupssuch as al-Qaeda are not susceptible to traditional international political pressures.12

By contrast, P-types are politically motivated because an attack is a pure cost interms of both resources and political capital. They consequently direct all second-period resources to political activity, from which they receive a benefit. In comparison toM-types, P-types have reached the point where the opportunity cost of escalation isunacceptably high. Elsewhere, we have analysed joint consideration of M-types andP-types in a bargaining context13 and Siqueira has done so in terms of the incidence of

10 Such periods have been identified by Walter Enders and Todd Sandler, ‘Patterns of Transnational Terrorism,1970–1999: Alternative Time-Series Estimates’, International Studies Quarterly, 46 (2002), 145–65; WalterEnders and Todd Sandler, “Transnational Terrorism 1968–2000: Thresholds, Persistence, and Forecasts’,Southern Economic Journal, 71 (2005), 467–82.

11 Michael Doran, ‘The Pragmatic Fanaticism of al Qaeda: An Anatomy of Extremism in Middle EasternPolitics’, Political Science Quarterly, 117 (2002), 177–90.

12 Cilluffo, Marks and Salmoiraghi, ‘The Use and Limits of US Intelligence’, p. 65.13 Sandler and Arce, ‘Terrorism and Game Theory’.

Terrorist Signalling and the Value of Intelligence 577

competing-faction violence.14 Neither of the articles referred to above addressed thepotential for inferring terrorists’ type through past attack patterns.

Upon receiving a signal in terms of first-period attacks, the government either concedes(C) or does not concede (D). Governments often have a different response to spectacularattacks; consequently, we define an attack of at least (resource) level R* to be such thata non-conceding government significantly increases its level of deterrence/defensivepolicies to limit successful future attacks.15 An example is to harden targets throughincreased security, thereby decreasing the probability of a logistical success in asecond-period attack. In this way, the discount factor for a second-period attack subsequentto a first-period attack of at least level R* is given as . By comparison, the discount factorapplied to all other second-period attacks is given by , where . Following 11September 2001 (9/11), the United States created the Department of Homeland Security(DHS) to harden a wide range of targets (for example, airports, airplanes, public places,borders, ports and critical infrastructure), thereby greatly lowering . The US response isconsistent with 9/11 attacks signalling the likely presence of a militant group, wherebydefensive measures are prudent in the absence of concessions.

We assume that terrorists receive resource level R in each period, where R R*. In thefirst period, terrorists select their attack level from the dichotomous signal set a, A, wherea [0, R*) and A [R*, R]. An A-attack is considered large enough for the governmentto increase its defensive posture, thereby inducing discount factor if a second-periodattack occurs.

The game is illustrated in Figure 1, with a timeline that is given as follows:

1. Nature (N) selects the terrorist’s type from M, P.2. In the first period, terrorists select their signal from the set a, A, where A a as

defined above. The dotted lines connecting nodes in Figure 1 are the government’s(G) information sets, which are labelled according to the signal the governmentreceives: GA or Ga.

3. Upon receiving this signal, the government either concedes (C) to the terrorists or holdsfirm (D).

4. If the government does not concede, terrorists combine the remainder of theirfirst-period resources with their second-period resources. How these resources are putto use depends upon the terrorist’s type/preferences, as specified by their payoffs.Militants (M-types) will expend all available resources in a second-period attack, whileP-types will use them towards non-violent means.

Payoffs are expressed symbolically as P for P-types, M for M-types, and G for thegovernment. They are calculated as follows:

1. Each terrorist type receives resource level R in each period.2. The government faces the costs of the attack levelled against it in the first period: A

or a.

14 Kevin Siqueira, ‘Political and Militant Wings within Dissident Movements and Organizations’, Journal ofConflict Resolution, 49 (2005), 218–36.

15 Daniel G. Arce and Todd Sandler, ‘Counterterrorism: A Game-Theoretic Analysis’, Journal of ConflictResolution, 49 (2005), 183–200; Todd Sandler and Kevin Siqueira, ‘Global Terrorism: Deterrence versusPreemption’, Canadian Journal of Economics, 39 (2006), 1370–87. In Overgaard, ‘The Scale of Terrorist Attacksas a Signal of Resources’, the act of not conceding is described as a response, which we interpret as an increaseddefensive posture.

578 A R C E A N D S A N D L E R

Fig. 1. Incomplete information about terrorists’ preferences

3. If the government concedes, it incurs second-period costs of S 0. Terrorists receivea payoff equal to their net remaining funds: R A or R a, plus vR, where v is the‘victory’ parameter that increases the value of second-period resources relative to thosediscounted by or . Essentially, v is a third discount factor.

4. If the government does not concede:

i. P-types receive R A R or R a R, the discounted present value of theirremaining resources put to political use.

ii. M-types receive a benefit equal to the discounted value of their remaining resources,which they expend in a second-period attack. Subsequent to an A-level attack, thispayoff is discounted by because the government responds to such an attackwith increased defensive policies. The discounted value of the two attacks istherefore A (R A) R 2R (1 )A. Similarly, after an a-attack,M-type terrorists gain 2R (1 )a. In either case, the government’s payoffs aredefined by the zero-sum nature of attacks, so that they lose an amount equal to theterrorists’ payoff.

The critical levels of belief in this model correspond to the conditional probabilitiessuch that the government concedes at information sets GA and/or Ga. This occurs whenits belief that it is facing an M-type meets or exceeds a threshold level. Belief i

corresponds to nodes i 1, 2, 3, 4, where 1 2 1, 3 4 1. G concedes at GA ifits expected payoff is such that:

EG[CGA] A S A2 [2R (1 )A]1 EG[DGA]; i.e., if

1 S/(2R A) LA. (1)

When the government G experiences an A-level attack, it will concede provided that itsbelief that it is facing an M-type exceeds the lower bound LA given in Condition 1. The

Terrorist Signalling and the Value of Intelligence 579

lower is LA, the more likely that a concession will occur. From Condition 1, we haveLA/S 0. As the costs of concession increase, the government is less likely to concede.

Lapan and Sandler recognized that the value of S may be determined through adeclaration or commitment by the government never to concede to terrorists’ demands.16

Such a commitment has the effect of reducing the government’s options, because, as Sincreases, it becomes less likely that the government will concede regardless of the priorprobability of M-types.17 The beliefs embodied in Condition 1 also imply that LA/R 0,so that the government is more apt to concede as terrorists’ resources increase. Thisfollows because a larger R means that the government incurs greater damage from amilitant group’s second-period attacks if the government holds firm. Condition 1 alsoimplies that LA/(/) 0. Recall that at GA the D strategy corresponds to an increasein the government’s defensive posture relative to that at Ga, leading to a greater discountingof second-period attacks where . As defensive measures are more effective, /increases; consequently, the government must be more certain that it is facing an M-typeto concede. We denote the reverse of the inequality in Condition 1 as 1, indicating thecondition on beliefs such that the government does not concede at GA.

Similarly, the government concedes at Ga if EG[CGa] a S a3 [2R (1 )a]4 EG[DGa], which indicates the following threshold:

4 S/(2R a) La. (2)

The signs on La/S and La/R are the same as those associated with LA for identicalreasons. Here, the comparative effect of versus , which applied for LA, does not comeinto play because it is only through an attack of level A R* that the government increasesits defensive posture (in relative terms), resulting in discount factor . Finally, Condition 2 denotes the condition under which Condition 2 is reversed, in which case thegovernment selects D at Ga.

S IGNALLING EQUILIBRIUMS AND THE VALUE OF INTELLIGENCE

Once again, incomplete information raises the concerns that politically motivated terroristsmay be seeking a quick resolution to their grievances by posing as militant types, and/ormilitant types have purposely avoided spectacular attacks to forestall a heightened focuson security by their targets. As an example of the latter phenomenon, Enders and Sandlerpresciently stated that authorities should focus on intelligence and prophylactic measuresin anticipation of upturns in terrorist incidents involving casualties following fairly lengthylulls of greater than two years.18 By 9/11, the US was well beyond a two-year lull. In thisway, the value of intelligence that we investigate corresponds to eliminating or reducingthe occurrence of ex post regret associated with misreading terrorists’ true intentions. Onesuch occurrence is ex post P-regret, meaning that the government concedes to P-types,which, under complete information, the government would hold firm against. Another

16 Lapan and Sandler, ‘Terrorism and Signalling’. The Irangate hearing following the Reagan administration’sarms-for-hostages negotiations was an effort by the US Congress to raise S to subsequent administrations.

17 This is akin to a sense of government resolve – see Robert Powell, ‘The Dynamics of Longer BrinkmanshipCrises’, in Peter C. Ordeshook, ed., Models of Strategic Choice in Politics (Ann Arbor: University of MichiganPress, 1989), pp. 151–75.

18 Walter Enders and Todd Sandler, ‘Is Transnational Terrorism Becoming More Threatening? A Time-SeriesInvestigation’, Journal of Conflict Resolution, 44 (2000), 307–32.

580 A R C E A N D S A N D L E R

possibility is ex post M-regret, where, under complete information, the government wouldhave preferred either concession or increased security in the face of escalated militantattacks. Clearly, either type of ex post regret is only possible in a pooling equilibrium whereboth types send the same signal. Consequently, we begin with an examination of thepooling equilibriums, followed by a characterization of the separating equilibrium whereeach type sends a different signal.

An A-pooling equilibrium occurs under Conditions 1 and 2 so that the government’s(local) strategy at GA is C and at Ga it is D. Together, these strategies comprisethe behavioural strategy CD. Henceforth, we adhere to the convention of listingthe government’s strategy at GA first and its strategy at Ga second. Given Conditions 1and 2, P-types undertake an A-attack in period 1 if P[A, CD] R A vR R a R P[a, CD]. This simplifies to

R (A a)/(v ), (3)

thereby defining a resource constraint to be met for this equilibrium to hold.Furthermore, for M-types to engage in an A-attack, it must be the case thatM[A, CD] R A vR 2R (1 )a M[a, CD]; i.e.,

R [A (1 )a]/[(1 ) (v )]. (4)

Information set Ga is not reached in an A-pooling equilibrium. Nevertheless, actionsoff-the-equilibrium path must be justified in terms of the consistency and rationality ofthe set of beliefs and actions specified there. A set of beliefs that supports D at Ga is thatthe government believes that it is more likely to be facing a P-type at Ga. This is consistentwith the upper bound on 4 given in Condition 2, implying that the government’s beliefthat it is facing an M-type is low. Furthermore, P-types would send the out-of-equilibriumsignal a 0, implying that Condition 3 rather than Condition 4 is the binding constrainton R. Finally, the A-pooling equilibrium occurs with ex post P-regret because thegovernment is potentially conceding to P-types to whom it would not have conceded undercomplete information. For purposes of comparison, all equilibrium conditions aresummarized in Table 1.

An example of this pooling equilibrium is the internationalization of the Palestiniancause.19 The premier example of a Palestinian-based spectacular (A-level attack) is the1972 Munich Olympics hostage incident staged by the Black September PLO offshoot,resulting in the death of eleven Israeli Olympian competitors and five terrorists. Whatactually occurred in the aftermath of the ill-fated attempt to concede to the Black Septemberterrorists is entirely consistent with the payoffs that follow information set GA. TheEuropean reply to this security failure was immediately to establish special anti-terroristunits that successfully acquitted themselves in subsequent hostage incidents (for example,Grenzschutzgruppe Neun’s rescue of a hijacked Lufthansa aeroplane at Mogadishu,Somalia on 18 October 1977),20 thereby implying a discount factor of for futureattacks. During the same time period, the PLO was granted special observer status in theUnited Nations, and, by the end of the 1970s, the PLO had formal diplomatic relations withmore countries than did Israel, consistent with the vR component of payoffs.21

19 Hoffman, Inside Terrorism, pp. 67–86.20 Lufthansa flight 181, a Boeing 737, was hijacked en route from Mallorca to Frankfurt on 13 October 1977.

The plane was stormed in Mogadishu, following stop-overs in Rome, Larnaca, Dubai and Aden.21 Hoffman, Inside Terrorism, p. 75.

Terrorist Signalling and the Value of Intelligence 581

TABLE 1 Summary of Equilibriums

Conditions on Value ofEquilibrium beliefs Forms of regret intelligence

A-pooling 1 S/(2R A) Ex post P-regret:C at GA; D at Ga 4 S/(2R a) potential S

concessionsto P-types

a-pooling 1 S/(2R A) Ex post P-regret:C at GA; C at Ga 4 S/(2R a) potential S

concessionsto P-types

a-pooling 1 S/(2R A) Ex post M-regret:D at GA; D at Ga 4 S/(2R a) M-types escalate (2R a S)R [(1 )A (1 )a]/2( )

Separating EquilibriumD at GA; D at Ga 1 1 None actions makeR [(1 )A (1 )a]/2( ) 3 1 information

complete.

Next, consider an a-pooling equilibrium with concession. When Conditions 1 and2 hold, the government’s strategy is CC.22 It follows that P[a, CC] P[A, CC] andM[a, CC] M[A, CC] because A a. For example, instead of increasing counterterror-ism measures (inducing ), governments may accommodate terrorists.23 Indeed, severalEuropean nations (France and Greece in particular) have allegedly accommodated M-typesin order to tacitly obtain immunity from attacks.24 Furthermore, Overgaard argued that attimes concessions made to the ANC, IRA and PLO can be understood in terms of ex postP-regret, because these organizations’ commitment to their military wings is not wellunderstood.25

In the prior literature on signalling and terrorism, ex post regret occurred under anA-pooling equilibrium in Lapan and Sandler and an a-pooling equilibrium in Overgaard.26

Neither type of pooling equilibrium took place in the other model, owing to differencesin preferences posited for terrorists in each case. As either type of pooling equilibrium canresult in our model, we are able to measure and compare the value of intelligence in aunified framework. Specifically, the value of intelligence under P-regret is the difference

22 Beliefs consistent with Condition 1 do not violate forward induction as M-types have the greater incentiveto send an out-of-equilibrium signal of A.

23 See the discussion in Dwight R. Lee, ‘Free Riding and Paid Riding in the Fight against Terrorism’, AmericanEconomic Association Papers and Proceedings, 78 (1988), 22–6.

24 For example, a revolutionary organization, known as the 17 November, had an alleged arrangement withthe Greek government, whereby the terrorists directed attacks against non-Greek targets in return for sanctuary,see The Economist, issue no. 1831 (London: The Economist, 1984). From 1975 until the summer of 2002, the17 November operated with impunity, carrying out 146 attacks and twenty-two assassinations. A failed bombingattempt on 22 June 2002 at the Port of Piraeus in Athens led to the first-ever arrest for the group.

25 Overgaard, ‘The Scale of Terrorist Attacks as a Signal of Resources’.26 Lapan and Sandler, ‘Terrorism and Signalling’; Overgaard, ‘The Scale of Terrorist Attacks as a Signal of

Resources’. In the former study, ex post regret occurred when conceding to a low-resource type that initially attacksat a high (A) level.

582 A R C E A N D S A N D L E R

between the government’s payoff for conceding to a P-type, as occurs in equilibrium, andits payoff for not conceding, as happens under complete information.

RESULT 1. The value of intelligence under P-regret is S, regardless of whether anA-pooling or a-pooling equilibrium occurs.

This result holds because the difference between not conceding or conceding to a P-typeis S in either pooling equilibrium. As S is partially determined by the government’s publicstance towards concessions, it follows that a hard-line government is going to place greatervalue on intelligence because concessions implicitly increase the cost of P-regret. This alsoholds for terrorists bent on the annihilation of their targets, as S is commensurately high.This justifies US investments in intelligence and the creation of the DHS after 9/11. It isalso consistent with Israeli investment in intelligence because of its perpetual dealings withmilitant terrorists who deny Israel’s right to existence.

Our model also identifies a new type of regret: ex post M-regret, where the governmentholds firm at either information set and is subsequently attacked in the second period byM-types. In this equilibrium, Conditions 1 and 2 hold, implying that the priorprobability of an M-type must be low.27 It is clear that P[a, DD] P[A, DD] becauseA a. In addition, M[a, DD] 2R (1 )a 2R (1 )A M[A, DD] requiresthat

R [(1 )A (1 )a]/2( ). (5)

This condition increasingly holds as the expected level of deterrence after an A-levelattack increases ( decreases), implying that if M-types expect a large response to afirst-period attack, then they will rationally make an intertemporal substitution favouringa second-period attack. This is a novel unintended consequence of terrorist deterrence(hardening targets). For example, elsewhere we have examined the public aspects ofcounter-terrorism policy and found that deterrence creates a public cost for those who donot harden targets, resulting in inefficiencies akin to the tragedy of the commons.28 Here,(anticipated) deterrence does not actually eliminate attacks, but instead leads to strategicintertemporal substitution of attacks, so that terrorists can catch the government lessprepared when launching their offensive.

The film, The Battle of Algiers, poignantly depicts this escalating pattern of tactics,which does not occur in prior signalling models. The Front de Liberation Nationale (FLN)began with a policy of weeding marginal revolutionary elements – drunks and prostitutes– out of the Casbah district, something the imperial French probably did not even interpretas terrorism; i.e., a 0. Indeed, Hoffman argued that prior to the French execution (byguillotine) of two FLN members, the terror campaign had been non-lethal by design –directed against inanimate symbols of French rule such as government offices andbuildings, military cantonments and police stations, but not deliberately against people.29

This was followed by escalating tactics such as shooting police, bombing civilian localesand conducting a general strike.30

27 As P-type have a payoff off the equilibrium path, R A vR, that is greater than its equilibrium payoff, thesebeliefs do not violate forward induction.

28 Arce and Sandler, ‘Counterterrorism’.29 Hoffman, Inside Terrorism, p. 62.30 The film is historically accurate since European civilians were only targeted after a bomb exploded in the

predominately Arab Casbah district (presumably by rogue French officials) in response to FLN activities againstFrench gendarmes.

Terrorist Signalling and the Value of Intelligence 583

A novel aspect of this pooling equilibrium is that Condition 2 places an upper-boundrestriction on terrorists’ resources for actions on the equilibrium path.31 Given limitedresources, M-types may rationally choose to attack at level a rather than A, and attack withgreater force (amassed resources) in the second period. The larger second-period attackis also preferred because it does not induce the government to initially harden targets theway an A-level attack would. This outcome is consistent with empirical evidence ofintertemporal substitution of attacks.

When Condition 5 holds, M-regret occurs under the auspices of an a-poolingequilibrium. In contrast to P-regret, M-regret is defined in terms of the opportunity costof one of two forgone alternatives. First, under complete information the governmentprefers to concede at node 4, rather than not concede. This is an intelligence concernregarding incomplete information about the type of terrorists the government is facing;here, the value of intelligence is the difference in the government’s payoffs for conceding(C) versus not conceding (D) at node 4; i.e., (2R a S). Under this form of M-regret,the value of intelligence is now a decreasing function of S. A tough public stance againstterrorists is tantamount to a commitment to weather subsequent attacks by M-types.Because R now enters into the value of intelligence, a policy of freezing assets (limitingR) reduces this value of M-regret. For example, a great deal of ETA assets were frozenfollowing 9/11, thereby decreasing both the Spanish government’s willingness to concedeto ETA and ETA attacks themselves. Any proactive counter-terrorism policy that curbsterrorist resources (such as, destroying terrorist training camps, capturing terrorists orinfiltrating groups) will also reduce the value of M-regret. Conversely, terrorists with lessrestricted access to a large amount of assets require a commensurately larger amount ofintelligence (for example, Abu Nidal Organization in the 1980s). Thus, the Tamil Tigersrun a commercial shipping network, 95 per cent of which is estimated to be the transportof legitimate commercial materials.32 An inability to freeze this source of income raisesthe value of intelligence about the Tamil Tigers in lieu of M-regret. Insufficientinternational proactive measures mean that R is high, so that M-regret leads to a highervalue of intelligence.33

Alternatively, a government might prefer to harden its targets at node 4, rather thanconcede.34 This is a security concern. Hardening targets at node 4 results in a payoff ofG 2R (1 )a, where discount factor replaces for hardened targets. Thedifference between the -based payoff and original -based payoff at node 4 is( )(2R a), which establishes the degree of security concern. Determining whichform of regret is the greater forgone alternative is crucial for formulating counterterrorismpolicy. To wit:

RESULT 2. M-regret is more of a security than an intelligence concern if S (2R a).

This result is novel because it gives a prescription for counter-terrorism policy to avoidM-regret. If the inequality in Result 2 holds, then policy should be focused on hardening

31 Condition 2 holds for the A-pooling equilibrium with P-regret, but Condition 2 constrains thegovernment’s belief at Ga, which is off the equilibrium path, and therefore met by 4 0, where no restrictionon R results.

32 Peter Chalk, ‘Liberation Tigers of Tamil: EELAM’s (LTTE) International Organization – A PreliminaryAnalysis’, Commentary No. 77, Canadian Intelligence Service, Ottawa, Canada, 2000.

33 Such insufficient measures are identified by Todd Sandler, ‘Collective versus Unilateral Responses toTerrorism’, Public Choice, 124 (2005), 75–93.

34 We thank an anonymous referee for this suggested extension.

584 A R C E A N D S A N D L E R

targets – a security concern. For example, if the government’s resolve is high, therebyincreasing S, then security should be commensurately raised regardless of the size of pastterrorist attacks (i.e., even in the absence of a spectacular). If, by contrast, the inequalityis reversed, then security is less of a policy concern than intelligence. Moreover,intelligence should be focused on a judicious assessment of militant terrorists’ demandsto induce them to abandon violence. Indeed, as the left-hand side of the inequality in Result2 is the value of information under P-regret, S, this result shows that such a focus runsthe risk of P-regret. Result 2 recognizes the trade-off between P-regret and M-regret atinformation set Ga.

Finally, when Condition 5 is reversed, a separating equilibrium is possible whereM-types engage in an A-attack, P-types execute an a-attack, and the government does notconcede to either type. This corresponds to the Conditions 1, 2 and 5. In thisscenario, there is no regret because the government recognizes that M-types are makingthe A-attack so that signalling acts as a perfect substitute for intelligence. Indeed, followingBayes’s rule, we have 1 1 and 3 1.

Thus far, we have interpreted a policy of asset freezing as reducing R, for which theCondition 5 for a separating equilibrium is increasingly met. Militants will attack moreheavily in the first period, anticipating that their resources may be frozen thereafter.Moreover, P-types will set a 0 so as to avoid having their assets frozen and maximizepolitical benefits. If, in addition, M(A, DD) P(a, DD), then this separating equilibriumcaptures the publicity rationale for terrorism. Many organizations (for example, PLO,Hezbollah and Hamas) have turned militant because of difficulty in creating recognitionof their cause through traditional political channels. If the government is not going toconcede, terrorism has the effect of greatly increasing public awareness.

This separating equilibrium and the a-pooling equilibrium with M-regret are essentiallytwo sides of the same coin. In anticipating a response, militants will either attack moreheavily in the first period, as is the case in the separating equilibrium, or they will bidetheir time and attack more heavily in the second period. Which side of the coin comes updepends upon whether Condition 5 or 5 holds. As either condition is independent of thegovernment’s public stance towards conceding (S), all that matters is the (anticipated)reaction to an attack () and the ability to reduce assets (R). The greater the level ofdeterrence and, thus, the lower is , the more likely that Condition 5 holds, implying apooling equilibrium with ex post M-regret and escalating attacks. More successful terroristorganizations are able to determine an effective level of violence that is at once ‘tolerable’for the local populace, tacitly acceptable to international opinion and sufficientlymodulated not to provoke massive government crackdown and reaction.35 In contrast, theTupamaros in Uruguay was a terrorist group whose level of violence was unacceptable forthe local populace and a government offensive destroyed them. The Italian Red Brigadesmet a similar fate following the 17 December 1981 kidnapping of General James LeeDozier, the senior US officer at NATO’s southern European command. Callous acts, suchas the 6 May 1978 murder of the former premier Aldo Moro, turned public opinion againstthe Red Brigades. The trade-off inherent in Conditions 5 and 5 endogenously definesthe edge of brinkmanship as it relates to the escalating behaviour of militant terrorists.

If, moreover, is time-variant, then our result is indicative of Faria’s terror cycles, wherethere is an inverse relationship between government deterrence (via law enforcement inFaria) and terrorist activities.36 We offer no formal repeated-game analysis, but, by

35 See Hoffman, Inside Terrorism, p. 162.36 Joao Ricardo Faria, ‘Terror Cycles’, Studies in Nonlinear Dynamics and Econometrics, 7 (2003), article 3.

Terrorist Signalling and the Value of Intelligence 585

extension, a non-stationary suggests two types of cycles through a state-dependentdetermination of whether Condition 5 or 5 holds. This is consistent with the empiricalresults that identified two cyclical components of terrorism: a high-activity and alow-activity series which are likely by-products of intertemporal substitution ofresources.37 Terrorists’ high-activity series cannot be sustained, akin to the separatingequilibrium in our model. In contrast, the low-activity series can be escalated, againconsistent with an a-pooling equilibrium with M-regret. Previous signalling models werenot indicative of such empirical findings.

The M-regret and separating equilibrium also share an important message about thedifference between successful counter-insurgency tactics and the resolution of terrorism.In either case, military tactics reduce , but may buttress the equilibrium conditions underwhich M-types attack in the second period. Defensive postures affect the magnitude, butnot the occurrence of signalling equilibriums with second-period attacks. This reinforcesthe definition of terrorism in the opening of this article, particularly when terrorists’ goalsare religious/ideological. Tactical counter-terrorism policies that are orthogonal to thesegoals do not temper terrorist actions, but instead encourage intertemporal substitution,which then places a further premium on intelligence.

CONCLUDING REMARKS

In a recent paper, Hoffman and McCormick characterized terrorism as a signalling gamewhere target governments are ill-informed about terrorist groups’ ‘objectives, resources,and commitment’.38 Given the short-term nature of most terrorist groups, with new groupsappearing each year and others splintering, governments are faced with the never-endingchore of trying to assess the threat of terrorist groups under incomplete information. Amiscalculation of this threat can either mean that a government underestimates a group’smilitancy and comes to regret its own resolve to hold firm, or else that a government failsto recognize a group’s political intent and comes to regret its concessions. The rise offundamentalist terrorism means that both militant and political groups are prevalent in thepost-Cold War era.39 This diversity in intent and resolve of terrorist groups means thatregret (i.e., responding inappropriately to terrorist demands) may have greater con-sequences for governments now than in the 1970s and 1980s when groups were morehomogeneous and less militant on average. Thus, the value of intelligence, which limitsregret, has increased in recent time.

