Pirates of the Mediterranean: An Empirical

Investigation of Bargaining with Transaction Costs

Attila Ambrus∗ Eric Chaney† Igor Salitskiy‡

December 22, 2011

Abstract

This paper uses ransom prices and time to ransom for over 10,000 captives rescued

from two Barbary strongholds to investigate the empirical relevance of dynamic bar-

gaining models with one-sided asymmetric information in ransoming settings. We ob-

serve both multiple negotiations that were ex ante similar from the uninformed party’s

(seller’s) point of view, and information that only the buyer knew. Through reduced-

form analysis, we test some common qualitative predictions of dynamic bargaining

models. We also structurally estimate the model in Cramton (1991), to compare ne-

gotiations in different Barbary strongholds. Our estimates suggest that the historical

bargaining institutions were remarkably efficient, despite the presence of substantial

asymmetric information.

∗Harvard University and NBER.†Harvard University.‡Stanford University. We thank Ran Abramitzky, Gillian Weiss, seminar participants at Stanford and

NYU Abu Dhabi, and especially Mauricio Drelichman, Avner Greif and Greg Lewis for helpful commentsand discussions. The library staff at the Biblioteca Nacional de Madrid and the Archivo Histórico Nacionalfacilitated the data collection. Judith Gallego provided outstanding research assistance. Any remainingerrors are our own.

1

1 Introduction

In recent years, Somali pirates have hijacked hundreds of ships and demanded sizeable ran-

soms for the release of captured crews and cargoes. Although the uptick in piracy off the

coast of Somalia has focused international attention on ransom payments, such payments

have long provided an important source of income for criminal organizations. Despite their

economic importance, little empirical work has been done investigating the determinants of

ransoms.1

We begin to address this gap in the literature by investigating the empirical relevance

of theoretical work related to many ransoming situations. To this end, we use a historical

data set on over 10,000 captives ransomed from the Barbary Corsairs, during rescue missions

conducted by Spanish negotiating teams between 1575 and 1739. These North-African-based

Corsairs preyed on Christian European shipping in the Mediterranean and the Atlantic for

centuries. Like Somali pirates today they derived important revenues from ransoms paid for

captured crews and individuals.

Conceptually, we think about negotiations for the release of different captives as a dy-

namic bargaining game with asymmetric information. In particular, we assume that the

relevant uncertainty is one-sided, regarding the exact value of each captive for the rescuers.

This value contained a term that was impossible for the corsairs to observe: the amount of

money raised at home for the release of the given captive. For this reason, the captors could

only know the probability distribution of the value for the buyer, conditional on observables.

In reality, negotiations during each rescue mission were part of a meta-game, in which the

same captive could be bargained for during multiple missions. However, we do not observe

the set of captives who were present and feasible to bargain for at a given rescue trip, only

the set of rescued captives. For this reason, we focus on negotiations, and in particular the

time path of prices, within rescue missions. Qualitative evidence suggests that after each

1For the growing literature investigating piracy and privateering from an economic standpoint, see Leeson(2007, 2009) and Gathmann and Hillmann (2009).

2

day of bargaining there was a nontrivial chance that negotiations end for exogenous reasons,

which introduced a randomness in the duration of the rescue trip, and urgency in reaching

an agreement.

Our data set provides a unique opportunity to investigate the empirical relevance of dy-

namic bargaining models with asymmetric information for three reasons. First, contrary to

laboratory experiments examining dynamic bargaining, in our setting it is reasonable to as-

sume that the participants only cared about their own physical payoffs. Several experimental

papers, including Neelin et al. (1988) and Ochs and Roth (1989), show that the observed

play of subjects in sequential bargaining situations is far from the perfect equilibrium pre-

diction of corresponding models.2 These papers compellingly argue that the main reason for

this is that many subjects exhibit other-regarding preferences, and in particular reject offers

that would give them less than what they regard as a fair share of the surplus. This can

be clearly observed in ultimatum games, which are essentially one-period bargaining games,

as first shown in Guth et al. (1982). In contrast, the negotiations we examine were con-

ducted by professional bargaining teams on the Spanish side (with clearly laid out directives

from the court), and experienced traders on the corsairs’ side, for whom buying and selling

captives was a regular business activity.3

Second, as opposed to field data previously used in empirical research on dynamic nego-

tiations, we observe multiple negotiations by the same parties for captives who for practical

purposes were identical for the seller. This plausibly addresses endogeneity issues that have

hampered many previous empirical investigations of asymmetric bargaining models (Kennan

2For experiments on bargaining with asymmetric information, see Mitzkiewitz and Nagel (1993), Strauband Murnighan (1995), Croson (1996), Guth et al. (1996), Rapoport et al. (1996), and Schmitt (2004).The qualitative conclusion that play is far away from equilibrium predictions remains valid in the aboveexperiments, although incomplete information (in particular on the responder side) tends to lower bothaverage offers and the likelihood of acceptance of low offers.

3Another reason why observed behavior in the lab differs from theoretical predictions is that subjectsin the lab might be risk-averse, while most of the theoretical literature assumes risk-neutral parties. Giventhat the parties in our setting were typically engaged in negotiating for the release of many similar captives,it is reasonable to assume risk-neutrality within any given negotiation (with the possible exception of a fewhigh-ranked captives).

3

and Wilson (1989)).4

Third, we directly observe a portion of the buyer’s privately known evaluation: the

amount of earmarked money raised in Spain by his or her family, which could only be used

for the release of the earmarked captive. Our empirical use of information that only one of

the parties possessed adds to a growing empirical literature on adverse selection that aims

to collect and utilize such information (Finkelstein and McGarry (2006), Finkelstein and

Poterba (2006), Abramitzky (2009)). To the best of our knowledge, ours is the first paper to

empirically use such information in the context of bargaining under asymmetric information.

We conduct our investigation in two waves. First, we test reduced-form predictions that

are implied by a large class of bargaining models with one-sided asymmetric information, to

check the empirical relevance of these models. Second, we structurally estimate a particular

bargaining model, to derive comparative statics results and conduct welfare analysis.