By introducing a model that unifies the existing signalling analyses of terrorism, ourarticle offers a framework that is more descriptive of the complex world of post-9/11terrorism with militant and political terrorist groups co-existing. An important innovationis to allow for defensive and proactive policies. Defensive actions can motivateintertemporal substitutions by militant groups that strategically hold back on attacks tocatch a target government less aware. Proactive measures can reduce R and, thereby,influence the pooling and separating equilibriums. Government resolve, as reflected byhigh concession costs, also affects these equilibriums. We also give a characterization of

37 Enders and Sandler, ‘Patterns of Transnational Terrorism, 1970–1999’; Enders and Sandler, ‘TransnationalTerrorism 1968–2000’.

38 Hoffman and McCormick, ‘Terrorism, Signaling, and Suicide Attacks’, p. 244.39 Hoffman, Inside Terrorism.

586 A R C E A N D S A N D L E R

optimal (regret-minimizing) counter-terrorism policy that is based on the relationshipbetween terrorist resources and government resolve.

Our article demonstrates the trade-off between hardening of targets and intelligence.Recent game-theoretic work showed that international co-operation to shore up weak links(i.e., attractive soft targets) will be woefully inadequate owing to free-riding incentives.40

As a consequence, the value of intelligence remains high in the face of al-Qaeda’s globalnetwork. Moreover, other recent work highlighted the inadequacy of proactive policies bythe international community to destroy terrorist assets with respect to global terroristnetworks.41 This, in turn, keeps terrorists’ resources high, thereby raising the valueof intelligence in a world besieged by heterogeneous terrorist threats. The inadequacy ofinternational co-operation in terms of defensive and proactive counter-terrorism elevatesthe value of intelligence, given insufficient knowledge on the nature of the terrorist threat.

40 Sandler, ‘Collective versus Unilateral Response to Terrorism’.41 Arce and Sandler, ‘Counterterrorism’.

CBRN Attack Perpetrators: An EmpiricalStudy

Kate Ivanova

The Ohio State University at Newark

Todd Sandler

University of Texas at Dallas

Based on zero-inflated negative binomial regressions applied to theMonterey weapons of mass destruction data, this article assesses thefuture risks from chemical, biological, radiological, and nuclear (CBRN)terrorism. Once the threshold for CBRN attacks is surpassed, furtherattacks arise: the expected number of CBRN incidents is over one and ahalf times higher than past events. Religious cults and groups with atransnational orientation pose the largest CBRN threat to society. Otherthings constant, nationalists ⁄ separatists and religious fundamentalistsare not more apt to engage in CBRN terrorism than compared to‘‘other groups.’’ Democratic and corrupt regimes are the likely venuesfor CBRN incidents. Based on past incidents, rich countries are especi-ally vulnerable to CBRN terrorism. Thus, recent actions by the U.S.Department of Homeland Security to put more resources into guardingagainst CBRN attacks appear sound. This study indicates that nonfunda-mentalist terrorists also present CBRN risks to democracies. From a for-eign policy viewpoint, CBRN terrorism is not a problem that richdemocratic countries can confront alone, because the terrorists willmove to where there is the least vigilance. Our study indicates the likelyperpetrators and types of attacks that nations must cooperate to avoid.

Since the hijackings on September 11, 2001 (henceforth, 9 ⁄ 11) and the Tokyosubway sarin attacks on March 20, 1995, there is a worry that terrorists will resortto chemical, biological, radiological, and nuclear (CBRN) attacks (Roberts 2000;Tucker 2000; Gressang IV 2001). Such attacks would provide a means for surpass-ing the ‘‘media bar’’ imposed by 9 ⁄ 11, where future terrorist incidents must besufficiently catastrophic or costly to warrant media coverage beyond that of 9 ⁄ 11,with its near 3,000 deaths. The U.S. Department of Homeland Security (DHS)is taking the use of biological agents as a serious terrorist threat by allocating

Author’s Note: Kate Ivanova is an Assistant Professor; Todd Sandler is the Vibhooti Shukla Professor of Economicsand Political Economy. The authors thank Gary Ackerman of the Monterey Institute of International Studies forproviding the WMD data. We also thank the School of International Relations, University of Southern California,for funding data acquisition on rule of law and corruption. We have profited from the comments of three anony-mous referees. This research was partially supported by the U.S. Department of Homeland Security (DHS) throughthe Center for Risk and Economic Analysis of Terrorism Events (CREATE) at the University of Southern California,grant number N00014-05-0630. However, any opinions, findings, and conclusions or recommendations are solelythose of the authors and do not necessarily reflect the views of the DHS.

2007 International Studies Association.Published by Blackwell Publishing, 350 Main Street, Malden, MA 02148, USA, and 9600 Garsington Road, Oxford OX4 2DQ, UK.

Foreign Policy Analysis (2007) 3, 273–294

billions of dollars to Project BioShield that stockpiles vaccines to counter a biolo-gical attack (US [DHS] 2005). DHS Secretary Michael Chertoff stated that def-ense against CBRN terrorism and other potentially devastating terrorist incidentsis an essential priority of the DHS budget in the near-term (Chertoff 2005).

Terrorist experts, however, disagree about the threat posed by CBRN terror-ism. One group of experts stresses a host of deterrents to the use of CBRN weap-ons that include losing constituency support and funding, drawing a massiveretaliation (e.g., U.S. actions against the Taliban and al-Qaida after 9 ⁄ 11), sur-mounting the weaponization hurdle, accepting the handling risks, and ignoringthe cost-effectiveness of conventional terrorist attacks (Rapoport 1999; Dishman2001; Enders and Sandler 2006: 251–252). For example, Rapoport (1999) indi-cates that, on a per-incident basis, conventional terrorist attacks kill more peoplethan CBRN attacks.1 Another group of experts highlights factors that promotesuch attacks. These factors include the availability of information and expertise,heightened frustrations of terrorists, demonization of a target population, deep-seated grievances of perpetrators, and the possession of a millenarian, apocalyp-tic, or messianic vision (Vegar 1998; Roberts 2000; Simon and Benjamin 2000;Blum, Asal, and Wilkenfeld 2005; Enders and Sandler 2006:253).

Experts also differ on the likely perpetrator of CBRN incidents if such attackswere to take place. Many researchers characterize religious cults and religiousfundamentalists as the likely users of CBRN weapons, particularly when thesegroups address an ethereal audience, emphasize hatred of nonbelievers, and dis-play an inapposite relationship (see, especially, Gressang IV 2001; but also seeHoffman 1995; Betts 1998; Cameron 1998; Dishman 2001; Palfy 2003; Post2005). In contrast, other researchers argue that nationalists ⁄ separatists and othersecular actors (including loners) presented the greatest CBRN risk in the pastand will likely present the largest such risk in the future (Rapoport 1999; Tucker2001; Sinai 2005). In many ways, assessing CBRN risks and the likely perpetratorsis an empirical question that requires studying past events, because there arecompelling arguments on both sides of these debates.

The primary purpose of this paper is to apply statistical inferential proceduresto ascertain the likely perpetrators of CBRN terrorist attacks, based on data onCBRN incidents collected by the Monterey Institute of International Studies(2005). Although we suggest some logically drawn hypotheses, our main task isto ascertain which side of competing hypotheses in the literature is supported bythe data gathered to date on CBRN incidents. In addition, we determine if pastCBRN incidents are a determining factor of future attacks—that is, does the pastportend the future for CBRN attacks? We also investigate whether a terroristgroup’s transnational orientation supports its proclivity to employ CBRN attacks.For each class of potential perpetrators, we relate regime characteristics (i.e.,democracy, rule of law, and corruption) to its likely use of CBRN weapons in ter-rorist attacks. We find that, among groups, religious cults pose the greatestCBRN threat to date. Other things constant, a transnational orientation (i.e.,engaging in transnational terrorist attacks) also increases a group’s reliance onCBRN attacks. Past CBRN incidents increase the likelihood of future CBRNattacks for all perpetrators as a group and nationalists ⁄ separatists as a cohort.For each type of perpetrator, democracy increases the risks of CBRN attacks,while corruption also heightens this risk. Wealth, as measured by income percapita, augments the likelihood of CBRN incidents. These findings can informgovernments about likely threat and perpetrators of CBRN attacks.

The current study differs in a number of ways from a recent paper by Ivanovaand Sandler (2006) that also relied on the Monterey Institute’s weapons of mass

1 Ivanova and Sandler (2006) note that the average conventional terrorist incident killed one person, while theaverage CBRN attack killed just a half a person.

274 CBRN Attack Perpetrators

destruction (WMD) dataset (henceforth, called Monterey WMD data). This ear-lier study primarily presented odds ratio tests to investigate correlates to CBRNattacks; the current study presents a variety of regressions that explain the vari-ation in CBRN attacks. Unlike the earlier study, the current paper identifiesinfluences on various cohorts of potential CBRN terrorists. For example, we indi-cate how regime characteristics affect a cohort’s likely use of CBRN weapons. Inaddition, the current study investigates the underlying dynamics of CBRN attacksby ascertaining how past CBRN incidents affect current CBRN incidents. Eachcohort of perpetrators is analyzed separately, thereby displaying how regimecharacteristics can impact types of perpetrators differently.

The body of the paper contains five sections. In the first section, essential defi-nitions and concepts are given, along with a discussion of the datasets and varia-bles. Justifications are also indicated for examining CBRN incidents in isolationfrom traditional terrorist incidents. The second section puts forward the sixempirical hypotheses that underlie the empirical study. The relationship betweengroup type and CBRN terrorism is investigated in the third section. Followingthe presentation of the statistical model, we provide and discuss the statisticalresults. For alternative cohorts of perpetrators, we investigate the influence ofregime type, country wealth, and past CBRN terrorist incidents on current CBRNincidents in the fourth section. Conclusions and policy implications are drawn inthe final section. Our study is in the spirit of Ackerman’s (2005:141) recommen-dation for careful empirical analysis of past CBRN incidents to identify potentialterrorists and the factors that may determine their use of CBRN terrorism. Suchan exercise can inform intelligence and law enforcement agents, while helpingto formulate public policy.

Definitions, Datasets, and Variables

Terrorism is the premeditated use or threat of use of violence by individuals orsubnational groups against noncombatants to obtain political or social objectivesthrough intimidation of a large audience beyond that of the immediate victim.The presence of a political or social motive is a key ingredient of terrorism. Incontrast, criminal acts—for example, kidnappings for ransom, murder, or extor-tion—are not terrorist acts when there is no political or social agenda. Our defi-nition excludes state terror by identifying the terrorists as individuals orsubnational groups. Noncombatants are viewed as targets of terrorism, so thatroadside bombs against an occupying military force are not classified as terroristevents. To pressure a targeted country, terrorists try to create a general atmo-sphere of anxiety where everyone feels at risk. If terrorist attacks appear to berandom, then this elevates fear and a sense of general vulnerability. Govern-ments then must guard everywhere to reassure citizens that they are safe. Byresorting to mass-casualty terrorism (e.g., 9 ⁄ 11), terrorists achieve even greateranxiety that necessitates more elaborate and expensive countermeasures. Even asuggestion of a CBRN attack cajoles a liberal democracy, entrusted with protect-ing lives and property, to spend massive amounts on homeland security to coun-ter such attacks. Thus, there are circumstances where some terrorists may resortto such unconventional measures despite inhibitors, mentioned earlier.

Terrorist attacks are also distinguished by their national ⁄ international implica-tions. Domestic terrorism is homegrown with consequences for just the hostcountry, its institutions, citizens, property, and policies. For domestic terrorism,the victims, perpetrators, and audience are all from the venue country. By thesecriteria, the anthrax letter attacks following 9 ⁄ 11 was domestic terrorism, sincethe unknown terrorist appears to have been a U.S. citizen and the other criteriafor a domestic incident are met. In contrast, transnational terrorism involvesperpetrators or victims from two or more countries and has international

275Kate Ivanova and Todd Sandler

implications. The Madrid commuter train bombings of March 11, 2004 representa transnational terrorist incident because the perpetrators were foreign, as weresome of the victims. The 9 ⁄ 11 hijackings were transnational terrorist incidents,whose financial implications were felt on stock markets worldwide (Chen andSiems 2004). Moreover, 9 ⁄ 11 involved foreign perpetrators whose attacks harmedvictims from over 80 countries.

At the outset, we must be clear about the relationship between CBRN andWMD terrorism. The terrorism literature has in a misleading fashion character-ized WMD terrorism as terrorist events employing any mine, bomb, or devicethat releases chemicals, biological agent, or radiation in sufficient amount tocause deaths (Bunker 2000; Blum et al. 2005). There is no requirement in the lit-erature that mass casualties must result; the mere use of a CBRN device is suffi-cient to qualify as WMD terrorism. In practice, CBRN terrorism may kill orinjure many or few and, to date, have killed few. The anthrax letters in the Uni-ted States in 2001 murdered 5 and sickened 22 individuals, while the sarin attackon the Tokyo subway killed twelve and sickened 1,038 people. Although theMonterey WMD data equates CBRN and WMD incidents, as does much of the lit-erature, we resist this practice and do not refer to CBRN incidents as WMDevents. Rather, we refer to CBRN incidents when CBRN substances are soughtafter, acquired, or used for a terrorist attack.

To date, much larger casualty totals have been associated with some conven-tional terrorist events (e.g., 9 ⁄ 11 and the bombings of the U.S. embassies inKenya and Tanzania on August 7, 1998). Nevertheless, it is important to analyzeCBRN terrorist incidents, as they have the potential to involve large numbers ofcasualties and cause billions of dollars in damage (i.e., a dirty bomb in a denselypopulated city). Most conventional terrorist attacks do not have the same poten-tial to cause mass casualties or significant long-term expenses from cleanup. Thestudy of CBRN incidents as a separate phenomenon provides insights as to per-petrators and likely venue, such as rich liberal democracies. If CBRN and stand-ard terrorist incidents are combined into a single dataset, then thedistinguishing characteristics of CBRN events—for example, the marginal impactof yesterday’s CBRN incidents on today’s incidents—will be lost to the analyst.These specific features can inform public policy—for example, DHS efforts toredirect resources to guarding against CBRN attacks.

The Monterey WMD terrorism database tracks politically and criminally moti-vated incidents by substate actors that involve the acquisition and ⁄ or deploymentof CBRN agents since 1900. Because we are only interested in the application ofCBRN materials for terrorist purposes, we apply rigorous criteria for the inclu-sion of CBRN incidents in our investigation. First, we include incidents from1988 to 2004, because before 1988 CBRN incidents were relatively rare so thatthere is little variation in CBRN events to explain by inferential statistics. Second,we cull criminally motivated incidents (classified as Type II in the MontereyWMD data) that do not constitute terrorism. Third, we only include those eventsthat involve: (i) the actual use of CBRN substances by the terrorists; (ii) a CBRNthreat combined with possession (or simply possession); and (iii) attemptedCBRN acquisitions supported by substantial evidence. All ‘‘plots only’’ instances,where the perpetrators never took steps to acquire the CBRN substances areculled from the data. Moreover, hoaxes, pranks, and threats are also removed. Ifthe terrorists claimed to have used CBRN material but no such substance wasused, the incident is a prank. When a similar claim is accompanied by a fake sub-stance, the act is a hoax. Cases, where CBRN use is threatened but there is noevidence of possession, attempted acquisition, or execution, are termed threats.Such incidents are removed from our sample, because they do not really repre-sent a CBRN risk even though they may result in inconvenience and costs. Thus,we only maintain about 30% of the Monterey WMD incidents.

276 CBRN Attack Perpetrators

Table 1 categorizes our 314-event sample by geography, type of agent (sub-stance), type of perpetrator, and delivery system. Asia and North America (theUnited States and Canada) experienced the greatest incidence of CBRN terror-ism for the sample period, followed by Europe. The remaining areas were associ-ated with many fewer CBRN events. The most common CBRN agent waschemical substances (205 incidents), which account for almost two-thirds of allsample incidents. Biological events are second with 42 instances that include twounsuccessful attempts by Aum Shinrikyo to sicken people with anthrax. Radio-logical events (26) involve serious efforts by terrorists to obtain radiologicalsubstances, as well as dirty bombs by Chechen rebels that did not explode. Theeight nuclear events mostly involved al-Qaida’s efforts to acquire enricheduranium or Chechens’ actions to secure nuclear material or nuclear devices fromex-Soviet facilities. In the latter case, the evidence is mixed as to whether theChechens ever obtained a ‘‘suitcase bomb’’ or an SS-20 missile. Perpetratorsinclude a variety of terrorists: unknown perpetrators are associated with 108 inci-dents or over a third of the sample. Nationalists ⁄ separatists engaged in 66 events,

TABLE 1. Descriptive Categories for Sample Drawn from Monterey WMD Terrorism Database

Category Subcategory Incidents

Region Asia 98Australia and Oceania 7

Europe 44Latin America 16

Middle East and North Africa 20Russia and newly independent states 29

sub-Saharan Africa 12United States and Canada 85

Worldwide 3Type of agent Biological 42

Chemical 205Combination 7

Nuclear 8Radiological 26

Unknown 26Type of group ⁄ perpetrator Criminal organization 1

Left-wing 29Lone actor(s) 23

Nationalists ⁄ separatists 66Religious cults 28

Religious fundamentalists 28Right-wing 9Single-issue 21Unknown 108

Type of delivery Aerosol ⁄ spray 19Casual ⁄ personal ⁄ direct contact 42Consumer product tampering 18

Explosive device 27Food ⁄ drink 22

Injection ⁄ projectile 19Jug ⁄ jar ⁄ canister 13Letter ⁄ package 46

Not applicable (case of possession) 45Reaction device 3

Water supply 12Ventilation system 1

Unknown 47

277Kate Ivanova and Todd Sandler

while religious fundamentalists and cults together executed 56 CBRN incidents.Left-wing terrorists are associated with 29 CBRN incidents. Finally, Table 1 indi-cates the various delivery devices in which unknown (47), letter ⁄ package (46),and contact (42) garnered the highest frequencies.

Table 2 reports basic statistics for all identified groups for 1988–2004.2 Group-wise data are subdivided into five cohorts—nationalists ⁄ separatists, religious cults,religious fundamentalists, other groups (e.g., leftists), and all sample groups—toshowcase differences. In the top row, the number of groups for each cohort isindicated. The second row reports the number of transnational groups for eachcategory. Table 2 also lists the number of incidents, the number of injuries, andthe number of fatalities associated with CBRN activities by group cohorts. Foreach of these event characteristics, we report the mean, standard deviation, mini-mum (min) value, and maximum (max) value over the entire period.

According to Table 2, groups participating in CBRN events included 18nationalists ⁄ separatists, two religious cults, 14 religious fundamentalists, and 21other groups. Over half of the nationalists ⁄ separatists (11) and religious funda-mentalists (8) engaged in some transnational terrorist attacks, while less than athird of other groups (6) had perpetrated transnational terrorist attacks.Although nationalists ⁄ separatists and other groups had been responsible for two-thirds of CBRN sample incidents, religious cults had by far the highest mean(14). Of the 28 incidents, involving cults, Aum Shinrikyo was implicated in allbut a single incident, which was perpetrated by the Movement for the Restor-ation of the Ten Commandments of God, a doomsday cult in Kanungu, Uganda.

TABLE 2. Basic Statistics According to Group Identity (1988–2004)

Nationalists ⁄Separatists

ReligiousCults

ReligiousFundamentalists Others All

Number of groups 18 2 14 21 55Number of transnational groups 11 0 8 6 25Number of incidents 55 28 22 56 161

Mean 3.06 14.00 1.57 2.67 2.93Standard deviation 4.75 18.38 1.34 3.83 4.92Min 1 1 1 1 1Max 20 27 6 18 27

Number of injuries 58 11921 0 201 14512

Mean 3.22 596.00 0.00 9.57 26.38Standard deviation 11.97 842.87 0.00 27.65 161.15Min 0 0 0 0 0Max 51 1192 0 121 1192

Number of fatalities 38 8183 3054 39 12005

Mean 2.11 409.00 21.79 1.86 21.82Standard deviation 5.61 521.84 81.23 6.23 111.77Min 0 40 0 0 0Max 21 778 304 28 778

1With one outlier removed, total injuries for religious cults equal 153 with a mean of 76.5, standard deviation of108.19, and maximum of 153.2With one outlier removed, total injuries for all groups equal 412 with a mean of 7.49, standard deviation of 27.27,and maximum of 153.3With one outlier removed, total deaths for religious cults equal 40. Since only one group then remains, the meanand maximum are 40.4With one outlier removed, total deaths for religious fundamentalists equal 1 with a mean of 0.08, standard devi-ation of 0.28, and maximum of 1.5With two outliers removed, total deaths for all groups equal 118 with a mean of 2.23, standard deviation of 7.34,and maximum of 40.

2 Incidents involving unknown perpetrators or lone actors are not covered in these statistics.

278 CBRN Attack Perpetrators

Before a couple outliers are removed, cults were responsible for the largest num-ber of casualties for the sample period—1,192 of 1,451 injuries and 818 of 1,200deaths. After the removal of one injury incident and one death incident,3 thesefigures drop to 153 of 412 injuries and 40 out of 118 deaths. For religious funda-mentalists with the removal of an outlier, deaths drop from 305 to just 1.4 Gener-ally, CBRN incidents by religious cults and other groups involved the largestnumber of casualties, while these incidents by religious fundamentalists are likelyto result in very few casualties, especially with the Nigerian outlier (see footnote4) removed. We, however, keep the three outliers in the regression, because theunit of analysis is the number of incidents perpetrated by the groups and notthe number of associated casualties.

Based on the Monterey WMD data, Figure 1 displays the annual number ofCBRN terrorist events by group type for 1988–2004. These time series excludecriminal and unsubstantiated incidents, as described earlier. For the overallseries, the two most prominent peaks in CBRN activity took place in 1995and 2000. The former peak with 25 incidents coincided with increases in CBRNterrorists by cults, other groups, and nationalists ⁄ separatists, with cults being thelargest contributor. The 2000 peak is primarily due to a rise in CBRN terrorismby nationalists ⁄ separatists. Cycles appear to characterize CBRN events.

0

5

10

15

20

25

30

1988 1990 1992 1994 1996 1998 2000 2002 2004

Nu

mb

er o

f in

cid

ents

AllNationalists/separatistsCultsFundamentalistsOther

FIG. 1. Annual Number of CBRN Incidents by Group Type, 1988–2004.

3 The injury incident is the Tokyo subway sarin attack on March 20, 1995 by Aum Shinrikyo; the death incidentis the mass poisoning on March 17, 2000 of the followers of the Movement for the Restoration of the Ten Com-mandments of God. The Tokyo attack involved 1,039 injuries while the mass poisoning included 778 deaths.

4 The outlier is the massacre of Hausa military youths in Nigeria on February 21, 2000 where 304 died, some byarrows tipped with poison.

279Kate Ivanova and Todd Sandler

Other Data and Variables

To capture the relationship between perpetrators and regime characteristics, we,in part, utilize annual data drawn from the Polity Project, ‘‘Political RegimeCharacteristics and Transitions, 1800–2003’’ (Marshall and Jaggers 2004). Politydata are gathered by the Integrated Network for Societal Conflict Research (INS-CR) at the University of Maryland. The Polity database is constructed on the pre-mise that a political system does not have to be represented as either democraticor autocratic. Thus, INSCR treats democracy and autocracy as two dimensionsthat can be measured independently. According to Polity, democracy reflectsthree interdependent elements: (1) institutions and procedures that foster polit-ical participation, (ii) procedural constraints that curb executive power, and (iii)government-backed guarantees that protect civil liberties (e.g., freedom of associ-ation, freedom of speech, protection against unwarranted search and seizure,and due process under the law). Each of these three elements are assigned sub-jective codes that are then combined into an overall indicator between 0 and 10,with higher values associated with more democracy. In contrast, autocracyinvolves restraints on political participation, few limits on executive power, andsignificant restrictions on civil liberties. Subjective scores assigned to these threefactors are also aggregated into a single index that varies between )10 and 0,with lower values indicative of more autocratic rule. An overall composite isderived by summing the democracy and autocracy indicators. This democracycomposite score ranges from )10 to 10 with higher values reflecting democraticprinciples. Given Polity’s coverage only up through 2003, the democratic indica-tor is not available for 2004.

For 1998–2004, we rely on the International Country Risk Guide (ICRG),produced by the Political Risk Services (PRS) Group (2004), for two additionalregime characteristics: rule of law and honesty (or the absence of corruption).The ICRG index of law and order (i.e., rule of law) is based on two subcompo-nents: (i) the impartiality of the legal system; and (ii) people’s observance of thelaw.5 The second component is needed because a country with a high judicialsystem rating may still suffer from high crime rates and routine violation of thelaw. The rule of law variable is scaled from 0 to 6, where higher scores reflectstrong rule of law and lower scores indicate ‘‘a tradition of depending on phys-ical force or illegal means to settle claims’’ (Knack and Keefer 1995:225). TheICRG corruption index primarily measures the extent to which ‘‘high govern-ment officials are likely to demand special payments’’ (Knack and Keefer1995:25), but it also accounts for illegal payments associated with import andexport licenses, exchange rate transactions, tax assessments, policy activities, orloans. Like the rule of law index, the corruption indicator ranges from 0 to 6,with low values indicating corrupt regimes. We will, however, employ high valuesto reflect honest regimes with scrupulous government officials. Annual values ofthe rule of law and honesty indices are available for 1988–2004.

A final variable is an annual wealth measure for venue countries associatedwith CBRN incidents. Income per capita data come from the World Bank Group(2006).