In the reduced-form analysis, we investigate the relationships between the length of ne-

gotiations and release price, and how an observed increase in the buyer’s evaluation (in the

form of earmarked money for a captive) affects release price and the length of negotiations.

We find that in Algiers, where qualitative evidence suggests that the negotiating teams faced

higher time costs of bargaining, the data are consistent with the theoretical predictions. In

contrast, in Tetuan, where the time costs for negotiating were much more modest, we do not

find empirical support for the theory.

While our reduced form investigation allows us to test some general predictions of dy-

namic bargaining models with asymmetric information, we need a different approach to be

able to compare the bargaining process in the two main Corsair strongholds, Algiers and

Tetuan, and identify the main reasons why observed bargaining outcomes differ in these

two locations. This is because the effects of differences in the distributions of buyer values,

4Card (1990), for example, found virtually no relationship between agreed upon wage and the length ofnegotiations analysing Canadian employment contract data for the period 1964-1985 despite the fact that allrational models of bargaining (when the relevant private information is on the firm side) predict a negativerelationship between agreed upon wage and the length of negotiations. McConnell (1989), using US contractdata for the period 1970-1981, finds a statistically significant negative relationship between average wagesettlements and average strike duration, but this relationship is sensitive to the model specification.

4

and in time preferences of the bargaining parties (partly governed by the institutional back-

ground of negotiations) are complicated and intertwined in dynamic bargaining models. For

this reason, in the second half of the paper we further analyze our data on ransom negotia-

tions by structurally estimating the model in Cramton (1991). This approach enables us to

disentangle the effects of differences between Algiers and Tetuan along multiple dimensions.

We focus on the model in Cramton (1991) for two reasons. First, besides standard

exponential discounting, it allows for transaction costs, that is fixed costs that bargaining

parties had to pay for each additional time unit of negotiations. Second, the presence of

transaction costs, together with the delay arising from asymmetric information, implies that

in equilibrium there can be failed negotiations, as a buyer with low evaluation prefers quitting

negotiations to engaging in a long and costly bargaining process. This model is unique among

models of bargaining between a buyer and a seller since it facilitates both costly delays in

reaching agreement and failed negotiations, both of which are widespread in our data.5

Structural results indicate that transaction costs were modest and roughly equal in the

two strongholds. In contrast, discount rates were substantial in both settings, and in most

professions much higher in Algiers. This suggests that the dynamics of negotiations were

mainly driven by the relatively rapidly deteriorating physical conditions of hostages in captiv-

ity, as well as by the possibility of exogenously terminated negotiations. Qualitative evidence

suggests that both of these factors were more important in Algiers, in accordance with our

structural estimates.

Our structural approach also allows us to conduct welfare analysis and counterfactual

investigations.

Although in both settings the estimated proportion of failed negotiations is high, because

negotiations failed predominantly for captives with low evaluations, the resulting welfare

losses are relatively small: they tend to be around 10% of total potential surplus. Delay

5Dynamic bargaining models with no transaction costs imply that negotiations are never terminated. Atthe same time, a model with no discounting, only transaction costs, predicts immediate agreement, as shownin Perry (1986).

5

costs tend to be 7-8% of total potential surplus, with transaction costs only around 2%

of potential surplus. This means that according to our estimates, despite the presence of

substantial asymmetric information, the bargaining mechanism in this historical setting was

remarkably efficient, with realized surplus being roughly 80% of potential surplus. The

distribution of the realized surplus is estimated to be roughly equal in both settings, with

some variation across professions.

In the counterfactual investigations we investigate alternative market mechanisms that

could have been used by the parties: posted prices (take it or leave it offers from sellers),

and bundled negotiations (for released captives for whom we can confidently rule out that

they were part of bundled negotiations). We find that posted prices would have significantly

increased the surplus appropriated by the captive holders, but would have decreased real-

ized social surplus through an increased number of failed negotiations. Further bundling

would have increased social efficiency, without hurting either of the bargaining parties. This

suggests the possibility of coordination problems among sellers of different captives.

The remainder of the paper proceeds as follows. Section 2 provides a brief historical

background of the Barbary Corsairs, the process leading to captivity and the bargaining

process. Section 3 provides a theoretical overview of models of dynamic bargaining with

one-sided private information, and conducts reduced form tests of some common qualitative

predictions of these models. In Section 4 we provide a structural analysis of the model

developed by Cramton (1991).

2 Historical Background

The history of the Barbary Corsairs begins with the “Red Beard” (Barbarossa) brothers.6

These Muslim Greek-born brothers developed a reputation for military prowess, and even-

tually founded a corsairing state in Algiers (modern-day Algeria) in the early 16th century.

6For a detailed treatment of the history of the Barbary Corsairs see among a large literature Julien (1970),Abun-Nasr (1977), Bono (1998), Davis (2003), Panzac (2005) and Weiss (2011).

6

Soon after its foundation, this corsair state became part of the Ottoman Empire.

Algiers and the other Ottoman-controlled North African provinces (which controlled the

territories that roughly correspond to present day Tunisia and Libya) developed corsair fleets

that targeted Christian European shipping and coastal populations. In addition to these

Ottoman centers, Muslim refugees from Spain developed corsairing fleets in Salé, Morocco

(on the Atlantic coast) and Tetuan, Morocco (on the Mediterranean).7

At their height, the Barbary Corsairs significantly disrupted commercial routes in the

Mediterranean (and to a lesser extent the Atlantic) striking as far afield as Iceland. In

addition to their exploits at sea, the Corsairs made their mark on coastal settlement patterns

in regions in close proximity to Corsair strongholds (like Spain’s Mediterranean coast). Many

areas in these regions became depopulated as the local populations fled continuous corsairing

raids.8 One scholar estimates that between 1530 and 1780 the Corsairs enslaved over one

million European Christians (Davis 2001, 2003).

By the end of the 17th century the Corsairs began a slow decline. In Algiers, con-

temporaries attributed this decline to more determined reprisals by European powers and a

decreasing demand for slave labor (Davis 2001, p. 106). In Morocco, Mawlay Ismail (reigned

1672-1727) moved to curtail corsair activities in order to encourage legitimate commercial

activity and to centralize political power (Friedman 1983, p. 29). By the start of European

colonization in the 19th century, corsairing activities had largely ceased.

The remainder of this paper focuses on the corsairs that operated out of Algiers, Algeria

and Tetuan, Morocco since the captives in the data set were ransomed from these centers.

2.1 Bargaining for Captives in North Africa

Corsair centers across North Africa derived important revenues from the capture and sale of

captives. These captives were most often taken in land raids or at sea, although some captives

7See Coindreau (1948, p. 27) and Maziane (2007, pp. 200-201).8For the impact of piracy on Venetian commerce, see Tenenti (1967). For the impact of piracy on Spanish

coastal settlement patterns, see Friedman (1983, pp. 48-49).

7

were prisoners of war from the numerous military confrontations between the Corsairs and

European powers. After the Corsairs finished a raiding expedition, they brought home the

captured merchandise and captives. Captives were sold in local slave market after the leader

of the corsair center had taken his cut.9

A captive’s price in the slave market seems to have been primarily determined by two

factors. The first of these factors was related to the present value of a captive’s marginal

product. Older captives were valued less and captives with special skills (such as carpentry)

commanded higher prices. The second factor was a slave’s potential for ransom. Captives

believed to be desired for ransom by European powers were kept in special quarters. Slave

owners (throughout the text we refer to slave owners and corsairs interchangeably for ex-

positional ease) were eager to have their slaves ransomed and encouraged captives to write

letters home. These letters were carried by merchants and the ransoming missions back to

Europe where they were given to family members.

The Barbary Corsairs particularly valued captives from the Spanish Empire. Spanish

ransoming missions to Algiers and Tetuan occurred frequently and Spaniards were known

to command higher than average ransom prices (Friedman 1983, p. 57). Although the

corsairs were generally able to identify a captive’s nationality and rank in a general sense

(and used this information to divide captives between those more and less likely to be

ransomed), the exact amount that Spaniards were willing to pay for each captive was not

known. One historian has stressed that it was usually difficult for high-ranking captives to

pass as “normal” captives since the corsairs were “very crafty at learning if their captives

were nobles or ecclesiastics” (Friedman 1983, p. 151). Despite this fact, there are examples

of high-ranking captives successfully hiding their identity (Friedman 1983, p. 151). Those

who were of a lower rank often were indistinguishable from the corsairs view.10

Catholic religious orders ran virtually all of these ransoming missions in the period covered

9This section draws on Martínez (2004), Bono (1998) and Friedman (1983).10Friedman’s (1983, p. 149) statement that “the North Africans usually knew both the identities of their

captives” refers to elite captives. There is substantial evidence that the corsairs did not know the exactidentity of lower ranking captives (see, for example, Martínez 2004, p. 41; Friedman 1983, pp. 57, 143).

8

by the data. These religious orders negotiated (and paid if the negotiation was successful)

the captured individual’s ransom on behalf of the family. The funds for ransoming came

from the money that was earmarked for individual captives, money that had been donated

by the crown or wealthy individuals for the ransom of a specific type of captive (such as

women, children or soldiers) and a general fund for the ransoming of Spanish captives in

North Africa that came from alms throughout the year and bequests. These general funds

were often restricted, however, to be used to ransom captives from the areas in which these

alms were collected.

Consequently, Spanish ransoming missions to the Barbary States concentrated on freeing

two groups of individuals. The first group included “favored” captives such as women,

children, clerics, individuals who were captured in the “service of the crown” (such as soldiers

and royal emissaries), individuals from specific geographic areas and others in danger of

converting to Islam. The exact identity of the captives did not matter inasmuch as s/he

belonged to one of these groups. The second group contained the group of captives for

whom family and friends had donated money. Here, the exact identity of the captives

was extremely important since the ransoming missions were required to use these funds to

ransom the individual for whom they had been earmarked. The amount of earmarked money

sent for a captive often did not cover the ransom cost (the differences were made up from

the non-earmarked general funds) and these individuals do not seem to have been readily

distinguishable from other ransomed captives. The ransoming team gave special priority to

earmarked captives and attempted to rescue these captives as soon as possible (Friedman

1983, p. 146).

From the reign of Phillip II (reigned 1556-1598) onwards, royal authorities appointed

a notary to accompany these rescue missions or “redemptions”. This notary was required

to record all financial transactions and often provided anecdotes relevant to the bargaining

procedures. We used these records to construct our data set and historians have generally

stressed their quality and meticulous detail (Friedman 1983, p. 107). Summary statistics

9

are presented in table 1, and a detailed discussion of both the data construction and the

summary statistics is provided in the appendix.

The identity of the captives for which the ransom missions had earmarked donations

(known in Spanish as adjutorios) and the size of these donations constituted a source of

uncertainty for slave owners. Miguel de Cervantes, the renowned Spanish author, was captive

in Algiers from 1575 until his ransom in 1580. Cervantes —from a family of relatively modest

means— was captured and ransomed long before his rise to fame. His adjutorio provides a

good example of how the system of earmarked funds worked. In the notary’s records from

the ransoming expedition of 1580 to Algiers we read that:

In the town of Madrid on the 31st day of July of the said year [1579] [...] the

redemptors received 300 ducados [a money of account in early modern Spain...]