Empirical Hypotheses

To underline the empirical investigation, we present six hypotheses. These hypo-theses are either drawn from the literature or else are logically deduced. Thefirst hypothesis involves the temporal nature of CBRN incidents. Technologicalinnovations diffuse through the terrorism community owing to linkages among

5 See International Country Risk Guide (2005) (ICRG) for definitions for these components.

280 CBRN Attack Perpetrators

terrorist groups—that is, groups are known to share information and tactics.Thus, the discovery of a novel form of attack by one group may be passed alongto other groups. In some cases, the media greatly facilitate this transmission bymaking the method of attack public. Terrorists can then search libraries or theInternet for the necessary technical information to carry out the attack in prac-tice. When the same group is involved in multiple attacks, as was true for AumShinrikyo, economies of scale (i.e., falling unit costs with incidents) then makefuture CBRN attacks cheaper per incident once setup costs have been met.These setup costs include surpassing weaponization barriers, building a laborat-ory, obtaining the substances, acquiring knowledgeable personnel, and establish-ing the requisite infrastructure. Owing to these factors, today’s CBRN events areanticipated to be positively influenced by yesterday’s events, so that CBRNt (i.e.,events in period t) is positively influenced by CBRNt)1 (i.e., events in period t )1). This relationship may also hinge on learning economies that also lower unitcosts due to experience gained from past actions. Another positive aspect of yes-terday’s incidents on today’s actions stems from crossing the psychological andtechnical threshold that yesterday’s CBRN incidents may signal. Thus, we have:

Hypothesis 1:

Past CBRN incidents are an important positive determinant of today’s CBRN incidentsAs mentioned at the outset, the views on likely perpetrators of CBRN incidentsare controversial with two contrasting predictions in the literature. One group ofexperts sees religious cults and fundamentalists as more apt to engage in CBRNattacks than other groups, because these religious factions may demonize theirenemies, appear less restrained in their actions, view all nonsupporters as legit-imate targets, and not maintain a constituency (see, e.g., Betts 1998; Cameron1998; Dishman 2001; Palfy 2003). In the case of cults, leaders may be pursuingmillenarian, apocalyptic or messianic visions that justify any number of casual-ties—for example, Aum Shinrikyo’s apocalyptic redemption (Blum et al. 2005).One set of experts emphasizes such factors as promoting CBRN terrorism withits greater carnage potential in the case of religious terrorists. In contrast, otherexperts view opportunistic nationalists ⁄ separatists or others as a potential threat(e.g., Sinai 2005), while still others do not envision CBRN terrorism as appealingto nationalists ⁄ separatists owing to powerful inhibitors, that includes the benefit-cost effectiveness of conventional terrorism (Rapoport 1999). Monetary supportfrom a Diaspora may inhibit nationalists ⁄ separatists from CBRN attacks that mayalienate their funders. Quite simply, there is no agreement in the literature as towhom are the likely perpetrators of CBRN attacks—it is an empirical questionowing to opposing factors. As a refutable hypothesis, we offer:

Hypothesis 2:

Religious cults, followed by religious fundamentalists, are more prone to CBRN attacksagainst nonbelievers than other groupsWe place cults ahead of fundamentalists because the latter terrorists have betterdefined political goals (e.g., an Islamic state) that may make them possess someconstituency concerns.

A third hypothesis involves terrorist groups that engage in one or more trans-national terrorist events.6 Transnational terrorist groups can draw expertiseand funding from abroad, thereby putting CBRN terrorism within their reach.

6 Transnational orientation is ascertained by examining International Terrorism: Attributes of Terrorists Events(ITERATE) for CBRN perpetrators, who executed at least one transnational terrorist acts (Mickolus, Sandler, Mur-dock, and Flemming 2005).

281Kate Ivanova and Todd Sandler

Moreover, these transnational groups may be in a better position to obtainCBRN substances from laboratories and other facilities abroad (Blum et al.2005). Given their transnational orientation, such groups can stage a CBRNattack away from their home country, so that their nationals will not be inharm’s way. Thus, foreign venues may make the associated risks more acceptable.Transnational group may also execute large-scale, newsworthy CBRN attacks togain worldwide media attention. Given past incidents like 9 ⁄ 11 and the Madridcommuter train bombings, transnational terrorists must ratchet up the carnageto command similar media attention. Transnational terrorist groups are in amore competitive news market than domestic terrorists and this induces theformer to seek more ghastly actions. Such considerations lead to:

Hypothesis 3:

Groups with a transnational orientation are more prone to engage in CBRN attacksThe next three hypotheses involve the likely venue for CBRN terrorism. There isa growing literature that views democracy as encouraging terrorism owing tofreedom of association, availability of information, sources of funding, rights toprivacy, protection under the law, targets of opportunity, and restraints on gov-ernment (see, e.g., Eubank and Weinberg 1994, 2001; Weinberg and Eubank1998; Enders and Sandler 2006). Democracies also provide potential media cov-erage that terrorists seek. The same factors that support conventional terrorismalso provide a favorable environment for CBRN terrorism in democracies. This isparticularly true for CBRN incidents owing to a knowledge base (throughhigher-learning institutions and laboratories), protection from unwarrantedsearches, and myriad funding opportunities. Moreover, the shear volume of ship-ping in most rich democracies offers opportunities for CBRN ingredients toenter ports undetected. These risks of CBRN incidents are augmented by the vol-ume of tourism and business travelers to democracies. Hypothesis 4 indicatesthat the above considerations make democracies a likely venue for CBRN terror-ist attacks.

Hypothesis 4:

Democratic values and the rule of law are conducive to the staging of CBRN attacksFollowing 9 ⁄ 11, the Interpol chief, Ronald K. Noble (2001), stated that, ‘‘Themore sophisticated security systems, the best structures, or trained and dedicatedsecurity personnel are useless, if they are undermined from the inside by asimple act of corruption.’’ Corruption can foster CBRN terrorism by allowingterrorists to acquire the material through bribes of officials or individuals atsensitive laboratories. The presence of corruption also means that the acquisitionof CBRN substances may go unnoticed and ⁄ or unreported owing to questionablerecord-keeping practices. Corrupt businesses may sell essential ingredients toterrorists that can be used to assemble a CBRN weapon. Such considerationsgive:

Hypothesis 5:

Corrupt (honest) regimes are more (less) likely to experience CBRN incidentsA final hypothesis concerns the wealth of potential venue countries as measuredby the natural log (Ln) of the country’s income per capita. Rich countries areapt to be the venue for CBRN terrorism, insofar as these attacks are likely todraw more attention in wealthy than in poor countries. If the terrorists are aftera ransom, then wealthier countries present greater extortion possibilities. Richcountries also possess more laboratories and research facilities where CBRN

282 CBRN Attack Perpetrators

substances are available. Additionally, there are more individuals with access toand knowledge of CBRN materials in wealthy countries. Funds are more readilyavailable in rich countries to support CBRN weapon acquisition. Thus, we have:

Hypothesis 6:

Rich countries are a more likely venue for CBRN terrorism

Group Type and CBRN Terrorism

We first investigate the determinants of CBRN terrorism, based on past attacksand group characteristics. To construct our dependent variable, we calculate thenumber of CBRN incidents in period t, CBRNt, perpetrated by each identifiedgroup. The dataset of 55 terrorist groups excludes loners and unknown perpetra-tors (see Table 2). We assume that a group’s count of CBRN incidents either startfrom the year of their first incident, or from 1988 if its CBRN operations predatedthe start of our sample period. Thus, we implicitly assume that the group’s firstCBRN incident indicates its genesis or its ability to employ CBRN substances forterrorist acts. Because terrorist groups may not exist or use CBRN agents at thebeginning of the sample period, the number of years varies among groups.

The dependent variable consists of the number of CBRN terrorist incidentsper year, which is characterized by a preponderance of zeros and small values.The standard model for ‘‘thin’’ count data is a Poisson regression (Cameronand Trivedi 1998:3; Greene 2003:740). However, a shortcoming of a Poissonregression is that the conditional mean of the dependent variable is assumed toequal its conditional variance. If this underlying distributional assumption failsto hold (a likely scenario), then the coefficient estimates may be consistent, buttheir standard errors will be underestimated. A negative binomial regression gen-eralizes the Poisson regression and permits greater variation (overdispersion),not constrained to equal the mean.

The negative binomial regression assumes, for a given set of regressors, thatyit—the number of CBRN incidents perpetrated by group i in year t in ourmodel—is distributed with a probability density function:

f ðyit jxitÞ ¼Cðyit þ a1Þ

Cðyit þ 1ÞCða1Þa1

a1 þ lit

a1

lit

a1 þ lit

yit

; ð1Þ

with mean parameter lit ¼ expðx0itbÞ in which b is a vector of coefficients to beestimated. In equation (1), a is the dispersion parameter. This model impliesthat the conditional mean is given by:

lit ¼ expðb0 þ b1Nationalistsit þ b2Cultsit þ b3Fundamentalistsit þ b4TransnationalitÞ:ð2Þ

In equation (2), Nationalistsit refers to a dummy variable that equals 1 if theperpetrator is classified as a nationalist ⁄ separatist group in the Monterey WMDdata and 0 otherwise. Similarly, Cultsit and Fundamentalistsit denote dummy varia-bles for religious cults and fundamentalists, respectively, with all other groupsused as the reference category. Finally, Transnationalit equals 1 if the group has atransnational orientation and equals 0 otherwise. Maximum-likelihood methodsare applied to estimate the negative binomial regression model.

We assume that observations from different years for the same group are cor-related, whereas any two observations from different years for alternative groupsare independent. To account for this correlation without assuming any particular

283Kate Ivanova and Todd Sandler

within-group correlation or form of heteroscedasticity, we use a robust varianceestimator clustered over groups. The estimator allows for heteroscedastic vari-ance between and within groups (Williams 2000:645). An advantage of this vari-ance estimator is that the nature of the within-group dependence does not haveto be specified. As a consequence, estimations are robust not only to heterosce-dasticity, but also serial correlation.

The interpretation of coefficients for the negative binomial is less straightfor-ward than a linear regression model, for which estimated coefficient bj meansthat a one-unit change in the jth explanatory variable increases the expectedvalue of the dependent variable by bj units. Taking the natural log of the condi-tional mean and differentiating with respect to xj, we obtain:

bj ¼@E ½yjx@xj

1

E ½yjx ; ð3Þ

which is the percentage change in the dependent variable owing to a one-unitchange in the jth explanatory variable. As such, equation (3) is a semielasticity.If, however, an explanatory variable enters logarithmically, then the associatedcoefficient is a full elasticity giving the ratio of percentage change in the depend-ent variable to the percentage change in the independent variable. For indicator(dummy) variables, it is convenient to interpret the coefficients transformed toincidence rate ratios. For the negative binomial model, the incidence rate ratiofor a one-unit increase in indicator variable d, with all of the other variables (x2)held constant, equals

E ½yjd ¼ 1; x2E ½yjd ¼ 0; x2

¼ expðbjÞ:

This indicates that the expected count (or incidence rate) of an event is exp bj

times larger if the indicator is unity rather than zero. For a continuous variable,this would correspond to a one-unit increase.

Results

Table 3 presents the estimates of equation (2) with standard errors inparentheses. Models 1 and 2 have 433 observations for 55 terrorist groups for1988–2004. In contrast, Models 3 and 4 have just 378 observations, because 55observations are lost by lagging CBRN. To test between the negative binomialand Poisson regressions, we focus on the dispersion parameter a. For all fourmodels, we reject the hypothesis that the dispersion parameter is zero at the .01level, so that the negative binomial model is appropriate. The Wald test indicatesthat the overall model is significant at the .01 level.

Models 3 and 4 include CBRNt)1, which allows us to test Hypothesis 1, whilecontrolling for potentially relevant but omitted variables. CBRNt)1 is highly signi-ficant in both models, thus indicating that, for each group, the expected numberof CBRN incidents is over one and a half times higher than that in the perviousyear. This finding strongly supports Hypothesis 1. The chi-squared statistic withone degree of freedom for the likelihood ratio test to compare Model 1 and 3 is295,7 which is significant at the .01 level indicating a much better fit for Model 3than for Model 1. A similar calculation supports Model 4 over Model 2; hence,our remarks are focused on the coefficients in Model 3 and 4. Comparing coeffi-cient estimates, we see that the models display reasonable robustness.

Because most of the independent variables are indicator variables, the coeffi-cients are transformed to incidence rate ratios—that is, exp bj. For model 3, the

7 This statistic equals 2 · |)317.92 + 170.12|.

284 CBRN Attack Perpetrators

expected number of CBRN incidents for nationalists ⁄ separatists and fundamen-talists is not significantly different than that for ‘‘all other groups.’’8 In Model 3,the expected number of CBRN incidents for religious cults is over 11 timeshigher than that for all other groups. Moreover, this coefficient is significant atthe .01 level, thus partly supporting Hypothesis 2. The same general messagecomes from Model 4 regarding religious cults being much more prone than thecomparison group to engage in CBRN terrorism. In Model 3, the coefficient ontransnational orientation indicates a six time greater likelihood than the compar-ison group to engage in CBRN attacks. Thus, Hypothesis 3 is supported.

In Model 4, we add transnational interaction terms for nationalists ⁄ separatistsand for fundamentalists to ascertain whether such an orientation has any influ-ence on the use of CBRN terrorism by these two types of groups. We do notinclude an interaction with cults since neither sample cult is classified as transna-tional. The coefficient on the nationalists interaction term is insignificant. Thissuggests that nationalists ⁄ separatists with a transnational orientation do not getmore or less involved in CBRN terrorism. Although the expected number ofCBRN incidents for fundamentalists is much lower than that for the comparisongroup in Model 4, a transnational orientation slightly increases the anticipateduse of CBRN terrorism by fundamentalists.

Regime and Group Type: Their Influence on CBRN Terrorism

Next, we investigate whether regime characteristics and country wealth affectfour perpetrator cohorts’ use of CBRN substances in terrorist acts. These cohortsinclude all perpetrators, nationalists ⁄ separatists, religious cults and fundamental-ists, and all other actors. Unlike the last section, all other actors refer not only toterrorist groups that do not belong to one of the three group categories, but alsoto lone and unknown actors (see Table 1 where there are 23 lone and 108unknown perpetrators). We combine cults and fundamentalists into a singlecohort, because there are only two cults. By subdividing perpetrators, we can

TABLE 3. Negative Binomial Regressions (Standard Errors Adjusted for Clustering on TerroristGroups) (1988–2004)

Model 1 Model 2 Model 3 Model 4

CBRNt-1 1.61*** (0.13) 1.62*** (0.13)Nationalists ⁄ separatists 1.05 (0.44) 1.53* (0.36) 1.22 (0.70) 0.76 (0.70)Religious cults 7.90*** (2.85) 9.10*** (3.27) 11.07*** (6.22) 9.33*** (5.32)Religious fundamentalists 0.73 (0.30) 1.15 (0.48) 0.47 (0.29) 5.80E-07*** (4.37E-07)Transnational groups 2.82*** (0.92) 3.81*** (1.97) 6.28*** (3.53) 4.80** (3.62)Nationalists · transnational 0.56 (0.36) 1.83 (2.10)Fundamentalists ·transnational

0.48 (0.35) 1.02E+06*** (1.05E+06)

a 2.15*** 2.12*** 2.81*** 2.81***Wald test (v2) 45.64*** 46.17*** 112.78*** 969.69***Log-likelihood )317.92 )317.10 )170.12 )169.43Observations 433 433 378 378

Note: Dependent variable is the number of CBRN incidents per year. Coefficients are transformed to incidence-rateratios [i.e., exp(b) rather than b]. Standard errors (in parentheses) are similarly transformed. The constant is notshown.*Significant at the .10 level.**Significant at the .05 level.***Significant at the .01 level.

8 ‘‘All other groups’’ involve groups that are not nationalists ⁄ separatists, cults, or fundamentalists.

285Kate Ivanova and Todd Sandler

determine whether regime characteristics, past CBRN incidents, and wealthaffect the classes of perpetrators differently. Regime characteristics includedemocracy, rule of law, and honesty indices described earlier. The ensuingempirical investigation allows us to test Hypotheses 1, 4–6.

To explain the variation in the number of CBRN incidents for the variouscohorts based on regime characteristics, we compute the number of CBRN inci-dents that took place in each sample country in each year. Our sample includesnot only countries that did not experience any CBRN attacks, but also countriesthat experienced one or more CBRN incidents during the sample period.Because the value of the dependent value is always zero for the former countries,while the value is positive for some years and zero otherwise for the latter coun-tries, we assume that the zero and nonzero counts in this setting are generatedby different processes. That is, there are countries that are never at risk of CBRNterrorist attacks (i.e., terrorists never find them to be attractive targets), whilethere are other countries that are at risk of CBRN terrorist events where terror-ists may or may not strike in any given year. Terrorists’ locational choice for aspecific CBRN event is based on a two-step process. First, they decide whichcountries are potential venues. Second, in a particular year, terrorists choosewhich of these potential sites to stage a CBRN incident.

The negative binomial regression model, discussed in the previous section,only accounts for one source of overdispersion, namely unobservable individ-ual heterogeneity (i.e., certain unidentified socio-political characteristics of thecountries that may or may not attract terrorists). In addition to individualheterogeneity, a zero-inflated negative binomial (ZINB) model considersanother source of overdispersion—that is, excess zeros arising from the two-step data-generating process (Greene 1994). Countries can fall into two categ-ories: with probability /, a country may never experience a CBRN incident,and with probability 1–/, a country may be at risk for CBRN incidents. Prob-ability / is a function of the characteristics z of the country and is deter-mined by a logit model. Both zero and positive counts in the second groupare generated by a negative binomial process in which the exponential meanis modeled as

lit ¼ exp½b0 þ b1Democracyit þ b2Honestyit þ b3Lawit þ b4LnðGDP=PopulationÞit ;ð4Þ

where Democracyit, Honestyit, and Lawit refer to the polity, rule of law, and honestyindices, respectively, and Ln(GDP ⁄ Population)it denotes logged gross domesticproduct (GDP) per capita. Hence,

yit = 0, with probability /it;yit = negative binomial[lit], with probability 1–/it; and

/ ¼ expðz0itcÞ1þ expðz0itcÞ

;

where c is a vector of coefficients to be estimated for the logit model.We include a constant and past CBRN incidents (i.e., CBRNt–1) in vector zit

CBRNt–1 is used as an explanatory variable in the logit model to test for any poss-ible state-dependence effects. Terrorists may repeatedly stage their attacks in thesame countries on account of networks and infrastructure formed from pastactions. If, moreover, terrorists have to meet setup costs to achieve their firstattack in a particular venue, they will choose to strike in those countries whereCBRN attacks have been previously perpetrated by other terrorists, with whomthey can form linkages to reduce initial costs. Thus, under the zero-inflatedmodel, countries that have never experienced CBRN incidents will be predictedto have zero CBRN events in the current period.

286 CBRN Attack Perpetrators

We again assume that observations across countries are independent but thatany two observations within a country are correlated. Thus, we apply a robustvariance estimator clustered over countries. Although our sample includes bothcountries that have and have not experienced CBRN incidents, our sample sizeis restricted by the availability of data on the countries’ regime characteristics,used to predict the number of CBRN events. Since we only have data on demo-cracy until 2003, the time span of our study is from 1988 to 2003. Furthermore,we do not have data on democracy, corruption, and rule of law for all of thecountries in each of the years, so that we end up with 126 countries. The num-ber of available years for each country ranges from 2 to 16 (with an average of14.6 years per country). The resulting number of observations is 1729. (We‘‘lose’’ 106 observations due to the inclusion of the lag of the number of CBRNincidents in the logit model.)

In Table 4, we present the results of the estimation of equation (4) using thefour cohorts. For the three subsamples, we exclude certain perpetrators, but thenumber of countries and years that could serve as the venue and time of poten-tial attacks remains the same. Hence, the number of observations (i.e., 1729) ineach subsample is identical as that for the entire (All) sample. To account forcollinearity between the log of GDP per capita and rule of law (the correlation is0.65), we present the results of estimating an alternative specification where thelog of GDP per capita is dropped from the model. Thus, there are eight alternat-ive models, numbered (1)–(8), in Table 4. In Table 5, we include the lag of thedependent variable (i.e., CBRNt-1) as an additional determinant of the exponen-tial mean to account for any path dependence effects, associated with the num-ber of CBRN incidents in a country. This additional variable allows for a test ofHypothesis 1 for the various cohorts of perpetrators.

To judge between the negative binomial and zero-inflated negative binomialmodels, Greene (1994) proposes the use of a test by Vuong (1989) for non-nested models. However, since we rely on a robust variance estimator clusteredover countries, the Vuong statistic cannot be applied. We, thus, base our decis-ion to use the zero-inflated model on substantive justification, which Long(1997) views as the most compelling evidence. In our case, there are countrieswhere terrorists do not stage CBRN terrorist attacks for structural reasons. At thesame time, there are other countries where CBRN events are potentially anticipa-ted, but do not occur by chance in given periods. Additionally, the negativebinomial model for positive counts appears preferable to the Poisson model,because it is likely that there are unobserved sources of heterogeneity that differ-entiate the countries. This latter assumption is supported by the fact that we canreject the hypothesis that the dispersion parameter a equals zero for all samplesand specifications in Tables 4 and 5. Thus, we rely on the ZINB model to makepredictions about the expected number of CBRN events based on regime charac-teristics in different countries. The Wald test for all 16 models indicates that wecan reject the hypothesis that all coefficients are simultaneously zero at the .01level of significance. The results are broadly consistent for all comparative sam-ples and specifications in Tables 4 and 5.

For all samples, except Cults and Fundamentalists, the odds of CBRN eventsoccurring depend significantly on the number of CBRN incidents in the pre-ceding year. The negative coefficients on CBRNt–1 in the logit model indicatethat past CBRN incidents decrease the odds that the number of CBRN incidentswill be zero in the next period. Moreover, the positive coefficients on pastCBRN incidents in the negative binomial model in Tables 4 and 5 imply thatthe number of CBRN events is apt to be higher in those countries with morepast CBRN incidents. The effect of CBRNt–1 is marginally significant for theentire sample and for nationalists ⁄ separatists subsample. Thus, we concludethat past CBRN events have a much stronger influence on the odds of CBRN

287Kate Ivanova and Todd Sandler

TABLE 4. Zero-Inflated Negative Binomial Regressions on Regime Types (Standard Errors Adjusted for Clustering on Countries) 1988–2003

Independent All Nationalists ⁄ Separatists Cults and Fundamentalists All Other Actors

Variables (1) (2) (3) (4) (5) (6) (7) (8)

Negative binomial modelDemocracy 0.10** (0.04) 0.14*** (0.03) 0.12*** (0.04) 0.12*** (0.04) 0.12** (0.05) 0.14*** (0.05) 0.02 (0.08) 0.14*** (0.05)Honesty )0.52*** (0.11) )0.42*** (0.11) )0.56*** (0.11) )0.56*** (0.10) )0.32 (0.46) )0.11 (0.44) )0.65*** (0.16) )0.64*** (0.21)Rule of law 0.18 (0.16) 0.36** (0.16) )0.004 (0.14) )0.01 (0.13) 0.40 (0.27) 0.49* (0.26) 0.13 (0.24) 0.60** (0.29)ln (GDP per capita) 0.38** (0.16) )0.002 (0.15) 0.29 (0.22) 0.86*** (0.27)Constant )2.81*** (0.97) )0.96* (0.58) 0.44 (0.89) 0.43 (0.57) )4.59*** (1.19) )3.21*** (0.84) )6.09*** (1.37) )1.37 (1.22)

Logit modelCBRNt-1 )2.60*** (0.63) )2.69*** (0.67) )16.40*** (2.24) )38.68*** (2.22) )1.63 (1.08) )1.73 (1.05) )2.76*** (0.67) )2.79*** (0.62)Constant 2.07*** (0.35) 2.15*** (0.35) 3.23*** (0.30) 3.23*** (0.30) 2.99*** (0.74) 3.21*** (0.62) 2.46*** (0.53) 2.62*** (0.55)

a 1.40*** 1.46*** 0.79*** 0.78*** 1.39*** 1.07*** 1.36*** 1.58***Wald test (v2) 43.45*** 39.24*** 63.44*** 59.89*** 27.60*** 18.16*** 31.96*** 16.08***Log-pseudolikelihood )477.24 )481.58 )162.44 )162.44 )130.27 )130.93 )294.54 )302.36Observations 1729 1729 1729 1729 1729 1729 1729 1729

Notes: Dependent variable is the number of CBRN incidents per year (CBRNt). Standard errors are in parentheses. Each column provides the estimates from different parsings of the databased on the perpetrator’s identity—for example, all perpetrators (All) and nationalists ⁄ separatists.*Significant at the .10 level.**Significant at the .05 level.***Significant at the .01 level.

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terrorist incidents occurring than on the number of incidents in any particularyear.

The application of a robust variance estimator clustered over countries pre-vents us from conducting likelihood ratio tests to compare different specifica-tions of the model (such as Model 1 in Tables 4 and 5 or Model 1 and Model 2in Table 5) owing to the presence of log pseudolikelihood values. As the oddnumbered models in Table 5 represent the most complete specifications, wefocus our discussion on the coefficient estimates obtained from these models.

Democracy has a significant positive influence on the number of CBRN inci-dents across different samples and specifications, thereby partly supportingHypothesis 4. The rule of law, however, does not have a significant influence onthe number of CBRN incidents in the odd numbered models. Based on Model 1in Table 5, a one-point increase in the democracy index increases the expectednumber of CBRN incidents for all perpetrators by 9%. The size of this is approxi-mately the same for all samples with cults and fundamentalists displaying the lar-gest percentage increase. Honesty has a significant negative impact on the use ofCBRN terrorism by different types of perpetrators taken separately and together,which supports Hypothesis 5. According to Model 1, a one-point increase in thehonesty indicator results in 46% fewer CBRN incidents for the entire sample.The effect is particularly pronounced for religious cults and fundamentalists,where a one-point increase leads to a 56% decline in CBRN incidents. This sug-gests that corruption plays an important role in motivating religious groups toresort to CBRN substances. For the entire sample, the impact of corruption isabout four times greater than that of democracy. Wealth is a significant positiveinfluence of CBRN incidents for the entire sample and all other actors—the twobiggest numbers of perpetrators—thus supporting Hypothesis 6 for these sam-ples. Hypothesis 6 is not, however, supported for nationalists ⁄ separatists or cultsand fundamentalists. For models 1 and 7, the influence of income per capita isfairly large.