250 of these came from the hand of Leonor de Cortinas, the widow of Rodrigo

de Cervantes. The remaining 50 came from Andrea de Cervantes [... to aid] in

the ransom of Miguel de Cervantes from the said town [Alcala de Henares] [...]

who is captive in Algiers in power of Ali Mami, captain of the ships of the navy

of the king of Algiers. [The said Miguel] is 33 years old and has lost use of his

left arm. The redemptors then gave them 2 receipts [i.e. proofs of payment].11

In this trip, Miguel de Cervantes was rescued, although if he had not been rescued the

redemptors (i.e. the negotiating team) would have had to return the 300 ducados to his

family. It is important to note that individuals were only allowed to send funds with the

redemption if they had hard evidence (such as a letter) that the individual was being held

captive in the redemption’s destination.12

The surviving ransom books provide detailed bargaining instructions given to the ransom-

ing team. These instructions stress the importance of keeping the identity of these captives

secret and note that11AHN, códices, legajo 120, f. 3212See Friedman (1983, p. 112) and BNM, MSS 3819, f. 3.

10

the redemptors should feign indifference to the captives they most want to rescue,

and should pretend to only care about silver and not the captives. Since the Turks

are greedy and love silver more than the good service of their slaves, they don’t

want to miss the chance to make money [...so that] every day the redemptors

delay, they will save 20%.13

Qualitative evidence suggests that the redemption team largely followed these instruc-

tions, carefully guarding the identities of earmarked captives.14 This evidence is important

for the empirical analysis below, because it demonstrates that despite the corsairs’ attempts

to ascertain the value of captives to the ransoming teams, the corsairs could not distinguish

between many captives. The redemptors could obtain lower prices for these captives by

hiding their true valuations.

The earmarked and general funds were transported together. In Tetuan, the ransom

funds were kept in Ceuta (a Spanish enclave in North Africa) and were not observed by

the corsairs. In Algiers, the corsairs unloaded the ransom funds and knew the amount of

funds available (although some members of the rescue team successfully hid funds on their

persons) although they did not know what percentage of the treasury was earmarked nor

for whom they were destined (Friedman 1983, pp. 120-121). If the rescue team ransomed

a non-earmarked captives with earmarked funds, they would return the earmarked funds to

the donors using funds raised for subsequent ransoming missions.

We have not been able to find any direct references to the incentive schemes to motivate

the redemptors. Despite this fact, we do know that experienced redemptors were highly

valued (BNM, MSS 3870, f. 10; Martínez 2004, p. 94) and drawn from the highest level

of the redemption orders.15 This suggests that whatever the exact incentive scheme used,

skillful bargainers that could both obtain lower ransom prices and were willing to endure

13BNM, MSS 2974, ff. 5-6.14For examples see Garí y Simuell (1873, p. 288) or BNM, MSS 647, f.6.15At least for the Mercederian order during the late medieval era. One historian speculates this might

have been because “such senior brothers possess[ed] the prudence and experience necessary for the successof the mission” (Brodman 1986, p. 109).

11

hardship were highly valued.

In sum, rescue missions to the Barbary strongholds focused on rescuing two types of

captives. First, they used general funds to rescue captives with certain characteristics (such

as women, children or soldiers). Second, the redemptors sought to rescue “earmarked”

captives (those for whom money had been given).

2.2 Differences in the Bargaining Conditions between Algiers and

Tetuan

Historical evidence suggests differences in the bargaining conditions between Algiers and

Tetuan. We divide the historical evidence regarding these differences into those that af-

fected the discount rate of the redemptors and those that affected their transaction costs.

Transaction costs are independent of the value of the captive, whereas a higher discount rate

has a differential effect on the cost of waiting across captives of different values.

2.2.1 Differences that affected the discount rate

Algiers enjoyed greater military power —and poorer relations with Spain— than Tetuan. These

differences led to a larger captive population in Algiers and to a worse treatment of the slave

population in this stronghold (Martínez 2004, p. 60).16 Friedman (1983, p. 71) suggests

that differences in how captives were treated could lead to both higher discount rates for

the redemption team as well as to shorter negotiations. She remarks that in both corsair

strongholds even the most valuable captives could be treated quite poorly since “their captors

thought it would be easier to obtain high prices for important captives if they were kept in

miserable surroundings.” The captors presumably did this because the redemption team

incurred greater costs by leaving captives who were subject to more severe treatment in

16He notes that “it was not the same to be captive in Algiers or Morocco. From the start of the 16th

century until well into the 19th century, Algiers maintained hostile relations with the Spanish crown whichresulted in a larger number of Spanish captives. It was logical, then, that their treatment was more harshthan that faced by captives in Morocco.”

12

captivity.

In addition to differences in the treatment of captives between the two strongholds,

greater political instability in Algiers seems to have led to a higher discount factor for the

redemption team in this stronghold. Data on ruler durations in Algiers shows that the

average ruler remained in power for roughly three years (Stewart 2006, pp. 14-15). Although

we have not been able to locate ruler duration data for Tetuan qualitative evidence suggests

that this stronghold was subject to less ruler turnover, and its ruling oligarchy appears to

have been more stable. Martínez (2004, p. 105), for example, noted that Tetuan’s “relatively

more stable political situation made [it] a more desirable destination to ransom captives.”17

This increased political instability could abruptly lead to the end of negotiations (for one

example see Martínez 2004, p. 99).

2.2.2 Differences that affected transaction costs

In Tetuan, transaction costs seem to have been lower than in Algiers. When the redemption

team went to Tetuan, they hired a boat in Gibraltar to cross the straits to Ceuta. This boat

did not have to remain in port for the length of the negotiations and thus the ransoming

team did not have to pay for its rental during the negotiations. In addition, the proximity

of a Spanish enclave in Ceuta (and the possibility of rapid military intervention) greatly

reduced the risk of physical harm to the redemptors.18

In Algiers, the redemption team had to hire a ship that remained in port until the

redemption was over. In addition, there is qualitative evidence that the ransoming team

paid higher prices for items such as accommodation than they did in Tetuan. Finally, the

redemption team in Algiers faced a higher probability of capture or bodily harm than it did

in Tetuan. Thus an additional day of negotiations “increased the risk of capture of the entire

17See Friedman (1983, p. 131) for additional evidence of political instability in Algiers.18There are no documented examples (to the best of our knowledge) of the redemption team being held

captive in Tetuan. In Algiers, however, the redemption team was held captive on at least one ocassion(Friedman 1983, pp. 136-138) and was threatened with death by fire on another (Garí y Simuell 1873, p.326). See also the discussion in Friedman (1983, p. 142).