For the negative binomial regression, the marginal effect of a regressordepends on the expected value of the count variable, which depends on thevalues of all independent variables. Marginal effects are computed with all varia-bles held at their means. Based on the coefficient estimates of Tables 5 and 6presents the marginal effect of democracy, honesty, rule of law, and log of GDPper capita on the expected number of CBRN events. Of all of the explanatoryvariables, CBRNt–1 has the largest marginal impact on the expected number ofCBRN incidents for all but the cults and fundamentalists sample. This impact isparticularly important for nationalists ⁄ separatists, where an increase in one inci-dent in the previous year, with all variables held at their means, raises the expec-ted number of CBRN events by 0.36. The marginal effects of democracy andhonesty, though significant, are not very large. For example, in Model 1, if acountry’s democracy score improves by one unit, then the expected number ofCBRN events increases by just 0.007. If, similarly, a country’s ranking in terms ofthe honesty index increases by one, then the expected number of CBRN inci-dents decreases by 0.036. These marginal effects are small since there have notbeen many CBRN incidents to date.

Concluding Remarks

Currently, the Monterey WMD data indicates that CBRN terrorism has not beenvery deadly even though the number of terrorism-based CBRN events hasincreased since 1988. On average, a CBRN incident has been only half as deadlyas a conventional terrorist incident. Nevertheless, the authorities must be con-cerned about such events because some terrorists are clearly interested in usingCBRN substances. CBRN incidents could some day result in mass death and

289Kate Ivanova and Todd Sandler

TABLE 5. Alternative Zero-Inflated Negative Binomial Regressions on Regime Types (Standard Errors Adjusted for Clustering on Countries) 1988–2003

Independent All Nationalists ⁄ Separatists Cults and Fundamentalists All Other Actors

Variables (1) (2) (3) (4) (5) (6) (7) (8)

Negative binomial modelCBRNt-1 0.18* (0.09) 0.19** (0.09) 0.21* (0.11) 0.21* (0.12) 0.48 (0.30) 0.48 (0.34) 0.11 (0.11) 0.15 (0.14)Democracy 0.09** (0.03) 0.12*** (0.03) 0.11*** (0.04) 0.11*** (0.04) 0.13** (0.06) 0.15*** (0.05) 0.03 (0.07) 0.13** (0.05)Honesty )0.46*** (0.09) )0.37*** (0.09) )0.47*** (0.11) )0.47*** (0.10) )0.56* (0.29) )0.44 (0.37) )0.58*** (0.19) )0.52** (0.23)Rule of law 0.14 (0.15) 0.29* (0.15) )0.04 (0.15) )0.04 (0.14) 0.29 (0.32) 0.41 (0.29) 0.12 (0.24) 0.50* (0.26)ln (GDP per capita) 0.32** (0.15) 0.01 (0.15) 0.28 (0.26) 0.75*** (0.26)Constant )2.74*** (0.91) )1.15** (0.57) 0.04 (0.84) 0.07 (0.57) )4.53*** (1.48) )3.18*** (0.85) )5.70*** (1.23) )1.65 (1.34)

Logit modelCBRNt-1 )2.84*** (0.95) )2.97*** (1.09) )16.83*** (1.23) )16.66*** (1.23) )1.31 (1.03) )1.42 (1.08) )2.92*** (0.85) )2.99*** (0.89)Constant 1.79*** (0.51) 1.85*** (0.50) 3.04*** (0.35) 3.04*** (0.35) 1.88 (1.28) 2.01 (1.47) 2.27*** (0.75) 2.37*** (0.81)

a 1.66*** 1.73*** 0.85*** 0.84*** 2.33*** 2.21*** 1.63*** 1.94***Wald test (v2) 78.12*** 68.99*** 80.18*** 80.35*** 36.95*** 41.86*** 82.37*** 56.36***Log-pseudolikelihood )472.04 )475.48 )161.50 )161.50 )125.28 )126.08 )293.22 )299.90Observations 1729 1729 1729 1729 1729 1729 1729 1729

Notes: Dependent variable is the number of CBRN incidents per year (CBRNt). Standard errors are in parentheses. Each column provides the estimates from different parsings of the databased on the perpetrator’s identity—for example, all perpetrators (All) and nationalists ⁄ separatists.*Significant at the .10 level.**Significant at the .05 level.***Significant at the .01 level.

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TABLE 6. Marginal Effects Evaluated at the Sample Mean of Regressors (Based on Table 5)

Independent All Nationalists ⁄ Separatists Cults and Fundamentalists All Other Actors

Variables (1) (2) (3) (4) (5) (6) (7) (8)

CBRNt-1 0.194** (0.075) 0.218** (0.088) 0.358*** (0.125) 0.352*** (0.123) 0.015 (0.010) 0.017* (0.009) 0.090** (0.035) 0.114** (0.044)Democracy 0.007** (0.003) 0.010*** (0.003) 0.002** (0.001) 0.002** (0.001) 0.001** (0.001) 0.001*** (0.001) 0.001 (0.002) 0.005** (0.003)Honesty )0.036*** (0.010) )0.031*** (0.009) )0.011** (0.005) )0.011** (0.005) )0.005** (0.002) )0.004 (0.003) )0.019** (0.009) )0.021* (0.011)Rule of law 0.011 (0.012) 0.024* (0.012) )0.001 (0.003) )0.001 (0.003) 0.003 (0.003) 0.004 (0.003) 0.004 (0.008) 0.020** (0.010)ln (GDP per capita) 0.025** (0.012) 0.0002 (0.003) 0.003 (0.003) 0.025** (0.011)

Notes: Dependent variable is the number of CBRN incidents per year (CBRNt). Standard errors are in parentheses. Each column provides the estimates from different parsings of the databased on the perpetrator’s identity—for example, all perpetrators (All) and nationalists ⁄ separatists.*Significant at the .10 level.**Significant at the .05 level.***Significant at the .01 level.

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significant economic losses. Thus, recent action by the DHS in the United Statesto prepare for such events appears to be prudent. The real question is howmuch to spend and whom to protect against. Another question concerns the for-eign policy implications of this preparation.

We have applied inferential statistics to provide a picture of the likely risksfrom CBRN terrorism. The picture that emerges is that past CBRN incidents leadto future incidents regardless of the class of perpetrator. An increase of oneCBRN incident in the previous year leads to a 0.194 to 0.358 increase of CBRNevents in a given country per year. Once terrorists surpass the threshold associ-ated with CBRN terrorism, they generally continue such attacks. Thus, past inci-dents inform policymakers as to where the greatest risks lie. Past CBRN incidentshave the greatest marginal impact on future incidents, followed by corruptionand then democratic principles.

Religious cults and groups with a transnational orientation pose the largestthreat, based on an analysis of past data. Contrary to the views of some experts(e.g., Hoffman 1995; Cameron 1998; Post 2005), religious fundamentalists andnationalists ⁄ separatists do not present as significant of a CBRN concern. Demo-cratic principles and protection are conducive to CBRN terrorism, while regimehonesty is not supportive of such terrorism. Other things constant, rich countriesare more likely venues for CBRN terrorism by loners and other actors, notusually identified in the literature as the likely culprits.

So what policy lessons should be drawn from this study? In terms of perpetra-tors, governments must be especially vigilant against cults, since they appear tobe the most likely to deploy such attacks. In addition, transnational terroristgroups—for example, al-Qaida—present a CBRN risk as they try to surpass thecarnage level of 9 ⁄ 11. The renewed strength of al-Qaida indicates CBRN con-cerns. Given the casualties associated with conventional terrorism relative to pastCBRN incidents, authorities need to recognize that conventional attacks stillrepresent the greater risks when allocating antiterrorism resources. Failed statesmay provide a haven for terrorists to organize and train, but rich democraticcountries have been the location for past CBRN terrorist incidents and the likelyvenue for future attacks. Thus, some resources must be allocated to curb suchattacks. This also means that rich liberal democracies must cooperate with oneanother in monitoring and addressing the CBRN threat. From a foreign policyviewpoint, this is not a problem that rich democracies can confront alone becausethe terrorist will set up shop where there is the least vigilance. Because corruptionhas been a prime determinant of CBRN incidents, rich democratic countries musttake extra precautions to screen and monitor personnel at laboratories, univer-sities, hospitals, and nuclear power plants where CBRN materials can be obtained.This is also true of infrastructure workers (e.g., truck drivers for nuclear waste).Given the current CBRN threat, governments must display a measured vigilancethat does not squander funds on what remains a moderate threat.

References

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294 CBRN Attack Perpetrators

ECONOMIC CONSEQUENCES OF TERRORISM IN DEVELOPED AND DEVELOPING COUNTRIES: AN OVERVIEW

By

Todd Sandler*

School of International Relations University of Southern California

Von Kleinsmid Center 330 Los Angeles, CA 90089-0043

USA tsandler@usc.edu

213-740-9695 323-256-7900 (fax)

Walter Enders

Department of Economics, Finance and Legal Studies

University of Alabama Tuscaloosa, AL 35487

USA wenders@cba.ua.edu

205-348-8972 205-348-0590 (fax)

* Todd Sandler is the Robert R. and Katheryn A. Dockson Professor of International Relations and Economics at the University of Southern California. Walter Enders is the Bidgood Chair of Economics and Finance at the University of Alabama.

ECONOMIC CONSEQUENCES OF TERRORISM IN DEVELOPED AND DEVELOPING COUNTRIES: AN OVERVIEW

Terrorism is the premeditated use or threat of use of violence by individuals or

subnational groups to obtain a political or social objective through the intimidation of a large

audience, beyond that of the immediate victim. Although the motives of terrorists may differ,

their actions follow a standard pattern with terrorist incidents assuming a variety of forms:

airplane hijackings, kidnappings, assassinations, threats, bombings, and suicide attacks. Terrorist

attacks are intended to apply sufficient pressures to a government so that it grants political

concessions. If a besieged government views the anticipated costs of future terrorist actions as

greater than the costs of conceding to terrorist demands, then a government will make some

accommodation. Thus, a rational terrorist organization can, in principle, reach its goal quicker if

it is able to augment the consequences of its campaign. These consequences can assume many

forms including casualties, destroyed buildings, a heightened anxiety level, and myriad economic

costs. Clearly, the attacks on September 11, 2001 (henceforth, 9/11) had significant costs that

have been estimated to be in the range of $80 to $90 billion when subsequent economic losses in

lost wages, workman’s compensation, and reduced commerce are included (Kunreuther, Michel-

Kerjan, and Porter, 2003).

Terrorism can impose costs on a targeted country through a number of avenues. Terrorist

incidents have economic consequences by diverting foreign direct investment (FDI), destroying

infrastructure, redirecting public investment funds to security, or limiting trade. If a developing

country loses enough FDI, which is an important source of savings, then it may also experience

reduced economic growth. Just as capital may take flight from a country plagued by a civil war

(see Collier et al., 2003), a sufficiently intense terrorist campaign may greatly reduce capital

inflows (Enders and Sandler, 1996). Terrorism, like civil conflicts, may cause spillover costs

2

among neighboring countries as a terrorist campaign in a neighbor dissuades capital inflows, or a

regional multiplier causes lost economic activity in the terrorism-ridden country to resonate

throughout the region.1 In some instances, terrorism may impact specific industries as 9/11 did

on airlines and tourism (Drakos, 2004; Ito and Lee, 2004). Another cost is the expensive

security measures that must be instituted following large attacks – e.g., the massive homeland

security outlays since 9/11 (Enders and Sandler, 2006, Chapter 10). Terrorism also raises the

costs of doing business in terms of higher insurance premiums, expensive security precautions,

and larger salaries to at-risk employees.

The size and the diversity of an economy have much to do with the ability of a country to

withstand terrorist attacks without showing significant economic effects. Yemen’s shipping

industry suffered greatly after the terrorist attacks on the USS Cole and the Limburg diverted half

of Yemen’s port activities to competitive facilities in Djibouti and Oman due to a 300% increase

in insurance premiums (US Department of State Fact Sheet, 2002). In a more diversified and

developed economy, such losses may have a temporary influence as resources are reallocated to

other sectors or better security measures are deployed to allay concerns. Moreover, developed

economies have better monetary and fiscal capabilities to limit macroeconomic impacts of

terrorist attacks than small developing countries. Thus, we should anticipate that developed

countries are more likely to display sector-specific reactions to terrorism attacks, while

developing countries are apt to exhibit some macroeconomic consequences to a particularly

vicious attack or a sustained terror campaign.

This paper has five purposes. First and most important, the paper takes stock of the

literature on the economic consequences of terrorism and evaluates the methodology used to

date. The literature dates back to the early 1990s, with most of the contributions coming after

9/11. Second, macroeconomic influences of terrorism are distinguished from microeconomic

3

sector- or industry-specific effects. Third, terrorism impacts in developed countries are

contrasted with those in developing countries. Fourth, we indicate how researchers can better

account for economic consequences in developing countries. Finally, data needs are addressed.

The remainder of the paper contains eight sections. Section 1 reviews concepts and

definitions that are necessary for understanding the economic consequences of terrorism. In

Section 2, we investigate how the United States, representative of other developed nations,

cushioned the blow and sped recovery from the unprecedented attacks of 9/11 through monetary,

fiscal, and other policies. Section 3 reviews and evaluates some macroeconomic studies of the

impact of terrorism, whereas Section 4 contrasts anticipated differences between how developing

and developed countries are affected by terrorism. In Section 5, we review and analyze past

microeconomic studies of the economic fallout from terrorism. Section 6 discusses past

methodologies. In Section 7, we indicate data availability and needs. Section 8 provides future

directions and conclusions.

1. Essential Concepts

Studies over the last decade have established that internal conflicts can have significant

economic consequences in terms of reduced growth within a conflict-ridden country (e.g.,

Collier and Hoeffler, 2004; Collier et al., 2003; Collier and Sambanis, 2002) and in neighboring

countries (Murdoch and Sandler, 2002, 2004). But a civil war is a broader conflict than

terrorism, since the former usually involves a minimum of 1000 deaths and may result in tens of

thousands of casualties, while a terrorist incident results, on average, in a single death (Sandler,

2003). Thus, a country may be plagued with terrorism in, say, ten of ten years, but experience

relatively few deaths and modest property damage. Civil wars may stem from an insurrection

that tries to overthrow the government. In other cases, civil wars can erupt from grievances

4

between groups with deep-seated differences (hatreds). Terrorism is a tactic that may or may not

be associated with a civil war, insurrection, or other form of political violence. As such,

terrorism typically involves little loss of life and property. Naturally, there are exceptions, such

as the March 11, 2004 Madrid train bombings or the December 21, 1988 downing of Pan Am

flight 107, where two to three hundred people perished, respectively. But even in these cases,

the loss of life, though tragic, is trivial compared with most internal conflicts so that the likely

macroeconomic impact of terrorist events is not anticipated to rival civil wars.

This prediction may change under a few scenarios: a large-scale attack like 9/11, a

protracted terrorist campaign with many deadly incidents, or some devastating attack on a

developing country’s primary sector (recall the Yemen shipping example). One should not

expect that a modest number of terrorist incidents in most countries will affect the countries’

income growth. This is an essential insight, because it indicates that indices of risks that include

internal conflicts and terrorism may be merely picking up significant disruptions associated with

the former. Additionally, sector-specific microeconomic influences are often the most likely

consequences from terrorism.

Cost distinction

There are numerous cost distinctions that could be drawn regarding terrorism losses.

Direct costs, for example, involve the immediate losses associated with a terrorist attack or

campaign and include damaged goods, the value of lives lost, the costs associated with injuries

(including lost wages), destroyed structures, damaged infrastructure, and reduced short-term

commerce. In contrast, indirect or secondary costs concern attack-related subsequent losses,

such as raised insurance premiums, increased security costs, greater compensation to those at

high-risk locations, and costs tied to attack-induced long-run changes in commerce. Indirect

5

costs may surface as reduced growth in gross domestic product (GDP), lost FDI, changes in

inflation, or increased unemployment. A judgment must be made as to how to distinguish

between direct and indirect costs, in which any distinction would strike some researchers as

arbitrary.

Fortunately, this distinction is not really necessary to characterize the economic impact of

terrorism, which can be represented in terms of some well-defined macroeconomic (e.g., real per

capita GDP growth) or microeconomic variable (e.g., reduced tourist receipts). These variables

then represent the consequences of terrorism in terms of aggregate or sectoral activity. If lost

output, casualties, and damaged infrastructure are sufficiently large, then they will affect the

economy’s productive capacity with macroeconomic or microeconomic repercussions. The

identification of these impacts is of greater importance than the mere tally of losses if policy is to

ameliorate the economic ramifications of terrorism. Thus, we concentrate on relating terrorism

to macroeconomic and microeconomic variables that policy can be designed to bolster.

Domestic versus transnational terrorism

Terrorism comes in two essential types: domestic and transnational. Domestic terrorism

is homegrown with consequences for just the host country, its institutions, citizens, property, and

policies. In a domestic terrorist incident, the victim and perpetrators are from the host country.

The Oklahoma City bombing on April 19, 1995 was a domestic terrorist event as was the

kidnapping of members of Parliament by Colombian terrorists. Many ethno-nationalist conflicts

(e.g., the Tamils of Sri Lanka) are associated with mostly domestic terrorism, unless the rebels

desire to target citizens from other countries to publicize their cause to the world. Domestic

events tend to outnumber transnational terrorist events by eight to one (Enders and Sandler,

2006).

6

In contrast, transnational terrorism involves more than one country. This international

aspect can stem from the victims, targets, institutions, supporters, terrorists, or implications. For

example, 9/11 is a transnational terrorist event because the victims were from many different

countries, the mission was financed and planned from abroad, the terrorists were foreigners, and

the implications of the events (e.g., financial and security) were global. A hijacking that

originates in one country but terminates in another country is an instance of transnational

terrorism as is the assassination for political ends of a foreigner on a city street. Transnational

terrorist attacks often entail transboundary externalities: actions or authorities in one country

impose uncompensated consequences on person or property in another country. Thus, spillover

costs can result so that the economic impact of a terrorist event may transcend the host country.

The toppling of the World Trade Center towers on 9/11 killed many British nationals and had

ramifications for British financial institutions. Chen and Siems (2004, Table 2, Figures 2-3)

showed that 9/11 negatively influenced average returns on stock markets globally. In fact, the

11-day cumulative average abnormal returns were larger on the London, Frankfurt, Paris,

Toronto, Amsterdam, Switzerland, Italy, and Hong Kong stock markets than on the New York

Stock Exchange following 9/11. The four blasts on 9/11 reverberated on capital markets

worldwide.

The distinction between domestic and transnational terrorism is of utmost importance

when determining the right data for calculating the economic consequences of terrorism.

Suppose that we want to relate the growth in real per capita GDP to the level of terrorism. Then,

for a country plagued by both domestic and transnational terrorism, it becomes imperative that

all forms of terrorism are included in the terrorism measure on the right-hand side of the

equation. This is also true for a country-specific study of terrorism’s consequences on

macroeconomic variables. If, however, one is interested in the impact of terrorism on a host

7

country’s net foreign direct investment (NFDI), then transnational terrorist attacks are most

germane, since these attacks pose a more direct risk on foreign investors’ interests. If only

transnational terrorist attacks are included as a determinant of GDP growth, and if, additionally,

domestic attacks tend to be correlated with transnational terrorist incidents, then the coefficient

on terrorism will be biased. Furthermore, the coefficient on terrorism may reveal little about the

true quantitative relationship when domestic terrorism greatly exceeds the number and/or

intensity of transnational terrorism.

Causality

A final preliminary concerns the causal nature between terrorism and the macroeconomic

variable that proxies the consequences of terrorism. If economic downturns can create

grievances that result in terrorism, then economic conditions may be both a root cause of

terrorism and a consequence of terrorism. Recently, researchers have established with panel

estimates that economic conditions, particularly downturns, can generate transnational terrorist

attacks.2 Given this evidence, a researcher must be prudent to test and/or correct for a potential

endogeneity bias.

2. Macroeconomic Effects of Terrorism

An economy as rich and diverse as that of the United States is anticipated to withstand

most terrorist events with little macroeconomic consequences. During most years, the United

States experienced few terrorist events on its own soil – e.g., in 1998, 2000, and the years

following 2001, there were no terrorist events in the United States (Sandler and Enders, 2004;

US Department of State, 1999-2004). Moreover, the breadth of US economic activities is

sufficiently diverse to absorb the impact of an attack by shifting activities to unaffected sectors.

8

The immediate costs of typical terrorist acts, such as kidnappings, assassinations, or bombings,

are localized, not unlike ordinary crimes. Currently, crimes such as identity thief have far greater

potential economic consequences than terrorism to developed countries. In most developed

countries, terrorism generally causes a substitution from sectors vulnerable to terrorism into

relatively safe areas and, thus, does not affect the entire macroeconomy.3 If airlines become

risky, factors of production will shift from the airline sector to other relatively safer sectors. Of

course, a terrorist act of the magnitude of 9/11 can shake confidence and influence sufficiently

many sectors to have macroeconomics repercussions. But as we show below, developed

countries are positioned to take actions to limit these impacts.

This representation is in marked contrast to small economies in which terrorism is

prevalent and affects daily activities as in Colombia, Israel, and the Basque region of Spain. For

these economies, terrorism can reduce GDP and curb development, especially during prolonged

campaigns (e.g., Israel since September 27, 2000). Protracted terrorism leads to the anticipation

of future events, which create risk premiums that limit activities in terrorism-prone sectors.

Investors, both at home and abroad, may decide to direct their assets to safer activities in other

countries. If terrorists succeed in scaring away investments, they may be emboldened to take

further actions to cause economic losses.

US experience in light of 9/11

Figure 1 provides strong evidence for the view that the US economy quickly rebounded

from 9/11. The vertical line in the center of each panel of Figure 1 represents the third quarter of

2001 (i.e., 2001:Q3) corresponding to 9/11. Panel 1 shows that real GDP was virtually

unchanged throughout 2000 and fell slightly in the first and third quarters of 2001. The key

feature is that real GDP began to grow sharply beginning in the fourth quarter of 2001 following

9

9/11. Panel 2 shows that the Conference Board’s measure of consumer confidence plummeted

right before the onset of the 2001 recession; however, immediately following 9/11, confidence

actually soared. Some of this increase might be attributed to the patriotism of the American

public. As displayed in Panel 3, the rebound in economic activity was buoyed by strong

consumer demand for durables. These “big-ticket” items are the most volatile component of

total consumption, which jumped in the fourth quarter of 2001. Panel 4 indicates that the

unemployment rate was rising prior to 9/11, and rose dramatically after the attack. Because the

unemployment rate is a lagging indicator of economic activity, this rate would likely have

increased even without 9/11. Thus, we must wonder what would have happened to

unemployment in the absence of 9/11 – i.e., the unemployment rate may have risen even faster.

There is an overwhelming consensus that well-orchestrated macroeconomic

policymaking cushioned the shock from 9/11 in the United States. The financial markets were in

disarray as bond market trading was suspended for a day and stock market trading did not

resume until the following week. During uncertain times, risk-averse asset holders increase the

proportion of highly liquid assets in their portfolios. As shown in Panel 5, the Federal Reserve

reacted to this surge in liquidity demand by sharply cutting the Federal Funds rate, thereby

keeping funds available for investment and other needs. Fiscal policy also performed a

supportive role. The first tax cut since 1985 was signed into law in May 2001, months before

9/11. As a direct of 9/11, the US Congress approved a $40 billion supplemental appropriation

for emergency spending for such items as search and rescue efforts at the four crash sites and

tightened security at US airports and other venues. In addition to the needed disaster relief, this

surge in government spending acted as a powerful stimulus to aggregate demand. Starting on

October 7, 2001, the war in Afghanistan also bolstered government spending. As shown in Panel

6, government saving (i.e., the negative of what many call the federal government’s budget

10

deficit) plummeted from uncharacteristic surpluses to record deficits. Although the government

budget deficit can have some long-term undesirable influences, US fiscal and monetary policies

clearly played an essential role in restoring consumer and business confidence.

3. Review of Macroeconomic Literature on Terrorism Impacts

The literature on the macroeconomic consequences of terrorism only began in 2003 and

involves only a handful of studies. One set of studies examines the influence of various terrorist

variables on real per capita GDP growth, while a second set of studies consists of case studies of

a country experiencing a long-term terrorist campaign.

Blomberg, Hess, Orphanides (henceforth BHO) (2004) examined a pooled cross section

of 177 countries from 1968 to 2000. Their estimating equation is:

0 1 2 3 0 4 5 6 7COM AFRICA ln ,i i i i i i i iy y I Y T I Eβ β β β β β β β ε∆ = + + + + + + + + (1)

where iy∆ is country i’s average per capita GDP growth rate, sβ are coefficients, COM is a

dummy variable for non-oil commodity exporters, AFRICA is a dummy for African countries,

0iy is country i’s initial income, iI Y is country i’s investment rate over the full sample, Ti is a

transnational terrorism indicator (e.g., a dummy for terrorism occurring in a given year), Ii

denotes the presence of an internal conflict in i, Ei indicates i’s involvement in an external

conflict, and iε is the error term. Their baseline regression indicated that non-oil commodity

exporters and African nations had lower average per capita GDP growth of 1.2% and 1.36%,

respectively. We are primarily interested in BHO’s terrorism variable’s impact on economic

growth. BHO found that if a country experienced transnational terrorist incidents on its soil in

each year of the sample period, then per capita income growth fell by 1.587 percentage points

over the entire sample period. Given the definition of Ti, each year of terrorism led on average to

11

a fall in growth of only 0.048% (=1.587/33). BHO’s initial terrorism measure treated a year with

50 deadly incidents the same as a year with a single nonfatal incident. Moreover, these authors

used just transnational terrorism incidents drawn from the International Terrorism: Attributes

of Terrorist Events (ITERATE) data set (Mickolus et al., 2004). Most sample countries would

have experienced a far greater amount of domestic terrorism, which was not directly controlled

in the study. BHO were careful to control for internal and external conflict: internal conflict had

a significant negative effect on growth for some empirical specifications, while external conflict

did not have a significant influence. The internal conflict measure may be picking up some of

the impact of domestic terrorism because the later is often correlated with such conflicts.

BHO’s study controlled for some endogeneity bias. An especially interesting part of their

study is their panel estimates for nondemocractic countries, OECD countries, African countries,

the Middle Eastern countries, and Asian countries. The panel estimates altered some right-hand

side variables compared with the cross-sectional regressions – e.g., COMi was dropped and trade

openness was added along with lagged per capita growth. Except for the African panel, BHO’s

terrorism indicator was not significant, which is a cause of concern. As a geographical area,

Africa displayed the least amount of terrorism in an average year (see Blomberg, Hess, and

Orphanides, 2004, Table 1; Enders and Sandler, 2005, Figures 5-6), yet Africa was the only

panel where the estimated terrorism coefficient was significant. This rather paradoxical finding

was never addressed. The full panel estimates gave a much greater impact of terrorism on

growth – i.e., terrorism in a single year reduced per capita GDP growth by over a half a percent

– compared with the cross-sectional estimates. No explanation was offered for this huge

difference in the consequences of terrorism between the two estimating procedures. We find it

worrying that terrorism’s average influence on growth for the entire sample is not reflected in

any of the panels where terrorism is the greatest concern. Moreover, their large cross-section

12

analysis did not discriminate between different time periods where terrorism changed in

character – for example, from left-wing groups to fundamentalist groups.

In another set of panel estimates, BHO (2004) changed their terrorism indicator to

terrorist incidents per capita. This change gives a significant terrorism impact on per capita GDP

growth for the full sample, the nondemocratic panel, the OECD panel, and the African panel.

Even though more panels displayed a significant impact of terrorism, the reader was never

informed why this terrorist indicator is preferred to the earlier indicator. Moreover, the impact of

terrorism varies widely between the full sample and the smaller cohort panels, leading one to

worry that the full sample “average” picture may not be representative of how smaller cohorts or

individual countries respond to terrorism.

Toward the end of the paper, BHO (2004) performed some panel estimates regarding

terrorism’s influence on investment share of GDP and government spending share of GDP.

These estimates are interesting because they tried to establish the pathway by which terrorism

effects economic growth. BHO found that terrorism increased the government spending share,

while it decreased the investment share. This reallocation can affect growth by diverting

government activities away from more productive activities to security. Moreover, reduced

investment will limit growth directly.

Gupta et al. (2004) focused on a sample of 66 low- and middle-income countries to

ascertain the impact of armed conflict and terrorism on macroeconomic variables. For their

econometric estimates, they used three structural equations, where the dependent variables are

growth of real per capita income, government revenue as a share of GDP, and defense spending

as a share of GDP. Unlike BHO, Gupta et al. (2004) were interested in the joint impact of

internal conflict and terrorism on these three macroeconomic variables. For the conflict

measure, they used the Internal Country Risk Guide (ICRG) rating on internal conflict. In this

13

study, the ICRG conflict measure did not have a significant negative direct impact on per capita

income growth. However, this index had a significant positive influence on the share of defense

spending, which, in turn, had a significant negative influence on economic growth. Thus,

conflict indirectly reduced economic growth by increasing the defense spending share of

government spending.

A real advantage of this study is that it has a cohort of developing countries unlike BHO,

who included countries at all stages of development, thereby making it difficult to draw

conclusions about developing countries. The main drawback of the Gupta et al. study is that it

really did not measure the effect of terrorism per se on macroeconomic variables, because no

direct measure of terrorism was used. The ICRG index can indicate high risk when civil conflict

is high but terrorism is low or absent. Moreover, the index may point to low risk in the face of

terrorism if the overall intensity of internal conflict is low.

A third cross-sectional study by Tavares (2004) examined the cost of terrorism in terms

of reduced per capita GDP growth. His sample period was 1987-2001 for a large unspecified

sample of countries. The estimating equation is:

0 1 , 1 2 3

4 5

Growth Growth Terrorism

Natural Disaster Currency Crisis Additional Controls ,it i t it it

it it it

GDPpc GDPpc GDPpcβ β β ββ β ε

−= + + ++ + + +

(2)

where GrowthGDPpc is per capita GDP growth. On the right-hand side of equation (2), there is

lagged per capita GDP growth, per capita GDP, a terrorism measure, a natural disaster index, a

currency index, additional controls, and an error term. The terrorism measure is either the total

number of attacks per capita or the total number of casualties per capita. Tavares (2004) drew

his terrorism variable from data provided by the International Policy Institute for

Counterterrorism (2003). This data consist of 1427 “selected” transnational terrorist events for

the 1987-2001 period.

14

Using instrumental variables to address the potential endogeneity between terrorism and

real per capita GDP growth, Tavares found that the terrorism variable had a small but significant

negative impact on GDP growth of 0.038% (Tavares, 2004, Table 4). Once additional

determinants of growth (e.g., an education variable, trade openness, primary goods exports, and

the inflation rate) were introduced into the estimating equation, terrorism was no longer a

significant or negative influence on economic growth. This raises a concern because many of

these additional variables are in standard analyses of growth, so that Tavares’ earlier findings

about the consequences of terrorism must be questioned. The absence of key growth variables in

his earlier equations suggests that they were misspecified.

Tavares (2004) went on to compare the costs of terrorism in democratic versus

nondemocratic countries. For our purposes, the key part of his regression equation is:

( )10.261 0.029 0.121 other explanatory variables,it it it it ity y T T R−∆ = ∆ − + × + (3)

where ity∆ is country’ i’s growth of per capita GDP in year t, 1ity −∆ is country i’s growth of per

capita GDP in year t − 1, Tit is the number of terrorist attacks in country i in year t, and Rit is a

measure of political rights in country i in year t. This last variable increases when the level of

political freedom rises.

Equation (2) is a dynamic specification for which current period growth is affected by

growth in the previous period. In contrast to Tavares’ original specification that ignored political

rights, all of the coefficients reported in equation (2) are statistically significant. The coefficient

on Tit indicates that a single terrorist incident in country i in year t reduces annual growth for that

year by 0.029%. Since the model is dynamic, this growth effect is persistent. These results are

consistent in size with those of BHO. An interesting finding involves the positive coefficient on

the interaction term Tit × Rit, for which the effect of a typical terrorist attack decreases as the level

15

of political freedom increases. That is, democracies are better able to withstand terrorist attacks

than other types of governments with less flexible institutions. Yet another interpretation is that

democracies are better prepared to weathered attacks because they rely on markets to allocate

resources.

Case studies

To date, there are two careful macroeconomic case studies on specific terrorism-ridden

economies. Both studies are careful and utilize methodologies that could be applied to other

countries – e.g., Colombia – that have experienced a prolonged campaign of terrorism. For the

Basque region, Abadie and Gardeazabal (2003) tried to estimate the per capita GDP losses that

are attributable to a twenty-year terrorist campaign. Because the Basque region differs from

other regions in Spain, the authors had to construct a “synthetic” comparison region by taking a

weighted average combination of other Spanish regions. The weights were chosen to yield the

values to key growth variables – e.g., real per capita GDP, investment share of GDP, population

density, and human capital measures – that are nearly identical to those of the Basque region

prior to its terrorism. The authors demonstrated that the Basque and synthetic regions displayed

similar per capita GDP values prior to 1975 and the start of the terror campaign. Thereafter, a

GDP gap opened that averaged 10% over the next twenty years. During high-terrorism episodes,

the gap exceeded 10%, while, during low-terrorism episodes, the gap closed somewhat. This is a

clever methodology where the synthetic region serves as the counterfactual control.

Eckstein and Tsiddon (2004) applied a vector autoregression (VAR) methodology to

investigate the effects of terrorism on the macroeconomy of Israel. These authors used quarterly

data from 1980 through 2003 to analyze the effects of terrorism on real GDP, investment,

exports, and nondurable consumer goods. Each of these variables served as a dependent variable

16

in their four-equation VAR system. Their measure of terrorism was a weighted average of the

number of Israeli fatalities, injuries, and noncasuality incidents. Their terrorism data included

domestic and transnational attacks in Israel. They found that the initial impact of terrorism on

economic activity was as short as a single quarter. Moreover, terrorism’s impact on exports and

investment was three times larger than on nondurable consumption and two times larger than on

GDP.

Eckstein and Tsiddon (2004) also employed their VAR estimates to calculate the

counterfactual time paths of the four macroeconomic variables under the assumption that all

terrorism ceased at the end of 2003:Q4. In this counterfactual exercise, real per capita GDP is

forecasted to grow 2.5% from the beginning of 2003:Q4 to 2005:Q3. If, however, terrorism held

steady, then the estimated VAR predicted a zero rate of per capita GDP growth. Finally, if

terrorism in Israel were to continue its upward trend, real per-capita GDP would fall by about

2%. The figures for investment were even more dramatic because investment would decline by

10% annually with this upward trend.

In another set of experiments, Eckstein and Tsiddon (2004) calculated the economic

consequences of the Intifada. They used their data to estimate the VAR through 2000:Q3 (the

beginning of the Intifada) and forecasted real GDP for quarters 2000:Q4 through 2003:Q4.

Forecasts were conducted assuming either no subsequent terrorism or terrorism at the levels that

actually prevailed for these three years. The differences in forecasts translated into a per capita

GDP loss of about 10% for terrorism continuing at its prevailing elevated level, which is quite

substantial.

The five key macroeconomic studies are summarized in Table 1 for ready reference. The

first column indicates the study and its basic methodology,4 while the second column provides a

short description of the study. In the right-hand column, some key findings are indicated.

17

4. Developed and Developing Countries Contrasts

The macroeconomic case studies have been for two small high-income countries. In

Tavares (2004) and BHO (2004), a wide range of countries have been included in the cross

section making it difficult to know anything specific about developing countries. This is

underscored by the failure in BHO (2004) of many of the regional panels for Asia and elsewhere

to yield significant findings for the terrorist variable. Within each regional sample, there was no

culling of the developed or richer countries. The cross-sectional study that investigated

developing countries per se is Gupta et al. (2004), which has some key failings. First, there is no

true terrorism measure, so that the ICRG index is more reflective of internal conflict than of

terrorism. Second, this study combined countries with vastly different types of internal conflict;

thus, the average picture that emerges may not reflect of what most developing countries

suffered from terrorism. Developing countries with similar terrorist campaigns should be

combined in the same panel. Third, the cross section included countries with diverse political

and economic institutions. Developed institutions should enable a country to better absorb

terrorist attacks. To date, there is no cross-sectional study of the consequences of terrorism on

developing countries.

There are a number of anticipated differences between how developed and developing

countries are able to handle terrorism. Developed countries possess more capable governmental

institutions that can apply monetary, fiscal, and other policies to recover from either a large-scale

attack or a prolonged campaign. The United States case, discussed above, is instructive. For

example, the insurance crisis caused by 9/11 was addressed by the US Congress approving

emergency insurance legislation to cover catastrophic terrorism losses in the short run

(Kunreuther, Michel-Kerjan, and Porter, 2003). Markets are better able in developed, than in

18

developing, countries to respond to terrorism-induced changes in risk. Developed countries are

also better equipped than developing countries to monitor their economies to determine the need

for monetary or fiscal stimuli following terrorist attacks. In addition, developed countries can

take decisive and effective security measures to restore confidence. Many less-developed

countries lack this capacity. Such security measures can speed recovery. Because developing

countries are more dependent on the rest of the world for demands for their products and

services, these countries are more vulnerable than richer countries to terrorism shocks in

neighbors and important trading partners. Compared with their richer counterparts, developing

countries are less diversified and more apt to experience a larger impact from a sector-specific

attack. The earlier Yemen shipping example illustrates this insight. Finally, the presence of

internal conflicts in many developing countries compromises their ability to address terrorist

attacks, which may resonate with other forms of internal strife.

These differences between developed and developing countries have implications for

panel studies. Such differences raise real issues with the information encapsulated in the average

picture given by large-scale panels that combine countries at all stages of development.

Moreover, these differences indicate that controls are needed for neighboring conflicts,

corruption, and internal conflicts. To date, only the last control is included in past panel studies.

Future studies of developing countries should take two forms: (i) case studies of specific

developing countries and (ii) panel studies of a homogeneous set of developing countries.

5. Microeconomic Consequences of Terrorism

There have been studies dating back to the early 1990s that have investigated the

microeconomic consequences of sector-specific attacks. In particular, studies have covered

tourism, trade, and financial sectors.

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Tourism

Attacks against tourist venues (e.g., airports, hotels, or attractions) or tourist mode of

transportation (e.g., airplanes) make a tourist consider the risks involved with their vacation

plans. Even a single heinous act at a popular terrorist venue can cause tourists to alter plans by

either vacationing at home or else going to a terrorism-free country for a holiday. Time-series

analysis has been used in a number of tourism studies to gauge the impact of terrorism in the

target country or region. A transfer function analysis is particularly suited to estimate the short-

and long-run effects of a terrorist attack on a country’s tourist industry. A very simple transfer

function for, say, the effect of terrorism on Spanish tourism is:

0 1 1 0 ,t t t ty a b y c x ε−= + + + (4)

where yt is the number of tourists visiting Spain in period t, xt is the number of terrorist incidents

in Spain in period t, and εt is the error term. This equation reflects that the number of tourists

visiting Spain in any period is affected by its own past, 1,ty − as well as the number of terrorist

events in Spain. Because periods with high versus low levels of tourism tend to cluster, we

expect b1 to be positive; a large yt tends to follow a large 1ty − . In (4), c0 measures the

contemporaneous effect of a terrorist incident on tourism; a negative c0 means that terrorism

negatively impacts tourism. Suppose that c0 = −3 and there are four terrorist incidents during a

particular period (i.e., xt = 4), then the contemporaneous influence of terrorism on tourism is then

−12. If the unit of measurement is a thousand, then terrorism has lost the country 12,000 tourists

following the attacks. If, moreover, b1 is not zero, then there is persistence in the system and

effects on terrorism could be long-lasting.

Equation (4) can be used to estimate the indirect effects on terrorism. To perform the

20

desired counterfactual analysis, a researcher would estimate equation (4) to obtain the

magnitudes of a0, b1, and c0 for a particular country. Once these values are ascertained, what

each value of yt would have been in the absence of terrorism (i.e., xt = 0) can be calculated. The

difference between this counterfactual value and the actual value of yt is then due to the effect of

terrorism. This analysis can be generalized in a number of directions: (i) additional lagged

values of the dependent variable; (ii) lagged values of the terrorism variable; and (iii) more

complicated causality between yt and xt. The first generalization allows for a more complex

autoregressive (AR) process where persistence can be long-term, while the second generalization

permits alternative impact patterns where terrorism may affect the dependent variable with a lag.

The third generalization can permit terrorism to affect tourism and vice versa, so that an equation

is required for each of these variables. In this case, a VAR methodology applies and causality

tests can fix the direction of dependency. A fourth generalization can allow for lagged values to

the error terms, so that a moving average (MA) process applies.

Enders and Sandler (1991) applied a VAR methodology to Spain for the 1970-91 period,

during which Euzkadi ta Askatasuna (ETA) and other groups had terrorist campaigns. During

1985-87, ETA directed its bombs and threats against the Spanish tourist trade and even sent

letters of warning to travel agents in Europe. Using monthly data, we showed that the causation

was unidirectional: terrorism affected tourism but not the reversed. Each transnational terrorist

incident was estimated to dissuade over 140,000 tourist after all monthly impacts were included.

This can translate into a sizable amount of lost revenue when multiplied by the average spending

per tourist. Transnational terrorist attacks denote the appropriate terrorism measure, because we

were interested in the costs to the foreign tourist trade.

In a follow-up study, Enders, Sandler, and Parise (1992) used an autoregressive

integrated moving average (ARIMA) analysis with a transfer function to investigate the impact

21

of transnational terrorism on tourism in Austria, Spain, and Italy for 1974-88 – three countries

with highly visible transnational terrorist attacks during this period. The dependent variable was

the share of tourist receipts from the region. These authors found that terrorism had a significant

negative lagged influence on these tourism shares that varied by country: two quarters for Italy,

three quarters for Greece, and seven quarters for Austria. Since it takes time for tourists to revise

plans, the lags are understandable. Losses varied by country: Austria lost 3.37 billion special

drawing rights (SDRs); Italy lost 861 billion SDRs; and Greece lost 472 million SDRs. The

authors also showed that some of the lost revenues left a sample of European countries for safer

venues in North America.

Drakos and Kutan (2003) applied the Enders-Sandler-Parise methodology to Greece,

Israel, and Turkey for 1991-2000. These authors used monthly transnational terrorism data,

drawn from ITERATE. In addition to the home-country impacts, Drakos and Kutan were

interested in cross-country or “spillover” effect – both positive and negative – that may arise if,

say, an attack in Israel shifts would-be Israeli tourists to safer venues in Italy, Greece, or

elsewhere. Their ARIMA model with a transfer function had an equation for each country’s

tourist shares, where, say, the share of tourism in Greece depends on: past tourist shares in

Greece; current and past terrorist attacks in Greece; current and past terrorist attacks in Israel;

and current and past terrorist attacks in Turkey. There was also an equation for tourist shares of

Italy, which was a relatively safe haven. Owing to transnational terrorist attacks, these authors

calculated that Greece lost 9% of its tourism market share; Turkey lost over 5% of its tourism

market share; and Israel lost less than 1% of its tourism market. Close to 89% of lost tourism

due to terrorism in Europe flowed to safer tourist venues in other countries.5 Drakos and Kutan

also uncovered significant spillover effects – low-intensity terrorist attacks in Israel reduced

Greek tourism revenues.

22

Net foreign direct investment

Foreign investors must be aware of all kinds of risks, including those posed by terrorism.

This risk is especially germane when a terrorist campaign specifically targets net foreign direct

investment (NFDI). Terrorist risks raise the costs of doing business as expensive security

measures must be deployed and personnel must be duly compensated, both of which reduce the

returns to NFDI. As these risks rise, investors will redirect their investments to safer countries.

Enders and Sandler (1996) provided estimates of the effects of terrorism on NDFI in two

relatively small European countries – Greece and Spain. Large countries – e.g., France,

Germany, and the United Kingdom – draw their foreign capital inflows from diversified sources

and are able to endure attacks without a measurable diversion of inflows. Large countries are

also better equipped to take defensive measures after an attack to restore confidence. Greece and

Spain were selected as case studies insofar as both experienced numerous transnational terrorist

attacks aimed at foreign commercial interests during the 1968-91 sample period.

For Spain, we applied an ARIMA model with a transfer function that associated NFDI to

its past values and to terrorist attacks; for Greece, we applied a VAR model that related NFDI to

its past values and to terrorist attacks. Once again, we modeled a counterfactual exercise,

analogous to those for tourism, to compute the terrorism-induced losses in NFDI in these two

economies. For Spain, there was a long delay of 11 quarters between the advent of a terrorist

incident and the response in NFDI. A typical transnational terrorist incident in Spain was

estimated to reduce NFDI by $23.8 million. On average, transnational terrorism reduced annual

NFDI in Spain by 13.5%. For Greece, the story was similar, transnational terrorism curbed

annual NFDI by 11.9%. These are sizable losses for two small economies that were heavily

dependent on NFDI as a source of savings during the sample period. We also investigated the

23

influence of terrorism on NFDI in a number of large economies, such as France and the United

Kindom, and found no significant terrorism influence on these countries’ NFDI.

Trade influence

In a recent contribution, Nitsch and Schumacher (2004) estimated the effects of

transnational terrorism on bilateral trade flows using a standard trade-gravity model. In their

model, trade flows between trading partners depend on terrorist attacks, the distance between the

two countries, an income variable, an income per capita variable, and a host of dummy variables.

They formally estimated the effects of terrorism within each country on all of the nation’s

trading partners. The data set consists of 217 countries and territories over the 1968-79 period.

Their terrorism data were drawn from ITERATE and only included transnational attacks, even

though domestic terrorism would have also affected trade flows. The authors found that the first

transnational terrorist attack reduced bilateral trade by almost 10%, which is a very sizable

influence that may be picking up the effect of domestic terrorism. At times, transnational

terrorism is highly correlated with domestic terrorism. Nitsch and Schumacher also found that a

doubling of the number of terrorist incidents reduced bilateral trade by 4%; hence, high-terrorism

nations had a substantially reduced trade volume. Although more recent terrorism data are

available, the authors only examined this historical period, which is not reflective of current-day

terrorism.

Financial markets

Chen and Siems (2004) applied an event-study methodology to investigate changes in

average returns of stock exchange indices to 14 terrorist and military attacks that dated back to

1915. An event study computes abnormal returns – negative or positive – following some shock

24

or occurrence, such as the downing of Pan Am flight 107 or 9/11. These authors showed that the

influence of terrorist events on major stock exchanges, if any, is very transitory, lasting just one

to three days for most major incidents. The sole exception is 9/11 where DOW values took 40

days to return to normal. These authors also showed that this return period varied according to

the stock exchange – exchanges in Norway, Jakarta, Kuala Lampur, and Johannesburg took

longer to rebound, while those in London, Helsinki, Tokyo, and elsewhere took less time to

rebound. Most terrorist events had little or no impact on major stock exchanges.

Eldor and Melnick (2004) applied time-series methods to ascertain the influence of the

Israeli terror campaign following September 27, 2000 on the Tel Aviv 100 Stock Index (TA

100). Given the continual nature of these terrorist attacks, the time-series method is clearly

appropriate. Analogous to the other time-series studies, they performed a counterfactual exercise

to determine losses to the value of the TA 100 index by using the estimated time-series equation

for returns but substituting a zero value in for terrorist attacks. Their analysis estimated that the

TA 100 was 30% lower on June 30, 2003, owing to the terrorist campaign. When these authors

investigated specific types of terrorist attacks, they found that only suicide attacks had a

significant impact. Their article also related the Israeli terrorist campaign to exchange rate

fluctuations.

By way of summary, Table 2 indicates the microeconomic studies, their methods, study

description, and major findings.

6. Methodology Discussion

To date, two basic methodologies have been applied to estimate macroeconomic and

microeconomic consequences of terrorism: panel estimates with large cross sections of countries

and time-series estimates with one or more equations. Each methodology has its advantages and

25

disadvantages as displayed in Table 3.

Our own view favors the time-series methods, which have been effectively used to come

up with estimates of tourism losses, NFDI losses, and stock market declines. The Eckstein and

Tsiddon (2004) study of Israel also illustrates that the same method can be employed to estimate

the consequences of terrorism on macroeconomic variables such as consumption per capita and

GDP per capita. Not only can time-series analyses lend themselves to counterfactual exercises,

but also they can be used for forecasting purposes. Although most time-series estimates do not

have antecedent behavioral models, the Eckstein and Tsiddon (2004) article shows that this need

not be the same, since their estimating equations stemmed from a dynamic theoretical model. By

incorporating a VAR analysis with multiple equations (i.e., one for each country), a researcher

can examine cross-border spillovers. This is demonstrated by Drakos and Kutan’s (2003)

analysis of tourism in the Mediterranean region.

Our concerns about cross-sectional studies involve the reliance on large samples, where

countries with wide-ranging incomes, security capacities, institutions, and terrorist experiences

are thrown into the same sample. This extreme heterogeneity for key variables means that the

“average” picture provided by the coefficient estimates may not be descriptive of the experience

of many of the sample countries. We believe that more insight is gained by doing the panel

estimates for a homogenous cohort of countries. Regarding the BHO (2004) study, we are

concerned that the geographical cohorts usually did not yield significant terrorism impacts for

the authors’ first terrorism measure, except for the region with the least terrorism; however, the

entire panel did yield significant consequences of terrorism. The logic of this finding is difficult

to accept. For this particular study, cohorts should have corresponded to countries with similar

income, institutions, and terrorism experience.

We are also concerned that so many different terrorism measures have been used. At

26

times, more than one measure is employed in the same study. Table 4 lists alternative measures

and the associated study. The most natural measure of terrorism is something that reflects the

frequency of attacks – e.g., the number of terrorist attacks, the number of casualties, or some

index of these measures (e.g., the index used by Eckstein and Tsiddon, 2004). The number of

casualties is a better measure than the number of events if attack intensity is to be captured. The

temporal nature (i.e., daily, monthly, quarterly, or annual) of the attack measure depends on data

availability and econometric considerations. That is, researchers often relied on quarterly totals

to eliminate zero or near-zero observations that would violate the underlying normal distribution,

associated with many time-series methods. Because time-series techniques require many data

points, monthly or daily values may be used to expand the number of observations. If zero

values becomes a problem, estimates can then be based on a discrete Poisson distribution.

The use of a dummy to measure the occurrence of terrorism in a given year loses a lot of

useful information. In addition, a per capita measure of terrorism implies that an incident in a

country with a large population has a smaller influence than in a country with a smaller

population. In fact, the impact of a large-scale event such as 9/11 is, we believe, independent of

the population size. In fact, the impact of terrorist events in general may actually be greater for

countries with larger populations, because there are then more people to intimidate. The logic of

normalizing terrorist incidents by population has never been adequately explained in the

literature. This process is especially worrying for the BHO (2004) study because terrorism was

not significant for most panel cohorts until terrorism was normalized by population. Why this

was the case was never explained. As mentioned earlier, the ICRG measure of internal conflict

does not really capture terrorism per se, and thus, serves as a poor measure.

7. On Terrorism Data

27

To date, much of the literature has relied on the ITERATE data set of terrorist events.

Based on newspaper and media accounts, ITERATE records many variables – e.g., incident date,

incident location by country, type of events, number killed, groups claiming responsibility, and

demands made – for transnational terrorist events from 1968:Q1 through 2004:Q4. ITERATE

does not classify incidents as transnational terrorism that relate to declared wars or major

military interventions by governments, or guerrilla attacks on military targets conducted as

internationally recognized acts of belligerency. However, ITERATE classifies attacks against

civilians or the dependents of military personnel as terrorist acts when such attacks are intended

to create an atmosphere of fear to foster political objectives. A number of judgments must be

made in terms of what ITERATE includes as a transnational terrorist event. For example, Irish

Republican Army (IRA) attacks in Northern Ireland are not included as transnational terrorist

acts. IRA attacks in England are, however, included.

ITERATE variables are grouped into four files: the COMMON file on incident

characteristics, terrorist characteristics, victim characteristics, and life and property losses; the

FATE file on the fate of the terrorists and extradition; the HOSTAGE file on target of terrorist

demands, negotiation behavior, results of negotiations, and other nations involved in incidents;

and the SKYJACK file on incident characteristics, airline information, location of the incident,

and the number of individuals involved. ITERATE allows a researcher to match terrorist

incidents with countries so as to compute losses from transnational terrorist campaigns. These

losses would have to be inferred from macroeconomic and microeconomic data drawn from

other sources, because ITERATE’s loss variable consists of mostly missing values. ITERATE

does not record domestic events, which are essential when computing the macroeconomic

consequences of terrorism if targeted countries are plagued by both transnational and domestic

terrorist events.