13

bargaining team” (Martínez 2004, p. 99).

3 Reduced form analysis of predictions of dynamic bar-

gaining models

In this section we conduct a reduced form analysis of predictions that are shared by a

large class of dynamic bargaining models. In Subsection 3.1 we provide a brief overview

of the theoretical models we consider, and highlight their common testable predictions. In

Subsection 3.2 we report the empirical results.

We note that the theoretical models that we take to the data are crude approximations of

the bargaining situation we examine, abstracting away from potentially important features

of negotiations. Below we mention a few of these aspects, calling attention to the importance

of incorporating them into models of dynamic bargaining in future work.

First, we treat every negotiation in isolation. In reality, the thousands of negotiations

in our data set were part of a meta-game. If negotiating for the release of a given captive

failed at a bargaining trip, there was a possibility of resuming negotiations at the next trip.

However, we only observe information on successful negotiations, therefore we have to base

our analysis on the negotiation within a given rescue mission (the one during which the

captive got released). We also abstract away from issues such as competition between the

Corsair strongholds to attract ransoming trips, as well as reputation-building, reputation-

erosion, or inventory-building by the negotiating parties.19

Second, the models we consider do not incorporate either budget constraints (upper

bound on the amount of money spent) or spending constraints (lower bound on the amount

of money spent). In reality, the rescuers faced a soft form of both constraints, at least

in Algiers, where they had to unload their money at the beginning of a trip. Spending

19This can be partly justified by the fact that the identities of the Spanish negotiators and the set of sellersoften changed from trip to trip.

14

more money than they had brought was costly, as it involved borrowing extra money at

high interest rate. But spending less than the total amount involved costs as well, as any

remaining money would have to be “wrestled back” from the political leaders of Algiers.

Third, in this section we do not take up the issue of negotiating for each captive separately,

or for a bundle of captives together. Although we do not directly observe whether the release

of a given captive was part of a bundled negotiation, there are many instances in our data

when similar captives were released at the same time and at the same price, suggesting that

bundling was commonly used. We do not know any theoretical work investigating this issue

in a dynamic bargaining context, although there is a clearly related literature on bundling

and pricing decisions of a monopolist seller in a static context.20 The main takeaway from this

literature is that some form of bundling is likely to be optimal for the seller. Our conjecture

is that similar results are likely to extend to dynamic bargaining situations.

3.1 Theoretical background and predictions

We consider negotiations for ransom between the Spanish rescue team and the captive holders

as a dynamic bargaining game with asymmetric information. In particular, the relevant

private information is the exact value of a given captive for the rescuers. Our motivation

here is that the value of a particular captive for the Spaniards always had a component not

known by the slave owners: the amount of earmarked money that was collected for a given

captive. Over time, the captors could learn the distribution of this private value conditional

on observables of a captive, but not the exact value for individual captives. In contrast, other

important parameters for the bargaining process, such as the parties’ time preferences and

transaction costs, or reservation values of different types of captives for the holders, could

either be observed by the parties through public information (such as interest rates charged

by money lenders, or the price that a certain type of captive could be sold at slave markets)

20See for example Adams and Yellen (1976), McAfee et al. (1989), Armstrong and Rochet (1999) andFang and Norman (2006). There is also a literature on bundling decisions in a mechanism design context,reaching similar conclusions. See Palfrey (1983), Chakraborty (1999), Armstrong and Rochet (1999), Averyand Hendershott (2000), Armstrong (2000) and Jehiel et al. (2007).

15

or learned over time.21

Besides considerations based on qualitative evidence, our data also rejects some of the

main predictions of an alternative class of models in which the relevant private information

is the bargaining parties’ patience. Bargaining in such contexts takes the form of a war-of-

attrition game in which one of the parties end up acquiring the whole surplus, which we do

not see any indication of in our data. Moreover, these models predict that settlement rates

over time should be monotonically declining. In the Supplementary Appendix we show that

this is not the case in our data.

3.1.1 Dynamic models of bargaining with one-sided asymmetric information

Dynamic bargaining models that assume one-sided private information regarding the value

of the object for the buyer are incomplete information extensions of the models proposed by

Stahl (1972) and Rubinstein (1982). Below we briefly summarize the most standard models

used in the literature. All the models reviewed here assume that there is one buyer and

one seller, bargaining for one indivisible object, and that all parameters besides the buyer’s

evaluation are commonly known by participants.

One set of models assume that only the uninformed party (the seller) can make offers,

and there is a fixed amount of time that has to elapse between offers. They are referred

to as screening models, as the seller’s offers at different points of time are accepted by only

certain buyer types, hence the seller screens different types of buyers throughout the bar-

gaining process. Sobel and Takahashi (1983) introduced a finite version of the model, while

Fudenberg at al. (1985) and Gul et al. (1986) extended the analysis to infinite-horizon. The

equilibrium dynamics in these models are simple: the seller proposes a decreasing sequence

of prices. In each round, there is a cutoff buyer type such that all remaining buyer types

above this level accept the proposal, while buyers with evaluation below this level reject it.

21Captive-holders might have privately known individual-specific evaluation for a certain type of captive,exceeding market price. However, for common type captives, the thickness of the market implies that theycould purchase additional captives of the same kind until the marginal benefit became equal to the marketprice.

16

The main intuition is that buyer types with higher evaluation are more impatient and willing

to pay higher prices to receive the object earlier.22

A major alternative to the above models is a class of models in which a player whose turn

it is to make an offer can wait before doing so, endogenizing the timing of the offer. They

are usually labeled as signalling models, because in such a framework a low valuation buyer

can credibly signal his type by waiting longer before making a (counter-)offer. The version

of the model investigated in Admati and Perry (1987) assumes alternating-offer bargaining,

with the seller making the first offer. After a rejected offer, there is a minimal required time

that has to lapse before the other player can make an offer, but the player can decide to wait

any additional amount of time. An important assumption in these models is that bargainers

can commit to not revising an offer until a counteroffer is made.23

Below we summarize two common implications of signaling and screening models de-

scribed above.