28

Tavares (2004) drew his terrorism incidents from data provided by the International

Policy Institute for Counterterrorism (IPIC) (2003), whose data set is located online. IPIC

describes its 1427 terrorist incidents for 1987-2001 as “selected” transnational terrorist incidents.

The data source does not, however, give its criteria for classifying an incident as a transnational

terrorist event. Moreover, IPIC does not provide its selection criterion; ITERATE records many

times the number of incidents during the same period. The IPIC selection criterion is particularly

important for judging potential biases. When sampling the incidents, we found many that would

not have satisfied ITERATE’s transnational criterion – e.g., some Palestinian incidents in Israel.

Until this year, the US Department of State (various years) maintained a transnational

terrorism data set that was released annually as Patterns of Global Terrorism. Except for a few

aggregate totals (e.g., total events, events by region, casualties by region, type of target, and type

of event), this data set is not in a form that can be used by researchers because the data files are

not available. The annual reports also contain short descriptions of “significant” attacks that

could be coded for a few variables. Nevertheless, many other events are not reported as

significant events, but could have important economic consequences. Bombs left near foreign

corporate offices may be insignificant if they caused damage but no injuries, but they could still

reduce NFDI.

The National Memorial Institute for the Prevention of Terrorism (MIPT) (2005) also

maintains an online data set on terrorism. From 1968 through 1997, the data consists of

transnational terrorism. Thereafter, MIPT tallies both domestic and transnational terrorist events.

The website makes it easy to make graphs and other displays. A researcher would have to

expend much effort to put the data in a form that would relate incidents by countries so that

statistical analysis on the economic consequences can be accomplished. The addition of

domestic events is very useful but there are only seven years of domestic events. A researcher

29

must be careful not to use the 1968-2004 data without purging the domestic incidents; otherwise,

there will be a huge inconsistency in data coverage in the post-1997 period.

There are a few data sets available for conducting specific country studies, which is

illustrated by the Abadie and Gardeazal (2003) study of Spain and the Eckstein and Tsiddon

(2004) study of Israel. In the latter case, the Israeli terrorism data came from the International

Policy Institute for Counterterrorism (2003) at the Interdisciplinary Center Herziliya

(http://www.ict.org.il). On a monthly basis, this data set includes the number of incidents,

causality figures, types of events, and other variables of interest. Domestic and transnational

events are included, a necessary inclusion for any country-specific study. We are, however, not

clear how this Israeli data set differs from the IPIC data used by Tavares (2004) for allegedly just

transnational terrorist attacks. Country-specific data sets are available for Colombia, Spain, and

few other countries (e.g., United Kingdom) that have faced significant terrorist campaigns.

The availability of country-specific data sets poses a real problem for panel studies,

because it will be a massive task to assemble sufficient domestic and transnational terrorist

incidents for a cohort of countries. The best alternative is to group together some terrorism-

ridden countries, where such data exist, for a small panel estimate. It would be interesting to

compare these countries’ terrorism-induced declines in real GDP per capita to the experience in a

cohort of rich countries whose terrorism is mostly transnational in character. When combining

country-specific data from different sources, coding consistency is an ever-present worry.

8. Concluding Remarks

Table 5 lists some of the main principles that we have gleaned regarding the economic

consequences of terrorism. A few of these principles are worth highlighting. Given the low

intensity of most terrorist campaigns, the economic consequences of terrorism are generally very

30

modest and short-lived. Terrorism is not on par with civil or guerilla wars and, in general,

should have very localized economic effects. The likely candidate countries for noticeable

macroeconomic impacts are either developing or small countries that experience a protracted

terrorist campaign. In general, the economic influence of terrorism is anticipated to surface in

specific sectors that face an enhanced terrorism risk, such as the tourist industry or foreign direct

investment.

Except for a couple of case studies, we do not view any of the current macroeconomic

studies as providing convincing quantification of the economic impact of terrorism. Future

studies need to include domestic and transnational terrorist incidents for a homogeneous panel,

for which sample countries are at analogous stages of development and confront similar kinds of

terrorist campaigns. Domestic terrorist data must satisfy consistent criteria when pulled from

different sources. We also support the need for additional case studies, especially of developing

countries. We see the need to extend VAR analysis to a few countries confronting terrorist

campaigns in the same region to capture cross-border influences. Spatial econometric estimation

can identify the dispersion of the economic consequences.

We view the microeconomic estimates of terrorism consequences as being quite

successful and informative. The methodology can be extended to other countries, especially

developed countries, as case studies and small panels. More effort should be expended to

identify sector-specific, cross-border spillovers – e.g., in the case of foreign direct investment. In

addition, the methods can be applied to vulnerable sectors previously unexamined.

31

Footnotes

1. For civil conflicts, these spatial spillovers are measured by Murdoch and Sandler

(2002, 2004).

2. Studies include Blomberg, Hess, and Orphanides (2004), Blomberg, Hess, and

Weerapana (2004), Li (2005), and Li and Schaub (2004). These studies investigated causes

beyond economic conditions – e.g., globalization, democracy, and government restraint.

3. On terrorism-induced substitution, see Enders and Sandler (1993, 2004, 2005).

4. Some studies utilized additional methodologies. For example, BHO (2004) also

presented a VAR analysis. Abadie and Gardeazabal (2003) did an event study of abnormal

returns of two portfolios of stocks: one for firms with business interests in the Basque region

and one for firms with business interests elsewhere. The performance of the former portfolio

was tied to terrorist events in the Basque region.

5. Sloboda (2003) also used a transfer function to analyze the effects of terrorism on

tourism revenues for the United States following the Gulf War of 1991.

32

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Chen, Andrew H. and Thomas F. Siems (2004), “The Effects of Terrorism on Global Capital

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Three Mediterranean Countries,” Journal of Conflict Resolution, 47(5), 621-41.

Eckstein, Zvi and Daniel Tsiddon (2004), “Macroeconomic Consequences of Terror: Theory

and the Case of Israel,” Journal of Monetary Economics, 51(5), 971-1002.

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33

Political Economy, 20(2), 367-86.

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Tourism: The Case of Spain,” Terrorism, 14(1), 49-58.

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Vector-Autoregression-Intervention Analysis,” American Political Science Review,

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34

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Conflict Resolution, 49(2), 278-97.

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35

Series Methods,” Tourism Economics, 9(2), 179-90.

Tavares, Jose (2004), “The Open Society Assesses its Enemies: Shocks, Disasters and Terrorist

Attacks,” Journal of Monetary Economics, 51(5), 1039-70.

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Terrorism,” [http://www.state.gov/s/ct/rls/fs/2002/15028.htm], accessed 12 December

2004.

Figure 1. Macroeconomic variables and 9/11Panel 1: Real GDP

(200

1:Q

3 =

100)

1999 2000 2001 2002 2003 200490

95

100

105

110

115

120

Panel 4: Unemployment rate

per

cen

t o

f la

bo

r fo

rce

1999 2000 2001 2002 2003 20043.5

4.0

4.5

5.0

5.5

6.0

6.5

Panel 2: Consumer confidence

(198

5 =

100)

1999 2000 2001 2002 2003 200460

70

80

90

100

110

120

Panel 5: Federal funds rate

per

cen

t p

er y

ear

1999 2000 2001 2002 2003 20041

2

3

4

5

6

7

Panel 3: Consumption of durables

(200

1:Q

3 =

100)

1999 2000 2001 2002 2003 200490

95

100

105

110

115

120

Panel 6: Federal government savings

Bill

ion

s o

f $

1999 2000 2001 2002 2003 2004-500

-250

0

250

Table 1. Macroeconomic studies of the impact of terrorism Study and method Description Findings

Blomberg, Hess, and Orphanides (2003) Cross section and panel

Growth in per capita income as a function of conflict, terrorism, and standard growth variables. Some runs control for endogeneity concerns. Entire sample and select cohorts are analyzed.

Terrorism has a small effect on per capita income growth for entire sample, but not for most cohorts. Terrorism reduces I/Y, while it increases G/Y.

Gupta, Clements, Bhattacharya, and Chakravarti (2004) Three-equation cross-section structural model.

Eq. (1) is for the determinants of real per capita GDP growth; eq. (2) is for the determinants of governmental revenue as a share of GDP; and eq. (3) is for the determinants of defense spending as a share of GDP. A conflict-terrorism index is a dependent variable in each equation.

The conflict index has no direct effect on economic growth; it has an indirect effect by increasing the defense spending share, which lowers economic growth.

Tavares (2004) Cross section

Growth in real per capita GDP is a function of logged growth in real per capita GDP, terrorism, other crises, and growth variables. Some runs account for simultaneity bias. Introduces an interactive term between terrorism and political rights as a determinant of growth in per capita GDP.

Terrorism has a small effect on growth when standard growth variables are left out. When these variables are included, terrorism has no influence. Evidence that countries with well-developed democratic institution can withstand terrorism attacks

Abadie and Gardeazabal (2003) Case study for Spain

Contrast the Basque region with terrorism and a “synthetic” region without terrorism. The latter is based on a weighted composite of other peaceful regions in Spain.

Finds a 10% average gap in per capita GDP that they attribute to terrorism over a twenty-year period

Eckstein and Tsiddon (2004) VAR for Israel

The four interactive time series include per capita GDP, investment, exports, and nondurable consumption.

Terrorism has a significant negative impact on per capita GDP, investment, and exports. Terrorism’s influence on investment and exports is three times its effect on per capita GDP. Counterfactual exercise shows that the high recent levels of terrorism resulted in a 2% annual decline in per capita GDP.

VAR denotes vector autoregression

Table 2. Microeconomic studies of the impact of terrorism Study and method Description Findings

Enders and Sandler (1991) VAR

Using monthly data for 1970-99, the study relates terrorism and tourism for Spain. A causality test establishes that terrorism affects tourism, but not the reverse.

A typical terrorist incident is estimated to scare away just over 140,000 tourists when all monthly impacted are combined.

Enders, Sandler, and Parise (1992) ARIMA with a transfer function

Relates share of tourist receipts to lagged shares of tourist receipts and lagged terrorist attacks. Focuses on Austria, Spain, and Italy for 1974-88. Other continental countries included to investigate out-of-region losses.

During sample period, tourist losses varied: Austria lost 3.37 billion SDRs; Italy lost 861 million SDRs; and Greece lost 472 million SDRs. The sample of Europe countries lost 12.6 billion SDRs of tourist receipts to North America.

Drakos and Kutan (2003) ARIMA with a transfer function

Using monthly data for 1991-2000, the study relates a country’s share of tourist receipts to terrorism. Focuses on Greece, Israel, and Turkey. Allows for terrorist-induced substitutions within and among regions.

Greece lost about 9% of its tourism market shares due to terrorism; Israel lost less than 1% of its tourism market share due to terrorism; and Turkey lost just over 5% of its tourism market share due to terrorism. About 89% of lost European tourism flowed to safer regions.

Enders and Sandler (1996) ARIMA with transfer function for Spain VAR for Greece.

Employs time-series methods to ascertain losses in net foreign direct investment (NFDI) due to terrorism. The sample period is 1968-91.

On average, terrorism reduced annual NFDI in Spain by 13.5%, while it lowered annual NFDI in Greece by 11.9%. There was a long lag between an incident and its impact on NFDI. Large rich countries weathered terrorism without displaying a loss in NFDI.

Nitsch and Schumacher (2004) Trade-gravity model

Terror attacks are added to a gravity model to ascertain their impact on bilateral trades for over 200 countries for 1960-93. Independent variables include a language dummy, a colonizer dummy, common border, and other controls.

Terrorist incidents in a trading partner reduce bilateral trade by almost 10%, compared with terrorism-free trading partners.

VAR denotes vector autoregression and ARIMA is autoregressive integrated moving average.

Table 2. continued Chen and Siems (2004) Events-study methodology

This study applies the events-study methodology to uncover how many days are required for stock markets to recover their value after a large-scale terrorist attack.

For the Dow, market value is recovered in 1 to a few days following large-scale terrorist attacks. For 9/11, the Dow recovered in 40 days. Major conflicts are associated with long recovery periods.

Eldor and Melnick (2004) Time-series methods

Relies on time-series methods to display the influence of terrorist attacks on the Israeli stock market. Daily observations are utilized.

The terrorist campaign beginning on September 27, 2000 lowered stock values on the Tel Aviv exchange by 30%. Only suicide attacks had a significant influence. The size of the attack in terms of casualties was a significant determinant of financial market losses.

Table 3. Measurement of economic consequences of terrorism: panel versus time series Panel estimation ! Advantages

• A wide variety of countries can be considered. • Variation in key variables (e.g., per capita GDP) is larger. • Degrees of freedom are large. • The influence of terrorism on cohorts can be compared and contrasted.

! Disadvantages

• The estimation’s average picture may not be descriptive of many (any) sample countries, especially when the panel includes vastly diverse countries.

• Data problems may arise from using different sources. • The dynamic effect of terrorism on key variables are not displayed. • Cross-border spillovers are difficult to identify.

Time-series estimation ! Advantages

• There is no need to construct a behavioral model with explicit exogenous and endogenous variables.

• Dynamic processes can be readily identified; i.e., can evaluate shocks and the pattern of adjustment over time.

• Forecasts can be provided. • Microeconomic impacts can be readily identified. • Cross-border spillovers can be estimated.

! Disadvantages

• The estimated model may be atheoretical with no antecedent behavioral model. • The number of countries examined is severely limited. • A large number of observations are required. • A generalized picture across nations is not given.

Table 4. Alternative measures for terrorism Number of terrorist attacks Drakos and Kutan (2003): monthly totals Eldor and Melnick (2004): daily totals Enders and Sandler (1991): monthly totals Enders and Sandler (1996): quarterly totals Enders, Sandler, and Parise (1992): quarterly totals Nitsch and Schumacher (2004): annual totals and totals for entire 1968-79 period Tavares (2004): annual totals Occurrence of terrorism in a given year (dummy variable) Blomberg, Hess, and Orphanides (2004) Nitsch and Schumacher (2004) Terrorism incidents per capita Tavares (2004): annual total attacks per capita

also broken down according to target, organization, and casualties. Blomberg, Hess, and Orphanides (2004) International Country Risk Guide ratings on international conflict Gupta, Clements, Bhattacharya, and Chakravarti (2004) Specific terrorist events Abadie and Gardeazabal (2003) Chen and Siems (2004) Terrorism index Eckstein and Tsiddon (2004): equally weights the number of attacks, the number of deaths, and the number of injured. Number of deaths from terrorism Abadie and Gardeazabal (2003)

Table 5. Economic impact of terrorism: summarizing principles • For most economies, the economic consequences of terrorism are generally very modest and

of a short-term nature. • Large diversified economies are able to withstand terrorism and not display adverse

macroeconomic influences. Recovery is rapid even from a large-scale terrorist attack. • Developed countries can use monetary and fiscal policies to offset adverse economic impacts

of large-scale attacks. Well-developed institutions also cushion the consequences. • The immediate costs of most terrorist attacks are localized, thereby causing a substitution of

economic activity away from a vulnerable sector to relatively safe areas. Prices can then reallocate capital and labor quickly.

• Terrorism can cause a reallocation from investment to government spending. • The effects of terrorism on key economic variables – e.g., net foreign direct investment – are

anticipated to be greatest in small economies confronted with a sustained terrorist campaign. • Some terrorist-prone sectors – e.g., tourism – have displayed substantial losses following

terrorist attacks. • Small countries, plagued with significant terrorist campaigns, display macroeconomic

consequences in terms of losses in GDP per capita.

January 2008 VITA for Todd Sandler PERSONAL DATA Name: Todd Sandler Marital Status: Married, 1 son (Tristan) Rank: Vibhooti Shukla Professor of Economics and Political Economy Wife’s Name: Jean Marie Murdock Address: School of Economic, Political and Policy Sciences Home Fax: 972-470-0103

University of Texas at Dallas Office Phone 972-883-6725 800 W Campbell Road Fax: 972-883-6486 Richardson, TX 75080-3021 e-mail: tsandler@utdallas.edu

EDUCATIONAL BACKGROUND:

B.A., (cum laude) State University of New York at Binghamton, 1968. M.A., State University of New York at Binghamton, 1970 (one semester at Texas A & M, 1968). Ph.D. in Economics, State University of New York at Binghamton, 1971.

DISSERTATION TITLE: A Contribution to the Theory of Devaluation MAJOR AREAS:

Public Economics and Public Choice Applied Microeconomic Theory International Political Economy International Relations Study of Terrorism Natural Resources and Environmental Economics Defense and Peace Economics International Trade and Finance

COURSES TAUGHT:

Intermediate Micro; Intermediate Macro; Mathematical Economics; Graduate Seminar in Micro; Graduate Micro I; Graduate Micro II; Graduate Macro I; Principles of Economics (Micro, Macro); Graduate Seminar in Public Finance; Public Choice; Environmental Economics; Graduate Managerial Economics; Graduate Welfare Theory; Graduate Theory of Public Goods and Externalities; Honors Microeconomic Principles, Honors Seminar on Terrorism; Undergraduate Public Finance; Seminar in Economics and Security; International Policy Analysis; Global Economy; International Terrorism and Liberal Democracy, Graduate Public Finance; Honors Game Theory; and Political Economy of Terrorism.

2

ACADEMIC POSITIONS:

• Vibhooti Shukla Professor of Economics and Political Economy, University of Texas at Dallas, August 2006 on.

• Joint appointment as Professor of International Relations, Economics, and Law, Law

School, University of Southern California, March 2005 on. • Robert R. and Katheryn A. Dockson Professor in International Relations and Economics,

University of Southern California, August 2000 on.

• Distinguished Professor of Economics and Political Science, Iowa State University, April 1995 to August 2000. Leaves of Absence:

Visiting Fellow, University of Keele, UK, Fall semester 1996. Visiting Distinguished Scholar, University of Newcastle, Australia, May 1996 to

June 30, 1996.

• Professor of Economics, Iowa State University, May 1986 to April 1995. (also given title of Professor of Political Science in September 1988)

Leave of Absence: Honorary Fellow, University of Wisconsin-Madison, January 1990 to June 1, 1990.

• Professor of Economics, University of South Carolina, August 1985 to May 1986.

• Professor of Economics, University of Wyoming, July 1979 to December 1985.

Leaves of Absence: Visiting Fellow, University of York, U.K., August 1983 to October 1983 and May

1984 to July 1, 1984. Visiting Fellow, Australian National University, September 1981 to December

1981 and May 1982 to September 1982. Visiting Scholar, Institute of Social and Economic Research, University of York,

U.K., Summer 1980. Visiting Fellow, University of Aberdeen, Scotland, June to July 1979.

• Associate Professor of Economics, University of Wyoming, June 1976 to June 1979.

Leave of Absence: NATO Fellow, Institute of Social and Economic Research, University of York,

United Kingdom, June 1977 to June 1978.

• Associate Professor of Economics, Arizona State University, September 1975 to June 1976. Leave of Absence:

Visiting Assistant Professor of Economics, State University of New York at Binghamton, September 1974 to August 1975.

• Assistant Professor of Economics, Arizona State University, Tempe, Arizona, September

1971 to August 1975.

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HONORS, GRANTS:

• Principal Investigator, Department of Homeland Security, CREATE grant, “Understanding Counterterrorism in a Globalized World,” $75,000, October 2006 to September 2007; $100,000, August 2007 to September 2008.

• Duncan Black Award for best article in Public Choice, 2005. • Co-recipient National Academy of Sciences Award for Behavioral Research Relevant to

the Prevention of Nuclear War, 2003. • Principal Investigator, Swedish Ministry of Foreign Affair, EGDI grant, “Regional Public

Goods,” $40,000, April 2001 to February 2002. • Honorary Visiting Professor, Department of Economics, University of York, October

1999-September 2002, October 2003 to September 2006. • Annual Award for Excellence in Honors Teaching for 1998. One award given per year

for best honors teacher at Iowa State University. • NATO-EAPC Research Fellowship, 1998-2000. • Quality of Communication Award, American Agricultural Economics Association 1998

for book, Global Challenges: An Approach to Environmental, Political, and Economic Problems, first prize.

• Quality of Communication Award, Honorable Mention, American Agricultural Economics Association, 1997 for co-authored book, The Theory of Externalities, Public Goods, and Club Goods, 2nd Edition.

• Visiting Distinguished Scholar, University of Newcastle, Australia, May-June 1996. • Quality of Research Excellence Award, American Agricultural Economics Association,

August 1995 for co-authored paper, “Agricultural Research Expenditures in the U.S.: A Public Goods Perspective,” first prize.

• Liberal Arts and Sciences College Outstanding Teacher at the Introductory Level, 1995. • Visiting Fellow, Federalism Research Centre, Australian National University, May-July

1994. • Senior Fellow, Institute for Policy Reform, Washington, DC, 1994. • Principal Investigator, National Science Foundation grant SBR92-22953 “Alternative

Theories and Tests of Alliance Behavior, Environmental Pacts, and Global Collective Action,” $85,680, June 1, 1993 to November 30, 1994.

• Senior Fellow, Institute for Policy Reform, Washington, DC, 1993. • Senior Fellow, Institute for Policy Reform, Washington, DC, 1992. • Senior Fellow, Institute for Policy Reform, Washington, DC, 1990-91. • Principal Investigator, National Science Foundation grant SES89-07646 “The Economics

of Terrorist Negotiations, The Effectiveness of Terrorist-Thwarting Policies, and Related Issues,” $97,711, July 1, 1989 to June 30, 1991.

• Australian National University Fellowship, 1981. • NATO Postdoctoral Fellowship in the Sciences (NSF) June 1977 to June 1978. • National Defense Education Association Fellowship (Title IV) Texas A & M, September

1968. • State University of New York at Binghamton Fellowship, September 1969 to June 1970.

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PROFESSIONAL ORGANIZATIONS: American Economic Association American Political Science AssociationAssociation of Environmental and Resource Economists China Economic Association International Defense Economics Association LIST Society Public Choice Society Public Economic Theorist Association Royal Economic Society Southern Economic Association Western Economic Association International Studies Association

REFEREED PUBLICATIONS:

“A Two-Country Investment Accelerator Model,” The Indian Journal of Economics, Volume 53, No. 1, July 1972, pp. 1-11.

“Fiscal Federalism, Spillovers and the Export of Taxes,” (with Robert B. Shelton), Kyklos,

Volume 25, No. 4, 1972, pp. 736-753. “The Rybczynski Theorem, The Gains from Trade and Nonhomogeneous Utility Functions,”

Indian Economic Journal, Volume 21, No. 1, July-September 1973, pp. 19-31. “Exchange Rate Systems, the Marginal Efficiency of Investment and Foreign Direct Capital

Movements: A Comment,” Kyklos, Volume 26, No. 4, 1973, pp. 866-868. “Optimum Population: A Further Look,” (with Timothy D. Hogan), Journal of Economic

Theory, Volume 6, No. 6, December 1973, pp. 582-584. “Devaluation, Capital Flows and the Balance of Payments: A Respecification,”

Weltwirtschaftliches Archiv., Volume 110, No. 2, June 1974, pp. 244-258. “The Short-Run Shifting of the Corporate Income Tax: A Theoretical Investigation,” (with

Jon Cauley), Public Finance, Volume 29, No. 1, 1974, pp. 19-35. “A General Class of Production Functions with Nonlinear Isoclines: Comment,” (with A.

Swimmer), Southern Economic Journal, Volume 41, No. 2, October 1974, pp. 307-308. “Public Goods Theory: Another Paradigm for Futures Research,” (with Jon Cauley),

Futures, Volume 6, No. 5, October 1974, pp. 423-428. “Pareto Optimality, Pure Public Goods, Impure Public Goods, and Multiregional Spillovers,”

Scottish Journal of Political Economy, Volume 22, No. 1, February 1975, pp. 25-38.

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“The Economic Theory of Alliances: Realigned,” in C. Liske, W. Loehr, J. McCamant (eds.), Comparative Public Policy: Issues, Theories, and Methods. (New York: John Wiley & Sons, 1975), pp. 223-239.

“Devaluation, Capital Flows and the Balance of Payments: A Reply,” Weltwirtschaftliches

Archiv., Vol. 111, No. 1, March 1975, pp. 162-163. “On the Economic Theory of Alliances,” (with Jon Cauley), Journal of Conflict Resolution,

Vol. 19, No. 2, June 1975, pp. 330-348. “The Challenge of Property Rights,” Futures, Vol. 7, No. 6, December 1975, pp. 523-525. “Intertemporal and Intergenerational Pareto Efficiency,” (with V. Kerry Smith), Journal of

Environmental Economics and Management, Vol. 2, No. 3, 1976, pp. 151-159. “Fiscal Federalism, Spillovers, and the Export of Taxes: Reply,” (with Robert Shelton),

Kyklos, Vol. 29, No. 2, 1976, pp. 315-316. “Multiregional Public Goods, Spillovers and the New Theory of Consumption,” (with Jon

Cauley), Public Finance, Vol. 31, No. 3, 1976, pp. 376-395. “The Externality Argument for In-Kind Transfers: A Defense,” (with Ryan Amacher),

Kyklos, Vol. 30, No. 2, 1977, pp. 293-296. “The Design of Supranational Structures: An Economic Perspective,” (with Jon Cauley),

International Studies Quarterly, Vol. 21, No. 2, June 1977, pp. 251-276. “Intertemporal and Intergenerational Pareto Efficiency Revisited,” (with V. Kerry Smith),

Journal of Environmental Economics and Management, Vol. 4, No. 3, September 1977, pp. 252-257.

“Impurity of Defense: An Application to the Economics of Alliances,” Kyklos, Vol. 30, No.

3, 1977, pp. 443-460. “The Properties and Generation of Homothetic Production Functions: A Synthesis,” (with A.

Swimmer), Journal of Economic Theory, Vol. 18, No. 2, August 1978, pp. 349-361. “Interregional and Intergenerational Spillover Awareness,” Scottish Journal of Political

Economy, Vol. 25, No. 3, November 1978, pp. 273-284. “Public Goods and the Theory of Second Best,” Public Finance, Vol. 33, No. 3, 1978,

pp. 330-344. “A Hierarchical Theory of the Firm,” (with Jon Cauley), Scottish Journal of Political

Economy, Vol. 27, No. 1, February 1980, pp. 17-29.

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“Burden Sharing, Strategy, and the Design of NATO,” (with John Forbes), Economic Inquiry, Vol. 18, No. 3, July 1980, pp. 425-444. Republished in James M. Buchanan and Robert D. Tollison (eds.), Theory of Public Choice - II (Ann Arbor, MI: University of Michigan Press, 1984), pp. 338-357.

“In Defense of a Collective Goods Theory of Alliances,” (with Jon Cauley and John Forbes),

Journal of Conflict Resolution, Vol. 24, No. 3, September 1980, pp. 537-547. “A General Theory of Interpersonal Exchange,” (with Jon Cauley), Public Choice, Vol. 35,

No. 5, 1980, pp. 587-606. “The Economic Theory of Clubs: An Evaluative Survey,” (with John Tschirhart), Journal of

Economic Literature, Vol. 18, No. 4, December 1980, pp. 1481-1521. “The Economics of Outer Space,” (with William Schulze), Natural Resources Journal, Vol.

21, No. 2, April 1981, pp. 371-393. “On the Number and Membership Size of Consumer-Managed Firms,” (with John

Tschirhart), Southern Economic Journal, Vol. 47, No. 4, April 1981, pp. 1086-1091. “The Social Rate of Discount for Nuclear Waste Storage: Economics or Ethics?” (with

William Schulze, David Brookshire), Natural Resources Journal, Vol. 21, No. 4, October 1981, pp. 811-832.

“A Theory of Intergenerational Clubs,” Economic Inquiry, Vol. 20, No. 2, April 1982, pp.

191-208. “A Theoretical and Empirical Analysis of NATO,” (with James Murdoch), Journal of

Conflict Resolution, Vol. 26, No. 2, June 1982, pp. 237-263. “Joint Products and Multijurisdictional Spillovers,” (with A. J. Culyer), Quarterly Journal of

Economics, Vol. 97, No. 4, November 1982, pp. 707-716. “Intertemporal and Intergenerational Pareto Efficiency: A Reconsideration of Recent

Extensions,” (with V. Kerry Smith), Journal of Environmental Economics and Management, Vol. 9, No. 4, December 1982, pp. 361-365.

“Joint Products and Interjurisdictional Spillovers: Some Public Goods Geometry,” (with A.

J. Culyer), Kyklos, Vol. 35, No. 4, 1982, pp. 702-709. “A Theoretical Analysis of Transnational Terrorism,” (with John Tschirhart and Jon Cauley),

American Political Science Review, Vol. 77, No. 1, March 1983, pp. 36-54. Republished in Rosemary O’Kane (ed.), Terrorism (Northampton, MA: Edward Elgar, 2005), pp. 444-462.

“Toward a Unified Theory of Nonmarket Institutional Structures,” (with Jon Cauley and

John Tschirhart), Australian Economic Papers, Vol. 42, June 1983, pp. 233-254.

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“On Commons and Tragedies,” (with Richard Cornes), American Economic Review, Vol. 73, No. 4, September 1983, pp. 787-792.

“Club Optimality: Further Clarifications,” Economics Letters, Vol. 14, No. 1, 1984, pp.

61-65. “The Theory of Public Goods: Non-Nash Behavior,” (with Richard Cornes), Journal of

Public Economics, Vol. 23, No. 3, April 1984, pp. 367-379. “Mixed Clubs: Further Observations,” (with John Tschirhart), Journal of Public Economics,

Vol. 23, No. 3, April 1984, pp. 381-389. “Intertemporal Incentive Allocation in Simple Hierarchies,” (with David Nickerson),

Mathematical Social Sciences, Vol. 7, No. 1, 1984, pp. 33-57. “Easy Riders, Joint Production, and Public Goods,” (with Richard Cornes), Economic

Journal, Vol. 94, No. 3, September 1984, pp. 580-598. “Complementarity, Free Riding, and the Military Expenditures of NATO Allies,” (with

James Murdoch), Journal of Public Economics, Vol. 25, No. 1-2, November 1984, pp. 83-101. Republished in Larry Neal (ed.), The International Library of Macroeconomics and Financial History: War Finance, Vol. 3 (Cheltenham, UK: Edward Elgar, 1994), pp. 539-557.

“The Simple Analytics of Pure Public Good Provision,” (with Richard Cornes), Economica,

Vol. 52, No. 1, February 1985, pp. 103-116. “Externalities, Expectations, and Pigouvian Taxes,” (with Richard Cornes), Journal of

Environmental Economics and Management, Vol. 12, No. 1, March 1985, pp. 1-13. “On the Consistency of Conjectures with Public Goods,” (with Richard Cornes), Journal of

Public Economics, Vol. 25, No. 1, June 1985, pp. 125-129. “Australian Demand for Military Expenditures: 1961-1979,” (with James Murdoch),

Australian Economic Papers, Vol. 44, June 1985, pp. 142-153. “Uncertainty and Clubs,” (with Fred Sterbenz and John Tschirhart), Economica, Vol. 52, No.

4, November 1985, pp. 467-477. “Joint Supply and the Finance of Charitable Activity,” (with John Posnett), Public Finance

Quarterly, Vol. 14, No. 2, April 1986, pp. 209-222. “The Commons and the Optimal Number of Firms,” (with Richard Cornes and Charles

Mason), Quarterly Journal of Economics, Vol. 101, No. 3, August 1986, pp. 641-646. “The Political Economy of Scandinavian Neutrality,” (with James Murdoch), Scandinavian

Journal of Economics, Vol. 88, No. 4, November 1986, pp. 583-603.

8

“Nonmarket Institutional Structures: Conjectures, Distribution, and Efficiency,” (with Jon Cauley and Richard Cornes), Public Finance, Vol. 41, No. 2, 1986, pp. 153-172.

“Terrorist Success in Hostage-Taking Incidents: An Empirical Study,” (with John Scott),

Journal of Conflict Resolution, Vol. 31, No. 1, March 1987, pp. 35-53. “Terrorism in a Bargaining Framework,” (with Scott Atkinson and John Tschirhart), Journal

of Law and Economics, Vol. 30, No. 1, April 1987, pp. 1-21. Republished in Isaac Ehrlich and Zhiqiang Liu, The Economics of Crime (Northampton, MA: Edward Elgar, 2006).

“Cycles and Substitutions in Terrorist Activities: A Spectral Approach,” (with Eric Iksoon

Im and Jon Cauley), Kyklos, Vol. 40, No. 2, 1987, pp. 238-255. “On Optimal Prices and Animal Consumers in Congested Markets,” Economic Inquiry, Vol.

25, No. 4, October 1987, pp. 715-720. “Free Riding and Uncertainty,” (with Frederic Sterbenz and John Posnett), European

Economic Review, Vol. 31, No. 8, December 1987, pp. 1605-1617. “Expectations, the Commons, and Optimal Group Size,” (with Charles Mason and Richard

Cornes), Journal of Environmental Economics and Management, Vol. 15, No.1, March 1988, pp. 99-110.

“Sharing Burdens in NATO,” Challenge, Vol. 31, No. 2, March/April 1988, pp. 29-35. “To Bargain or Not to Bargain: That Is the Question,” (with Harvey Lapan), American

Economic Review, Vol. 78, No. 2, May 1988, pp. 16-21. “The Calculus of Dissent: An Analysis of Terrorists' Choice of Targets,” (with Harvey

Lapan), Synthèse, Vol. 76, No. 2, August 1988, pp. 245-261. “Fighting World War III: A Suggested Strategy,” (with Jon Cauley), Terrorism: An

International Journal, Vol. 11, No. 3, Fall 1988, pp. 181-195. “Transfers, Transaction Costs, and Charitable Intermediaries,” (with John Posnett),

International Review of Law and Economics, Vol 8, No. 4, December 1988, pp. 145-160. “Externalities, Pigouvian Corrections, and Risk Attitudes,” (with Frederic Sterbenz), Journal

of Environmental Economics and Management, Vol. 15, No. 4, December 1988, pp. 488-504.

“On the Optimal Retaliation Against Terrorists: The Paid-Rider Option,” (with Dwight Lee)

Public Choice, Vol. 61, No. 2, 1989, pp. 141-152. “Public Goods, Growth, and Welfare,” (with Richard Cornes) Social Choice and Welfare,

Vol. 6, No. 3, July 1989, pp. 243-251.

9

“Demand for Charity Donations in Private Non-Profit Markets: The Case of the U.K.” (with John Posnett), Journal of Public Economics, Vol. 40, No. 2, November 1989, pp. 187-200.

“On Distinguishing the Behavior of Nuclear and Non-Nuclear Allies in NATO,” (with

Laurna Hansen and James Murdoch), Defence Economics, Vol. 1, No. 1, January 1990, pp. 37-55.

“Harvest Uncertainty and the Tragedy of the Commons,” (with Frederic Sterbenz), Journal

of Environmental Economics and Management, Vol. 18, No. 2, March 1990, pp. 155-167. “U.N. Conventions, Technology, and Retaliation in the Fight Against Terrorism: An

Econometric Evaluation,” (with Walter Enders and Jon Cauley), Terrorism and Political Violence, Vol. 2, No. 1, Spring 1990, 83-105.

“A Diagrammatic Approach for Teaching Some Aspects of Production-Cost Duality,”

Studies in Economic Analysis, Vol. 12, No. 2, Fall 1990, pp. 32-42. “Nash-Cournot or Lindahl Behavior? An Empirical Test for the NATO Allies,” (with James

Murdoch), Quarterly Journal of Economics, Vol. 105, No. 4, November 1990, pp. 875-894.

“The Triple Entente and the Triple Alliance, 1890-1914: A Collective Goods Approach,”

(with John A. C. Conybeare) American Political Science Review, Vol. 84, No. 4, December 1990, pp. 1197-1206.

“Assessing the Impact of Terrorist-Thwarting Policies: An Intervention Time Series

Approach,” (with Walter Enders and Jon Cauley), Defence Economics, Vol. 2, No. 1, December 1990, pp. 1-18.

“Economic Analysis Can Help Fight International Terrorism,” (with Walter Enders and

Harvey Lapan), Challenge, Vol. 34, No. 1, January/February 1991, pp. 10-17. Republished in Bernard Schechterman and Martin Slann (eds.), Violence and Terrorism, Annual Editions, Third Edition (Sluice Dock, CT: Dushkin Publishing Group, 1993), pp. 192-199.

“The Private Provision of Public Goods: A Perspective on Neutrality,” (with John Posnett),

Public Finance Quarterly, Vol. 19, No. 1, January 1991, pp. 22-42. “The Causality Between Transnational Terrorism and Tourism: The Case of Spain,” (with

Walter Enders), Terrorism: An International Journal, Vol. 14, No. 1, January-March 1991, pp. 49-58.

“NATO Burden Sharing and the Forces of Change: Further Observations,” (with James

Murdoch), International Studies Quarterly, Vol. 35, No. 1, March 1991, pp. 109-114.

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“An Econometric Technique for Comparing Median Voter and Oligarchy Choice Models of Collective Action: The Case of the NATO Alliance,” (with James Murdoch and Laurna Hansen), Review of Economics and Statistics, Vol. 73, No. 4, November 1991, pp. 624-631.

“Sharing Among Clubs: A Club of Clubs Theory,” (with Frederic Sterbenz), Oxford

Economic Papers, Vol. 44, No. 1, January 1992, pp. 1-19. “Agency Theory and the Chinese Enterprise Under Reform,” (with Jon Cauley), China

Economic Review, Vol. 3, No. 1, Spring 1992, pp. 39-56. Republished in Chinese in Economic Science, No. 3, 1993, pp. 47-56.

“After the Cold War, Secure the Global Commons,” Challenge, Vol. 35, No. 4, July/August

1992, pp. 16-23. “Controlling Stock Externalities: Flexible Versus Inflexible Pigovian Corrections,” (with Il-

Dong Ko and Harvey Lapan), European Economic Review, Vol. 36, No. 6, August 1992, pp. 1263-1276.

“A Time-Series Analysis of Transnational Terrorism: Trends and Cycles,” (with Walter

Enders and Gerald Parise), Defence Economics, Vol. 3, No. 4, November 1992, pp. 305-320.

“An Econometric Analysis of the Impact of Terrorism on Tourism,” (with Walter Enders and

Gerald Parise), Kyklos, Vol. 45, No. 4, 1992, pp. 531-554. “Tropical Deforestation: Markets and Market Failures,” Land Economics, Vol. 69, No. 3,

August 1993, pp. 225-233. “Multiproduct Clubs: Membership and Sustainability,” (with John Tschirhart), Public

Finance, Vol. 48, No. 2, 1993, pp. 153-170. “The Economic Theory of Alliances: A Survey,” Journal of Conflict Resolution, Vol. 37,

No. 3, September 1993, pp. 446-483. “Terrorism and Signalling,” (with Harvey E. Lapan), European Journal of Political

Economy, Vol. 9, No. 3, 1993, pp. 383-397. “State-Sponsored Violence As a Tragedy of the Commons: England's Privateering Wars

with France and Spain, 1625-1630,” (with John A. C. Conybeare), Public Choice, Vol. 77, No. 4, December 1993, pp. 879-897.

“The Effectiveness of Anti-Terrorism Policies: A VAR-Intervention Analysis,” (with Walter

Enders), American Political Science Review, Vol. 87, No. 4, December 1993, pp. 829-844. An abbreviated version was republished in Terrorism, Violence, and Insurrections, Vol. 11, No. 3, Summer 1995, pp. 1-5. Republished in War on Terrorism, edited by Alan O’Day (Aldershot, UK: Ashgate, 2004), pp. 401-416.

11

“Rent Seeking and Pesticide Legislation,” (with Sherry Wise), Public Choice, Vol. 78, No. 3-4, March 1994, pp. 329-350.

“Agricultural Research Expenditures in the U.S.: A Public Goods Perspective,” (with Jyoti

Khanna and Wallace Huffman), Review of Economics and Statistics, Vol. 76, No. 2, May 1994, pp. 267-277.

“The Comparative Static Properties of the Impure Public Good Model,” (with Richard

Cornes), Journal of Public Economics, Vol. 54, No. 3, July 1994, pp. 403-421. “Are Public Goods Myths?,” (with Richard Cornes) Journal of Theoretical Politics, Vol. 6,

No. 3, 1994, pp. 369-385. “Alternative Collective-Goods Models of Military Alliances: Theory and Empirics,” (with

John A. C. Conybeare and James Murdoch), Economic Inquiry, Vol. 32, No. 4, October 1994, pp. 525-542.

“Growth and Defense: Pooled Estimates for the NATO Alliance, 1951-1988,” (with

Elizabeth S. Macnair, James C. Murdoch and Chung-Ron Pi), Southern Economic Journal, Vol. 61, No. 3, January 1995, pp. 846-860.

“Charity Donations in the U.K.: New Evidence Based on Panel Data,” (with Jyoti Khanna

and John Posnett), Journal of Public Economics, Vol. 56, No. 2, February 1995, pp. 257-272. Republished in The Economics of Nonprofit Enterprises edited by Richard Steinberg (Northampton, MA: Edward Elgar, 2005).

“Privateering, State-Sponsored Violence as a Tragedy of the Commons: A Reply,” (with

John A. C. Conybeare), Public Choice, Vol. 82, No. 3-4, March 1995, pp. 363-364. “Management of Transnational Commons: Coordination, Publicness, and Treaty Formation,”

(with Keith Sargent), Land Economics, Vol. 71, No. 2, May 1995, pp. 145-162. Republished in Governing the Global Environment edited by Carlo Carraro (Cheltenham, UK: Edward Elgar, 2003).

“On the Relationship between Democracy and Terrorism,” Terrorism and Political Violence,

Vol. 7, No. 4, Winter 1995, pp. 1-9. “NATO Burden Sharing: 1960-1992,” (with Jyoti Khanna), Defence and Peace Economics,

Vol. 7, No. 2, May 1996, pp. 115-133. “A Game-Theoretic Analysis of Carbon Emissions,” in Roger Congleton (ed.), The Political

Economy of Environmental Protection: Analysis and Evidence (Ann Arbor: University of Michigan Press, 1996), pp. 251-272.

“Terrorism and Foreign Direct Investment in Spain and Greece,” (with Walter Enders),

Kyklos, Vol. 49, No. 3, 1996, pp. 331-352. “A Multiproduct Club Approach to Transportation Infrastructure Pricing,” (with Michael A.

Lipsman), Public Finance, Vol. 51, No. 4, Supplement 1996, pp. 453-472.

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“The Voluntary Provision of a Pure Public Good: The Case of Reduced CFC Emissions and the Montreal Protocol,” (with James C. Murdoch), Journal of Public Economics, Vol. 63, No. 2, February 1997, pp. 331-349. Republished in The Political Economy of Environmental Regulation edited by Robert N. Stavins (Northampton, MA: Edward Elgar, 2004).

“Voluntary Cutbacks and Pre-Treaty Behavior: The Helsinki Protocol and Sulfur

Emissions,” (with James C. Murdoch), Public Finance Review, Vol. 25, No. 2, March 1997, pp. 139-162.

“Conscription, Peacekeeping, and Foreign Assistance: NATO Burden Sharing in the Post-

Cold War Era,” (with Jyoti Khanna), Defence and Peace Economics, Vol. 8, No. 1, March 1997, pp. 101-121.

“The Impact of Defense and Nondefense Public Spending on Growth in Asia and Latin

America,” (with James C. Murdoch and Chung-Ron Pi), Defence and Peace Economics, Vol. 8, No. 2, April 1997, pp. 205-224.

“A Tale of Two Collectives: Sulfur Versus Nitrogen Oxides Emission Reduction in Europe,”

(with James C. Murdoch and Keith Sargent), Economica, Vol. 64, No. 2, May 1997, pp. 281-301.

“Collective Action and Tropical Deforestation,” International Journal of Social Economics,

Vol. 24, No. 7-9, 1997, pp. 741-760. “The Future Challenges of NATO: An Economic Viewpoint,” Defence and Peace

Economics, Vol. 8, No. 4, November 1997, pp. 319-353. “Club Theory: Thirty Years Later,” (with John Tschirhart), Public Choice, Vol. 93, No.3-4,

December 1997, pp. 335-355. “The Intergenerational Case of Missing Markets and Missing Voters,” (with Jacobus A.

Doeleman), Land Economics, Vol. 74, No. 1, February 1998, pp. 1-15. “Sharing the Financial Burden for UN and NATO Peacekeeping: 1976-96,” (with Jyoti

Khanna and Hirofumi Shimizu), Journal of Conflict Resolution, Vol. 42, No. 2, April 1998, pp. 176-195.

“When Does Partial Cooperation Pay?,” (with Wolfgang Buchholz and Christian Haslbeck),

Finanzarchiv, Vol. 55, No. 1, 1998, pp. 1-20. “Global and Regional Public Goods: A Prognosis for Collective Action,” Fiscal Studies,

Vol. 19, No. 3, August 1998, pp. 221-247. “Transnational Terrorism in the Post-Cold War Era,” (with Walter Enders), International

Studies Quarterly, Vol. 43, No. 1, March 1999, pp. 145-167. Republished in Dimensions of Terrorism edited by Alan O’Day (Aldershot, UK: Ashgate, 2004), pp. 475-497.

13

“Intergenerational Public Goods: Strategies, Efficiency and Institutions,” in Inge Kaul, Isabelle Grunberg, and Marc A. Stern (eds.), Global Public Goods: International Cooperation in the Twenty-First Century (New York: Oxford University Press, 1999), pp. 20-50. Republished in Governing the Global Environment, edited by Carlo Carraro (Cheltenham, UK: Edward Elgar, 2003), pp. 104-134.

“The Demand for UN Peacekeeping, 1975-96,” (with Jyoti Khanna and Hirofumi Shimizu),

Kyklos, Vol. 52, No. 3, 1999, pp. 345-68. “Equilibrium Existence and Uniqueness in Public Good Models: An Elementary Proof via

Contraction,” (with Richard Cornes and Roger Hartley), Journal of Public Economic Theory, Vol. 1, No. 4, October 1999, pp. 499-509.

“NATO Burden Sharing: Past and Future,” (with Keith Hartley), Journal of Peace Research,

Vol. 36, No. 6, November 1999, pp. 665-680. “Stakeholder Incentives and Reforms in China’s State-Owned Enterprises: A Common-

Property Theory,” (with Jon Cauley and Richard Cornes), China Economic Review, Vol. 10, No. 2, Fall 1999, pp. 191-206.

“Alliance Formation, Alliance Expansion, and the Core,” Journal of Conflict Resolution, Vol.

43, No. 6, December 1999, pp. 727-747. Republished in Arms Trade, Security and Conflict, edited by Paul Levine and Ron Smith (London: Routledge, 2003), pp. 137-157.

“Defence and Peace Economics: A Ten-Year Retrospective,” (with Keith Hartley), Defence

and Peace Economics, Vol. 11, No. 1, February 2000, pp. 1-16. “Pareto-Improving Redistribution and Pure Public Goods,” (with Richard Cornes), German

Economic Review, Vol. 1, No. 2, May 2000, pp. 169-186. “Is Transnational Terrorism Becoming More Threatening? A Time-Series Investigation,”

(with Walter Enders), Journal of Conflict Resolution, Vol. 44, No. 3, June 2000, pp. 307-332.

“Partners in Giving: The Crowding-In Effects of UK Government Grants,” (with Jyoti

Khanna), European Economic Review, Vol. 44, No. 8, August 2000, pp. 1543-1556. “Arms Trade, Arms Control and Security: Collective Action Issues,” Defence and Peace

Economics, Vol. 11, No. 5, September 2000, pp. 533-548. Republished in Arms Trade, Security and Conflict, edited by Paul Levine and Ron Smith (London: Routledge, 2003), pp. 209-220.

“On Sharing NATO Defense Burdens in the 1990s and Beyond,” (with James C. Murdoch),

Fiscal Studies, Vol. 21, No. 3, September 2000, pp. 297-327. Republished in The Economics of Public Spending, edited by David Miles, Gareth Myles, and Ian Preston (Oxford: Oxford University Press, 2003), pp. 237-266.

“Economic Analysis of Conflict,” Journal of Conflict Resolution, Vol. 44, No. 6, December

2000, pp. 723-729.

14

“Models of Alliances: Internalizing Externalities and Financing,” (with Kevin Siqueira), Defence and Peace Economics, Vol. 12, No. 3, May 2001, pp. 249-270.

“Transnational Public Goods: Strategies and Institutions,” (with Daniel G. Arce M.), European

Journal of Political Economy, Vol. 17, No. 3, September 2001, pp. 493-516. “Economics of Alliances: The Lessons of Collective Action,” (with Keith Hartley), Journal of

Economic Literature, Vol. 39, No. 3, September 2001, pp. 869-896. “A Cooperative Game Theory of Noncontiguous Allies,” (with Daniel G. Arce M.), Journal of

Public Economic Theory, Vol. 3, No. 4, October 2001, pp. 391-411. “Weakest-Link Public Goods: Giving In-Kind or Transferring Money in a Sequential Game,”

(with Simon Vicary), Economics Letters, Vol. 74, No. 1, 2001, pp. 71-75. “Agency Cost and the Crisis of China's SOEs: A Comment and Further Observations,” (with

Jon Cauley), China Economic Review, Vol. 12, No. 4, 2001, pp. 293-297. “Economic Growth, Civil Wars, and Spatial Spillovers,” (with James C. Murdoch), Journal of

Conflict Resolution, Vol. 46, No. 1, February 2002, 91-110. “On Financing Global and International Public Goods,” in Marco Ferroni and Ashoka Mody

(eds.), International Public Goods: Incentives, Measurement, and Financing (Dordecht, NL: Kluwer, 2002), pp. 81-117.

“Patterns of Transnational Terrorism, 1970-99: Alternative Time Series Estimates,” (with

Walter Enders), International Studies Quarterly, Vol. 46, No. 2, June 2002, pp. 145-165. “A Conceptual Framework for Understanding Global and Transnational Public Goods for

Health,” (with Daniel G. Arce M.), Fiscal Studies, Vol. 23, No. 2, June 2002, pp. 195-222. “Weakest-Link Public Goods: Giving In-Kind or Transferring Money,” (with Simon Vicary),

European Economic Review, Vol. 46, No. 8, October 2002, pp. 1501-1520. “Peacekeeping and Burden Sharing: 1994-2000,” (with Hirofumi Shimizu), Journal of Peace

Research, Vol. 39, No. 6, November 2002, pp. 651-668. “Assessing the Optimal Provision of Public Goods: In Search of the Holy Grail,” in Inge Kaul,

Pedro Conceição, Katell Le Goulven, and Ronald U. Mendoza (eds.), Providing Global Public Goods: Managing Globalization (New York: Oxford University Press, 2002), pp. 131-151.

“Economic Analysis of Civil Wars,” (with Håvard Hegre), Defence and Peace Economics,

Vol. 13, No. 6, December 2002, pp. 429-433. “Civil Wars and Economic Growth: A Regional Comparison,” (with James C. Murdoch),

Defence and Peace Economics, Vol. 13, No. 6, December 2002, pp. 451-464.

15

“The Participation Decision Versus the Level of Participation in an Environmental Treaty: A Spatial Probit Analysis,” (with James C. Murdoch and Wim Vijverberg), Journal of Public Economics, Vol. 87, No. 2, February 2003, pp. 337-362.

“An Evolutionary Game Approach to Fundamentalism and Conflict,” (with Daniel G. Arce

M.), Journal of Institutional and Theoretical Economics, Vol. 159, No. 1, March 2003, pp. 132-154.

“NATO Peacekeeping and Burden Sharing: 1994-2000,” (with Hirofumi Shimizu), Public

Finance Review, Vol. 31, No. 2, March 2003, pp. 123-143. “Health-Promoting Alliances,” (with Daniel G. Arce M.), European Journal of Political

Economy, Vol. 19, No. 2, June 2003, pp. 355-375. “Collective Action and Transnational Terrorism,” World Economy, Vol. 26, No. 6, June 2003,

pp. 779-802. “Pure Public Goods versus Commons: Benefit-Cost Duality,” (with Daniel G. Arce M.), Land

Economics, Vol. 79, No. 3, August 2003, pp. 355-368. “Terrorism and Game Theory,” (with Daniel G. Arce M.), Simulation & Gaming, Vol. 34, No.