Relationship between length of negotiations and price

The main prediction, shared by all rational models of dynamic bargaining with one-sided

private information on the buyer side is that there is a negative relationship between the

buyer’s value and the length of negotiations, otherwise high value buyers would find it worth

to imitate low value ones. A higher value of the buyer implies larger costs of time before

reaching an agreement, thus willing to wait longer becomes a credible proof that a buyer’s

value is low. This prediction in our setting implies that given a fixed setting of negotiations

and a homogenous set of captives (from the captors’ point of view) both the amount of

22Versions of the above models in which the buyer and the seller make offers alternatingly are screeningmodels with an element of signaling. The latter is because proposals by the buyer can reveal private infor-mation about his valuation of the object. These models typically have a severe multiplicity of equilibria, asthere is a lot of freedom in specifying the updated beliefs of the seller regarding the buyer’s valuation after anout-of-equilibrium proposal by the buyer. Rubinstein (1985), Grossman and Perry (1986), and Bikhchandani(1992) propose refinements of sequential equilibrium in related models that lead to a similar analysis as inpure screening models.23However, if one allows for nonstationary strategies, the signaling equilibrium outcome can be approx-

imated as a perfect Bayesian Nash equilibrium in the alternating-offer bargaining game with a fixed timebetween offers when time between offers is small (see Ausubel and Deneckere (1994)).

17

earmarked money and the release price of a captive should be negatively associated with the

length of the negotiations for the captive.

Effect of amount of uncertainty

Another common feature of different bargaining models, although one that proved to be

difficult to formalize analytically, is that more uncertainty leads to longer negotiations.24

This is easy to see in the limit case of no uncertainty: the unique perfect equilibrium in-

volves immediate agreement (see Rubinstein (1982)). Similar conclusions apply when the

uncertainty about the buyer’s value is small (see Rubinstein (1985)). For larger amounts

of uncertainty, because of the relative complexity of bargaining models with asymmetric

information, it is only possible to show that more uncertainty tends to lead to longer nego-

tiations in restricted classes of games or through numerical computations, as in Grossman

and Perry (1986) and Kennan and Wilson (1989). With the above caveats, the prediction in

our setting is that given two otherwise comparable homogenous group of captives, and the

same mean earmarked money, the group with higher variability of earmarked money should

be associated with lower prices and longer negotiation times.

3.2 Testing common predictions of models with one-sided asym-

metric information

This section uses data on privately owned individuals to investigate the empirical relevance

of the theoretical predictions shared by models outlined in the previous subsection.25

24Tracy (1986, 1987) conducts an empirical investigation along these lines, suggesting that the extent ofthe union’s uncertainty about the firm’s profits might be associated with variability of the firm’s marketvalue. He finds a significant positive empirical association between this measure of uncertainty and bothstrike incidence and duration, consistent with the theoretical prediction.25We limit the sample to privately-owned individuals because these individuals were not able to coerce the

redemption team to the same extent as the government was able to (Friedman 1983, pp. 130-131). Resultsfor government-owned captives, however, are qualitatively similar to those reported below although generallynot statistically significant. Pooling all captives generally increases significance.

18

3.2.1 Delay and Prices

As noted above, bargaining theory predicts that all else equal the release price of a captive is

negatively related to the length of negotiations. Below we focus on the relationship between

release price and the length of negotiations within a rescue trip. Recall that the possibility of

an exogenous breakdown of negotiations (leading to the end of the rescue trip) could imply

a low discount factor even over short time horizons, justifying a significant drop of prices

over the time horizon of a rescue trip.

We focus on the effect of within-trip delay on price, as opposed to the effect of a captive

not being rescued during previous rescue missions (between-trip delay) because while within-

trip delay is directly recorded in our data set, we only have a noisy measure of between-trip

delay. This measurement error stems from the fact that we only observe a captive’s time

spent in captivity before ransom. We do not observe the true measure of interest, namely

how many times a captive was negotiated for before his or her ransom. In addition to this

source of measurement error, the trade in slave across the Islamic world meant that many

captives spent much of their captivity in regions where the redemption missions did not go

before they were sold to an owner in a location where they could be ransomed. For these

captives, a long wait before ransom had nothing to do with strategic delay. Thus, time in

captivity is at best a noisy estimate for between-trip delay and its use is likely to result in

biased (attenuated) estimates of the causal effect of between-trip delay on prices. Consistent

with this discussion, we find evidence that our estimates of between trip delay suffer from

substantial attenuation bias.26

To estimate the effect of within-trip delay on equilibrium prices we use the specification:

100 ∗ ln(priceij) = αj + βdayselapsedij + γ X+ εij (1)

26In practice, we find that the coefficient on time in captivity -while statistically significant- is smaller inabsolute value than that on days elapsed. In a previous version of the paper we developed an instrumentalvariable strategy to address this problem and found evidence suggesting that the OLS estimates suffer fromattenuation bias.

19

where priceij is the ransom price of captive i in ransoming trip j, dayselapsedij measures

the days elapsed after the start of negotiations until captive i was ransomed andX is a vector

of covariates. We estimate regression (1) separately for the Algiers and Tetuan samples.27

The results are presented in panel A of table 2. The first three columns limit the sample

to Algiers, whereas the last three columns estimate equation (1) using the sample of captives

rescued from Tetuan. The results in Algiers are consistent with the theoretical predictions.

In particular, an increase of one day in the time to ransom is associated with a roughly

four percent decrease in a captive’s ransom price in columns (1) and (2). This result is

statistically significant and is robust to the introduction of controls in column (2). Controls

include a captive’s time in captivity, age at captivity, a gender dummy, a dummy equal to

one if the captive was younger than 16 when ransomed and profession dummies.