3, September 2003, pp. 319-337. “The Future of the Defence Firm,” (with Keith Hartley), Kyklos, Vol. 56, No. 3, 2003, pp. 361-

380. “Civil Wars and Economic Growth: Spatial Dispersion,” (with James C. Murdoch), American

Journal of Political Science, Vol. 48, No.1, January 2004, pp. 138-151. “Collective Goods, Common Agency, and Third-Party Intervention,” (with Kevin Siqueira),

Bulletin of Economic Research, Vol. 56, No.1, January 2004, pp. 1-20. “An Economic Perspective on Transnational Terrorism,” (with Walter Enders), European

Journal of Political Economy, Vol. 20, No. 2, June 2004, pp. 301-316. Republished in The Economic Analysis of Terrorism, edited by Tilman Brück (Abingdon, UK: Routledge, 2007), pp. 13-28.

“Too Much of a Good Thing? The Proactive Response Dilemma,” (with B. Peter Rosendorff),

Journal of Conflict Resolution, Vol. 48, No. 5, October 2004, pp. 657-671. “Transnational Terrorism 1968-2000: Thresholds, Persistence, and Forecasts,” (with Walter

Enders), Southern Economic Journal, Vol. 71, No. 3, January 2005, pp. 467-483. “The Dilemmas of the Prisoners’ Dilemmas,” (with Daniel G. Arce M.), Kyklos, Vol. 58, No.

1, January 2005, pp. 3-24. “September 11 and Its Aftermath,” (with Walter Enders), International Studies Review, Vol. 7, No. 1, March 2005, pp. 65-168.

16

“Counterterrorism: A Game-Theoretic Analysis,” (with Daniel G. Arce M.), Journal of Conflict Resolution, Vol. 49, No. 2, April 2005, pp. 83-200.

“After 9/11: Is It All Different Now?” (with Walter Enders), Journal of Conflict Resolution, Vol. 49, No. 2, April 2005, pp. 259-277.

“Collective versus Unilateral Responses to Terrorism,” Public Choice, Vol. 124, No. 1, July 2005, pp. 75-93. “NATO Benefits, Burdens, and Borders: Comment,” Defence and Peace Economics, Vol. 16,

No. 4, August 2005, pp. 317-321. “Donors’ Mechanisms for Financing International and National Public Goods: Loan or

Grants?,” (with Raechelle Mascarenhas), World Economy, Vol. 28, No. 8, August 2005, pp. 1095-1117.

“Recognizing the Limits to Cooperation behind National Borders: Financing the Control of

Transnational Terrorism,” in Inge Kaul and Pedro Conceição, (eds), The New Public Finance: Responding to Global Challenges (New York: Oxford University Press, 2006) pp. 194-216.

“Regional Public Goods and International Organizations,” Review of International

Organizations, Vol. 1, No. 1, March 2006, pp. 5-25. “Distribution of Transnational Terrorism among Countries by Income Classes and

Geography after 9/11,” (with Walter Enders), International Studies Quarterly, Vol. 50, No. 2, June 2006, pp. 367-393.

“CBRN Incidents: Political Regimes, Perpetrators, and Targets,” (with Kate Ivanova), Terrorism and Political Violence, Vol. 18, No. 3, Fall 2006, pp. 423-448. “Global Terrorism: Deterrence versus Preemption,” (with Kevin Siqueira), Canadian Journal of Economics, Vol. 50, No. 4, November 2006, pp. 1370-1387. “Do Donors Cooperatively Fund Foreign Aid?,” (with Raechelle Mascarenhas), Review of International Organizations, Vol. 1, No. 4, 2006, pp. 337-357. “The Impact of Transnational Terrorism on US Foreign Direct Investment,” (with Walter

Enders and Adolfo Sachsida), Political Research Quarterly, Vol. 59, No. 4, December 2006, pp. 517-531.

“Terrorists Versus the Government: Strategic Interaction, Support, and Sponsorship,” (with

Kevin Siqueira), Journal of Conflict Resolution, Vol. 50, No. 6, December 2006, pp. 878-898.

“Hirshleifer’s Social Composition Function in Defense Economics.” Defence and Peace

Economics, Vol. 18, No. 6, December 2006, pp. 645-655.

17

“New Face of Development Assistance: Public Goods and Changing Ethics,” (with Daniel G. Arce), Journal of International Development, Vol. 19, No. 4, May 2007, pp. 527-544. Republished in Reflexive Governance for Global Public Goods, edited by Eric Brousseau, Tom Dedeurwaerdere, and Bernd Siebenhüner (Cambridge, MA: MIT Press) forthcoming 2008.

“Applying Analytical Methods to Study Terrorism,” (with Walter Enders), International

Studies Perspectives, Vol. 8, No. 3, August 2007, pp. 287-302. “CBRN Attack Perpetrators: An Empirical Study,” (with Kate Ivanova) Foreign Policy

Analysis, Vol. 3, No. 4, October 2007, pp. 273-294. “Terrorist Signalling and the Value of Intelligence,” (with Daniel G. Arce) British Journal of Political Science, Vol. 37, No. 4, October 2007, pp. 573-586. “Terrorist Backlash, Terrorism Mitigation, and Policy Delegation,” (with Kevin Siqueira),

Journal of Public Economics, Vol. 91, No. 9, pp. 1800-1815. “Economic Consequences of Terrorism in Developed and Developing Countries: An

Overview,” (with Walter Enders) in Philip Keefer and Norman Loayza (eds.), Terrorism and Economic Development (Cambridge: Cambridge University Press, 2008), pp. 17-47, forthcoming.

“Treaties: Strategic Considerations,” University of Illinois Law Review, Vol. 2008, No. 1,

forthcoming. “9/11: What Did We Know and When Did We Know It,” (with Walter Enders and Beom S.

Lee), Defence and Peace Economics, Vol. 19, forthcoming 2008. “IMF Retrospective and Prospective: A Public Goods Viewpoint,” (with Joseph P. Joyce),

Review of International Organizations, forthcoming 2008. “Defensive Counterterrorism Measures and Domestic Politics,” (with Kevin Siqueira),

Defence and Peace Economics, Vol. 19, forthcoming 2008. “Hostage Taking: Understanding Terrorism Event Dynamics,” (with Patrick Brandt), Journal

of Policy Modeling, forthcoming 2008. BOOKS:

Public Goods and Public Policy (edited with William Loehr), (Beverly Hills, California:

Sage Publications, Inc., 1978), 240 pages. The Political Economy of Public Goods and International Cooperation, (with William Loehr

and Jon Cauley), Monograph Series in World Affairs, Vol. 15, Book 3, University of Denver, Graduate School of International Studies, 1978, 98 pages.

The Theory and Structures of International Political Economy (edited book), (Boulder,

Colorado: Westview Press, 1980), 280 pages.

18

The Theory of Externalities, Public Goods, and Club Goods (with Richard Cornes), (New York: Cambridge University Press, 1986), 303 pages.

International Terrorism in the 1980s: A Chronology of Events, Volume 1, 1980-1983 (with

Edward Mickolus and Jean Murdock), (Ames, Iowa: Iowa State University Press, 1988), 541 pages.

International Terrorism in the 1980s: A Chronology of Events, Volume 2, 1984-1987 (with

Edward Mickolus and Jean Murdock), (Ames, Iowa: Iowa State University Press, 1989), 776 pages.

The Economics of Defence Spending: An International Survey (edited with Keith Hartley),

(London: Routledge, 1990), 285 pages. Collective Action: Theory and Applications (Ann Arbor, Michigan: University of Michigan

Press, 1992), 237 pages. The Economics of Defense (with Keith Hartley), (Cambridge: Cambridge University Press,

1995), 400 pages. Republished in Japanese, Shoichi Fukaya translator (Tokyo: Nihon Hyoronsha Publishing Company, 1999); Republished in Chinese (Beijing: Beijing Institute of Technology Press, 2007).

Handbook of Defense Economics, vol. 1 (co-edited book with Keith Hartley) (Amsterdam:

North Holland, 1995), 606 pages. Republished in Chinese (Beijing: Economic Science Press, 2004).

The Theory of Externalities, Public Goods, and Club Goods, Second Edition (with Richard

Cornes), (New York: Cambridge University Press, 1996), 590 pages. Global Challenges: An Approach to Environmental, Political, and Economic Problems

(Cambridge: Cambridge University Press, 1997), 234 pages. The Political Economy of NATO: Past, Present, and Into the 21st Century (with Keith

Hartley), (Cambridge: Cambridge University Press, 1999), 292 pages. The Future of Development Assistance: Common Pools and International Public Goods

(with Ravi Kanbur and Kevin Morrison) Overseas Development Council Policy Essay No. 25 (Washington, DC: Overseas Development Council, 1999), 106 pages.

Economics of Defence (edited with Keith Hartley) Edward Elgar Critical Writings in

Economics, 3 Volumes (Aldershot, UK: Edward Elgar, 2001), 1573 pages. Economic Concepts for the Social Sciences (Cambridge: Cambridge University Press,

September 2001), 298 pages. Republished in Chinese (Taiwan: Booklife Publishing Company, 2004). Republished in Russian (Moscow: Ves Mir Publishing, 2006).

Regional Public Goods: Typologies, Provision, Financing, and Development Assistance

(with Daniel G. Arce M.) (Stockholm: Almqvist and Wiksell, 2002), 102 pages.

19

Economics of Conflict (edited with Keith Hartley) Edward Elgar Critical Writings in Economics, 3 Volumes (Aldershot, UK: Edward Elgar, 2003), 2100 pages.

Global Collective Action (Cambridge: Cambridge University Press, 2004), 299 pages. The Political Economy of Terrorism (with Walter Enders) (Cambridge: Cambridge

University Press 2006), 278 pages.

Handbook of Defense Economics, vol. 2 (co-edited book with Keith Hartley) Amsterdam: North-Holland, 2007), 697 pages. OTHER PUBLICATIONS:

“Devaluation: An Analysis and Some Timely Questions,” Arizona Business, Volume 19, No. 2, February 1972, pp. 18-24.

“The Dynamic Price Expectation Effect of Devaluation,” (with Nobuo Minabe), Osaka City

University Economic Review, January 1973, No. 8, pp. 13-23. “International Monetary Reforms,” Arizona Business, Volume 20, No. 1, January 1973, pp.

17-24. “Dollars, Deficits, and Devaluation,” (with Elmer Gooding), Arizona Business, Volume 20,

No. 5, May 1973, pp. 10-16. “The Demand for International Reserves: A Respecification,” (with Shigeo Minabe), The

Hikone Ronso, No. 29, August 1973, pp. 1-11. “Domestic and International Policy Implications of the Inflation-Unemployment Trade-Off,”

(with Phil Graves), Akron Business and Economic Review, Volume 5, No. 2, Summer 1974, pp. 9-14.

“On the Public Character of Goods,” (with William Loehr), in W. Loehr and T. Sandler

(eds.), Public Goods and Public Policy (Beverly Hills, California: Sage Publications, Inc., 1978), pp. 11-37.

“Explorations in the Economics of Outer Space,” (with William Schulze), in Todd Sandler

(ed.), The Theory and Structures of International Political Economy (Boulder, Colorado: Westview Press, 1980), pp. 175-195.

“Outer Space: The New Market Frontier,” (with William Schulze), Economic Affairs, Vol. 5,

No. 4, July-September 1985, pp. 6-10. “Defense Burdens and Prospects for the Northern European Allies,” (with James Murdoch),

in David Denoon (ed.), Constraints on Strategy: The Economics of Western Security (New York: Pergamon-Brassey, 1986), pp. 59-113.

20

“Economic Methods and the Study of Terrorism,” (with Scott Atkinson et al.), in Paul Wilkinson and A. W. Stewart (eds.), Contemporary Research on Terrorism (Aberdeen, Scotland: Aberdeen University Press, 1987), pp. 376-389.

“NATO Burden Sharing: Rules or Reality?” in the International Economic Association 1985

Volume entitled, Peace, Defence and Economic Analysis (London: Macmillan, 1987), pp. 363-383.

“Britain, Europe, and the Atlantic Alliance,” Institute of Economic Affairs, IEA Inquiry

Paper No. 10, London: IEA, September 1989. “Swedish Military Expenditures and Armed Neutrality,” (with James Murdoch), in Keith

Hartley and Todd Sandler (eds.), The Economics of Defence Spending: An International Survey (London: Routledge, 1990), pp. 148-176.

“On Terrorism, Guerrilla Warfare, and Insurrections,” Defence Economics, Vol. 3, No. 4,

November 1992, pp. 259-261. “Terrorism: Theory and Applications,” (with Walter Enders) in Keith Hartley and Todd

Sandler (eds.), Handbook of Defense Economics (Amsterdam: North-Holland, 1995), pp. 213-249.

“The Future of NATO,” Economic Affairs, Vol. 17(4), December 1997, pp. 15-21. “Os Desafios à NATO na região do Mediterrâneo e em outras Áreas,” Economia & Defesa,

Vol. 90, No. 2, Summer 1999, pp. 35-62. “A Radical Approach to Development Assistance,” (with Ravi Kanbur and Kevin M.

Morrison), Development Outreach, Vol. 1, No. 2, Fall 1999, pp. 15-17. “Challenges to NATO in the Mediterranean and Beyond,” in Jurgen Brauer and Keith

Hartley (eds.), The Economics of Regional Security: NATO, The Mediterranean, and Southern Africa (Reading, UK: Harwood Academic Publishers, 2000), pp. 71-92.

“On Partnerships, CDF, and Collective Action,” posted at World Bank website:

http://www.worldbank.org/html/oed/topics/cdfproceedings/pdfs/annex_sandler.pdf. “Financing Global and International Public Goods,” in Christopher D. Gerrard, Marco

Ferroni, and Ashoka Mody (eds.), Global Public Policies and Programs: Implications for Financing and Evaluation (Washington, DC: Operations Evaluation Department, World Bank, 2001), pp. 183-192.

“Understanding Global Public Goods,” OECD Observer, No. 228, September 2001, pp. 15-

17. “What Economics Tells Us to Prevent Terrorism,” An Interview in Challenge, Vol. 45, No.

3, May/June 2002, pp. 5-12.

21

“Nash, Game Theory, and Global Challenges,” in Constantina Kottaridi and Gregorios Siourounis (eds.), Game Theory: A Festschrift in Honor of John F. Nash Jr. (published in Greek, Athens: Eurasia Publications, 2002), pp. 148-152.

“Terrorism and Game Theory, An Interview,” Swiss Military Review, No. 12, December

2002, pp. 4-5. “Global Challenges and the Need for Supranational Infrastructure,” in Omar Azfar and

Charles Cadwell (eds.), Market-Augmenting Government: The Institutional Foundations for Prosperity (Ann Arbor, MI: University of Michigan Press, 2003), pp. 269-294.

“Biosphere, Markets, and Governments: Comment,” in Omar Azfar and Charles Cadwell

(eds.), Market-Augmenting Government: The Institutional Foundations for Prosperity (Ann Arbor, MI: University of Michigan Press, 2003), pp. 175-176.

“What Do We Know about the Substitution Effect in Transnational Terrorism,” in Andrew

Silke (ed.), Researching Terrorism: Trends, Achievements, Failures (Ilford, UK: Frank Cass, 2004), pp. 119-137.

“Regional Public Goods: Demand and Institutions,” in Antoni Estevadeoral, Brian Frantz,

and Tam Nguyen (eds.) Regional Responses to Globalization: Regional Public Goods and Development Assistance (Washington, DC: Inter-American Development Bank and Asian Development Bank, 2004), pp. 11-30.

“Regional Public Goods: The Comparative Edge of Regional Development Banks:

Comments,” in Nancy Birdsall and Liliana Rojas-Suarez (eds.), Financing Development: The Power of Regionalism (Washington, DC: Center for Global Development, 2004), pp. 123-127.

“The Political Economy of Transnational Terrorism,” (with B. Peter Rosendorff), Journal of Conflict Resolution, Vol. 49, No. 2, April 2005, pp. 171-182. “Introduction: Security Challenges and Threats in a Post-9/11 World,” (with Carlos P.

Barros and Christos Kollias), Defence and Peace Economics, Vol. 16, No. 5, October 2005, pp. 327-329.

“Transnational Terrorism: An Economic Analysis,” in Harry W. Richardson, Peter Gordon,

and James E. Moore II (eds.), The Economic Impact of Terrorist Attacks (Aldershot, UK: Edward Elgar, 2005), pp. 11-34.

“ Economic Methods and the Study of Terrorism: An Evaluation,” in Jeffrey Victoroff (ed.),

Tangled Roots: Social and Psychological Factors in the Genesis of Terrorism (Amsterdam: IOS Press, 2006), pp. 115-129.

“Regional Public Goods and Regional Cooperation,” in Secretariat of the International Task

Force on Global Public Goods (ed.), Meeting Global Challenges: International Cooperation in the National Interest: Cross-Cutting Issues (Stockholm: Secretariat, 2006), pp. 143-178.

22

“Terrorism: A Game-Theoretic Approach,” (with Daniel G. Arce) in Todd Sandler and Keith Hartley (eds.), Handbook of Defense Economics, Vol. 2 (Amsterdam: North-Holland, 2007), pp. 775-813.

“Defense in a Globalized World: An Introduction,” (with Keith Hartley) in Todd Sandler and

Keith Hartley (eds.), Handbook of Defense Economics, Vol. 2 (Amsterdam: North-Holland, 2007), pp. 607-621.

DATA SET:

International Terrorism: Attributes of Terrorist Events 1978-1987 (ITERATE 3) (with

Edward Mickolus, Jean Murdock, and Peter Fleming). Distributed by Vinyard Software, Inc., Falls Church, VA, 1989. Update 1988-1989 (ITERATE 4) Vinyard Software, Inc., Falls Church, VA, 1990.

EDITING AND OTHER ACTIVITIES:

• Editorial Board, International Studies Perspectives, January 2007 on. • Editorial Board, American Journal of Political Science, January 2006-December 2008. • Associate Editor, Review of International Organizations, January 2006 on. • Co-Editor of special issue of Defence and Peace Economics on “Security Challenges and

Threats in a Post-9/11 World,” Vol. 16, No. 5, October 2005. • Co-Editor of special issue of Journal of Conflict Resolution on “The Political Economy

of Terrorism,” Vol. 49, No. 2, April 2005.

• Chairman, Editorial Board, Journal of Conflict Resolution, April 2004 on.

• Co-Editor of special issue of Defence and Peace Economics on “Internal and External Threats: Defence Economics Analysis,” Vol. 14, No. 6, December 2003.

• Co-Editor of special issue of Defence and Peace Economics on “Economic Analysis of

Civil Wars,” Vol. 13, No. 6, December 2002. • Editorial Board, Terrorism and Political Violence, January 2004 on.

• Editorial Board, Nação e Defesa, March 2002 on. • Editorial Board, European Review of Economics and Finance, January 2002 on.

• Editorial Board, Public Finance Review, July 2000 on.

• Editorial Board, Fiscal Studies, June 2000 on.

23

• Guest Editor of special issue of Journal of Conflict Resolution on “Economic Analysis of Conflict,” Vol. 44, No. 6, December 2000.

• Co-Editor of Tenth Anniversary issue of Defence and Peace Economics, Vol. 11, No. 1,

February 2000.

• Associate Editor, Bulletin of Economic Research, February 2000 on. • Advisory Board on book series, Institutional Analysis, University of Michigan Press,

edited by Workshop in Political Theory and Policy Analysis, Indiana University, 1999 on.

• Editorial Board, International Studies Quarterly, January 1999-December 2003, January

2004-December 2007.

• Associate Editor, Journal of Public Economic Theory, May 1997-December 2005.

• Editorial Board, Social Science Quarterly, March 1996-April 2005.

• Editorial Board, Defence and Peace Economics, January 1995 on. Advising Editor from January 1999 on.

• Editorial Council on Journal of Environmental Economics and Management, January

1986 to December 1987, reappointed for January 1992-December 1993, reappointed for January 1994 December 1995, January-December 1996, January-December 1997, January-December 1998, January-December 1999, January-December 2000, January-December 2001.

• Editorial Board on Monograph Series in World Affairs, University of Denver, Graduate

School of International Studies, 1979 on.

• Editor of Defence Economics, September 1988-December 1994. (First issue appeared January 1990).

• Editor of special issue of Defence Economics on Terrorism, Guerrilla Warfare, and

Insurrections, Vol. 3, No. 4, November 1992. • Executive Board, International Defense Economics Association, 1990 on.

• Executive Board Member of Economists Allied Against the Arms Race (ECAAR), Israel

Section, 1994 on.

• Associate Editor of Journal of Environmental Economics and Management, January 1988 to January 1990.

24

• Advising Board Member for Annual Editions: Violence and Terrorism, Duskin Publishing Group, 1989 on.

• Co-editor of Journal of Conflict Resolution for the June 1982 issue. • Editorial Board on Sage Series on Comparative Economy and Public Policy, 1975 to

1978. • Associate Editor, Intermountain Economic Review, September 1972 to June 1974.

• Reviewer for NSF, major economics journals, and major political science journals.

DISSERTATIONS DIRECTED:

Murdoch, James. “Contribution to the Economics of Military Alliances,” defended in

October 1982. He is professor of economics at University of Texas-Dallas. Sepassi, Reza. “A Contribution to the Theory of Clubs,” defended in January 1983. Ko, Il-Dong. “Issues in the Control of Stock Externality Problems with Inflexible Policy

Measures,” defended on September 1988 (received Research Excellence Award from ISU). He is a research fellow at Korea Development Institute.

Khanna, Jyoti. “Theory and Econometric Analysis of State Government Demand for Public

Agricultural Research,” defended on February 28, 1990. She is an associate professor of economics at Colgate University.

Wise, Sherry. “Rent-Seeking in Pesticide Policy,” defended on June 2, 1991. She is an

economic analyst at the Environmental Protection Agency, Washington, DC. Lipsman, Michael. “A Theory of Transportation Clubs with Special Application to the

Domestic Aviation System,” defended on November 9, 1994. He is an economic analyst at Iowa Legislative Fiscal Bureau, State Capital, Des Moines.

Sargent, Keith. “A Spatial Econometric Model for Transboundary Air Pollution Control

Treaties: An Analysis of Noncooperative International Behavior,” defended on March 26, 1997. He is an economic analyst at the Environmental Protection Agency, Washington, DC.

Siqueira, Kevin. “Issues of Collective Action: Common Agency, Partial Cooperation, and

Clubs,” defended on August 26, 1998. He is an associate professor at University of Texas at Dallas.

Shimizu, Hirofumi. “UN Peacekeeping as a Public Good: Analyses of the UN Member

States' Peacekeeping Financial Contribution Behavior,” defended on August 13, 1999. He is an Assistant Professor at the National Defense Academy in Japan.

25

Yang, Chia-yen. “The Institutional Choice of Public Good Provision,” defended on March 29, 2000.

McCulloch, Russel. “Impure Thoughts of Charitable Giving,” defended on January 24,

2003. Mascarenhas, Raechelle, “An Empirical Analysis of Foreign Aid and the Provision of

International Public Goods,” defended June 6, 2005. She is an assistant professor at Whitman College, Walla Walla, WA.

Ivanova, Kate, “Corruption, Rule of Law and International Interaction in Environment

Pollution and CBRN Terrorism,” defended June 28, 2006. She is an assistant professor at The Ohio State University at Newark. Awarded honorable mention as best dissertation for 2006 at USC College of Liberal Arts and Sciences.

MASTERS DIRECTED:

Hansen, Laurna. “Conventional Versus Strategic Expenditures in NATO: A Public Goods

Approach,” defended on June 28, 1988 (received Research Excellence Award from ISU). She is a research associate at the Sandia National Laboratory, Livermore, CA.

Tanner, Thomas Cole. “The Spatial Theory of Elections: An Analysis of Voters' Predictive

Dimensions and Recovery of the Underlying Issue Space,” defended on April 12, 1994 (received a Research Excellence Award from ISU).

Holland, Stephen P. “Some Economic Policies for Ameliorating the Tragedy of the

Commons,” defended on May 13, 1994. He received a fellowship as a Ph.D. student in economics at University of Michigan.

Twait, Christine. “Determining the Barriers to Small Business Pollution Prevention,”

defended on April 19, 1995 (received a Research Excellence Award from ISU). She is a grant coordinator in the Business College, University of Northern Iowa, Waterloo, IA.

Kondo, Masahiro. “Theoretical and Empirical Analysis of Military Expenditures of Japan,

South Korea, and North Korea,” defended on May 6, 1998. Alonso, Julio C. “Narcotraffic, Guerrilla Warfare, and Antinarcotics Foreign Aid,” defended

on July 5, 2000. CONSULTANCY:

1980 on Consultant to book publishers 1984-1999 Consultant for James Savarese & Associates, a division of Ogilvy

& Mather, Public Relations Firm.

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October 1983 to Consultant on “The Economics of Defense in 1980s,” A October 1984 grant given by the Office of Net Assessment, Department of

Defense. Principal investigator in charge of the assessment of the U.K., France, and West German's future in NATO. Project coordinator was David Denoon, New York University.

Summer 1987 Consultant with David Denoon, James Murdoch on a project for

U.S. Department of Defense. September 1990-96 Consultant for Institute of Defense Analyses, Alexandria, VA. 1998-99, 2001-05 Consultant and author for Global Public Goods Projects for UN

Development Program. 1999 Author of paper for a project, Market Augmenting Governance,

IRIS, University of Maryland. 1999 Project on reforming foreign assistance for Overseas Development

Council. 1999-2002, 2005 Consultant for World Bank on various projects. 2001 Author of paper for a project on Health-Promoting Global Public

Goods, Institute for Global Health, University of California at San Francisco.

2002 Consultant for Inter-American Development Bank on projects on

Regional Public Goods

2004-2005 Consultant for the International Task Force for Global Public Goods, Stockholm, Sweden.

2006-2007 Senior advisor on global public goods for UNIDO, Geneva,

Switzerland.