In column (3) we restrict the Algerian sample to captives that were rescued in the first

(observed) ransoming trip to arrive in Algiers after they had been taken captive. This is

the cleanest estimation of within trip delay, comparing only individuals for whom previous

ransom trips likely did not generate any extra information on their value for the captors

(at least to the extent that we can measure this quantity). Here the point estimate of the

coefficient of the days elapsed variable decreases in absolute value, but remains statistically

significant.

In columns (4)-(6) of panel A of table 2 we present the results for Tetuan. Here, the

estimated β is close to zero and insignificant for every specification.

The next set of regressions examines the effect of earmarked money for an individual cap-

tive, a component of the value of the captive for the rescuing team that we directly observe,

on the release price of the captive, and on the time of negotiations. Note that qualitative

evidence suggests that conditional on covariates earmarked money can be considered exoge-

nous. If this assumption is true, then the results in panels B and C can be interpreted as

causal.27We omit all captives ransomed in two extremely long negotation trips that took over 270 days because

these outliers distort the results.

20

In panel B of table 2 we estimate regression (1) replacing the variable dayselapsedij with

the indicator variable earmarkedij which is equal to one if captive i in ransoming trip j had

money sent for his rescue from Spain. Our estimates show that earmarked has a large and

significant effect on a captive’s release price, increasing it by roughly 35% in Algiers, and by

a little bit less in Tetuan.

In Panel C of table 2 we again estimate regression (1) replacing the dependent variable

ln(priceij) with dayselapsedij and dayselapsedij with earmarkedij. In other words, we are

interested in examining whether earmarked captives were rescued earlier than other captives.

Results in columns (1) and (2) show that earmarked captives were rescued roughly 0.40 days

earlier in the negotiations, although the point estimate decreases in absolute value and

becomes statistically insignificant when we limit the sample to captives rescued in the first

ransoming trip to arrive in Algiers after they had been taken captive. In Tetuan the point

estimates are negative but insignificant, for all specifications.

3.2.2 Uncertainty and Delay

Theoretical considerations suggest that all else equal greater uncertainty should lead to

longer negotiations. In order to measure uncertainty, we use the coefficient of variation (the

standard deviation divided by the mean) of earmarked money by profession and by corsair

center (that is we calculate the coefficient of variation of earmarked money by profession in

both Tetuan and Algiers).28 Although this metric is imperfect at best, results in panel D of

table 2 provide some support for the theoretical prediction.

We estimate a regression of the form

dayselapsedipj = αj + β1Ep + β2σpEp+ γ X+ εij (2)

where dayselapsedipj is the days elapsed after the start of negotiations until captive i was

28Here we use disaggregated professions as given in the original sources instead of the aggregated categoriesused throughout the rest of the paper to increase statistical power.

21

ransomed which varies by captive i in profession p in ransoming trip j. Ep denotes the mean

amount of money sent for captives in profession p, σpEprepresents the coefficient of variation

of this quantity and the vector X contains controls (which includes a dummy indicating how

a captive was captured, the captive’s age when captured and dummy variables equal to one

if the captive was a child or female). The theory predicts that the coefficient β2 will be

greater than zero.

Results in columns (1)-(3) estimate equation (2) in the Algerian sample. The point

estimate show that a unit increase in the coefficient of variation of a professions was associated

with captives from that profession being ransomed between 0.36 and 0.57 days later in the

negotiations. Results for Tetuan, however, are of the “wrong” sign and are not statistically

significant.

3.2.3 Summary of the reduced form analysis

We find that in Algiers, where qualitative evidence suggests higher impatience and transac-

tion costs, the theoretical predictions regarding relationships among release price, length of

negotiations, and amount of uncertainty are generally supported by the data. At the same

time in Tetuan, where qualitative evidence points to lower discount rates and transaction

costs, we do not find empirical support for the predicted relationships. This may be because

the effects we are trying to estimate are small, and we have a relatively small number of

observations (our Tetuan sample is roughly one-half of the size of the Algerian sample), or

because for low amounts of impatience the qualitative predictions of dynamic bargaining

theory are not valid for real world negotiations.

4 Structural analysis

Although the large number of captives has allowed us to investigate the empirical relevance

of some general predictions of bargaining models in a reduced-form manner, such techniques

22

do not allow for a detailed comparison between negotiations at different locations, given that

there are only two of them, and they can differ in many important dimensions (distributions

of buyer evaluations, discount factors, and transaction costs). In this section we investigate

differences in bargaining outcomes between Algiers and Tetuan through structural analysis,

using the model in Cramton (1991) as our theoretical framework.

Our paper is one of the first conducting structural estimation of a dynamic bargaining

model in a buyer-seller setting with asymmetric information. In the context of negotiations

for out of court settlements in medical malpractice cases, Waldfogel (1995) and Sieg (2000)

estimate bargaining models with one round of negotiations, while Watanabe (2004) considers

a finite horizon dynamic bargaining model.29 Merlo et al. (2008) consider the problem of a

homeowner wanting to sell their house, and estimates a model which for simplicity assumes

that potential buyers are bidding automatons, instead of strategic players. Most recently,

Keniston (2011) estimates a model of bargaining with two-sided asymmetric information,

using data generated by a field experiment in the context of bargaining for the fare between

riksha drivers and passengers in India.30 There are important differences between both the

data analyzed and the methodology used in Keniston’s paper and ours. First, while Keniston

(2011) investigates a context in which the stakes for bargaining are low, in our context the

agreed upon price for the release of a hostage was typically multiple of the annual income of

the person. Second, Keniston (2011) assumes uncertainty on both sides, and both regarding

valuations and time costs. Third, Keniston (2011) does not impose a unique equilibrium

selection and allows for the possibility of any equilibrium to be played, but for tractability

of the estimation procedure it only requires beliefs on the opponents’ actions to be correct

along the equilibrium path (along the lines of self-confirming equilibrium in Fudenberg and

Levine (1993)). Instead, we focus on a specific sequential equilibrium in the Cramton model,

29There is also a small earlier literature computing point estimates of parameters of dynamic bargainingmodels, based on US data on wage negotiations between unions and employers (see Fudenberg et al. (1985)and Kennan and Wilson (1989)).30For other field experiments in bargaining contexts, investigating unrelated issues to the current paper,

see Ayres and Sigelman (1995) and Castillo et al. (2011).

23

motivated by general features of our data (no pooling of buyer types after time 0).

Subsection 4.1 summarizes the theoretical model. Subsection 4.2 provides the econo-

metric model specification. Subsection 4.3 describes the estimation procedure. Subsection

4.4 presents the main findings. Lastly, in Subsection 4.5 we conduct welfare analysis and

counterfactual investigations.

4.1 Theoretical model

The model we selected for the structural analysis is the one featured in Cramton (1991),

because it introduces a transaction cost for bargaining (on top of discounting), that is a

fixed cost per unit of time that a player has to incur until the negotiations are over. This

further facilitates the possibility of terminating negotiations in equilibrium, if a party foresees

that they would have to incur too high transaction costs before reaching an agreement.31

Qualitative evidence suggests that both of these features are potentially important in our

context.

Formally, we consider the following specification of the model. We treat each captive as

a unique commodity, initially owned by a monopolist seller. If the seller and the buyer agree

on price p after negotiations with length t, the seller and buyer get the following utilities:

Us = (p− S) · e−rt

Ub = (B − p) · e−rt − cr(1− e−rt)

where S represents the seller’s evaluation (outside option) for the captive, B is the buyer’s

evaluation, r is the discount rate for the parties, and the c is the transaction costs per unit

of time. All of the above parameters are commonly known for the bargainers, besides B.

31As Fudenberg et al. (1985) points out, introducing transaction costs and the possibility of exit to a purescreening model such as in Fudenberg and Tirole (1983) results in only trivial equilibria existing, in whichevery buyer type quits the negotiations immediately. As Perry (1986) shows, negotiations end immediatelyeven if exit is not a possibility, and the party with the lower transaction cost gets all the surplus. Thereforescreening models with transaction costs cannot explain delay in negotiations.

24

Only F (B), the cumulative distribution function of the buyer’s valuation, is known by the

seller.

The above specification entails various simplifying assumptions. One is that the trans-

action cost of the seller is zero. Here we are motivated by the fact that the negotiations

were in corsair territory, where the sellers were not exposed to any kind of danger during the

negotiations. Another is that the we assume the same discount factor for the seller and the

buyer. We apply this restriction mainly for the tractability of the model and the resulting

estimations.

Negotiations involve alternating-move bargaining, with the seller making the first offer.

A party whose turn it is to make a move can delay making the offer, for any amount of time.

Moreover, any party can decide to terminate negotiations and quit, at any point during the

game.

The game has typically many equilibria. We focus on the equilibrium featured in Cramton

(1991). This is the only equilibrium in which buyer types who stay in the game after time 0

fully separate. This is consistent with our observation that the empirical density function of

the times of agreement is fairly smooth, with no obvious candidate for a point of time where

a significant fraction of buyer types are pooled together (see Section 2 of the supplementary

appendix on observed settlement rates).

The equilibrium exhibits the following intuitive structure: The seller makes an offer

immediately, without waiting. Buyer types with high enough evaluations immediately accept

the offer. Buyer types with low enough evaluation turn down the offer and quit negotiations,

to save transaction costs. Finally, buyer types in an intermediate range turn down the initial

offer of the seller, and then delay making the counter-offer, for an amount of time that is

specific to the given type, thereby fully revealing the type of the buyer. Correspondingly, the

counter-offer that the buyer makes after the delay is the unique subgame-perfect equilibrium

price that would prevail in a game where the type of the buyer was commonly known.

Solving for this equilibrium backwards, for a given valuation B in the intermediate region,

25

equilibrium price in the continuation game after the buyer’s type is revealed, hence the

counter-offer of the buyer is:

p(B) =1

2(B + S) +

λ

2

where it is convenient to use λ = cr.

Assume now that the seller’s initial offer is p(b). As shown in Cramton (1991), the optimal

strategy for the buyer given this first offer is:

1. if B b, the buyer accepts without delay;

2. if b0(b) < B < b, the buyer waitsΔ(B, b) = −1rlog(λ+B−S

λ+b−S ) and then make counter-offer

p(B) which is immediately accepted, where b0(b) = λ(−1 + 2(1 + (b− S)/λ));

3. for values B b0 negotiation is terminated.

Lastly, the seller makes his first offer maximizing his expected payoff in the continuation

game:

b ∈ argmaxB(1− F (B))xB + u(B) (3)

s.t. u(b) =b

b0(b)

xB · e−rΔ(B,b)dF (B).

4.2 Econometric specification

The primary outcomes we observe are the duration of negotiations (Δ) and agreed upon price

(p). We do not observe the total value of a captive for the ransoming team (B). The first

observation we make is that we cannot fit our data perfectly by adjusting valuation B for

each observation. Any specification of private values would predict a negative relationship

between price and duration, which does not hold perfectly for the data. Hence, we assume

that we observe the duration and price data with errors. Denote Ω the set of parameters

which characterize equilibrium outcome for a given B. In our main specification we assume

26

that data is generated by the following process involving multiplicative errors:

p = p(B,Ω)eεp

Δ = Δ(B,Ω)eεd

where (εp, εd) are distributed normally with parameters N(0,Σ), independently from the

buyer’s valuation.

While assuming multiplicative errors is standard, and gives an interpretation of the er-

ror term that is independent of the unit of measurement of prices and duration, it has a

disadvantage in our setting: it introduces a sharp distinction between negotiations of zero

vs strictly positive equilibrium duration. In order to smooth out predictions, we assume a

minimal necessary time for negotiations, Δ0, equal to a small exogenous constant (0.5 days).

We change predicted equilibrium durations less than Δ0 (including negotiations predicted

to end with immediate agreement) to be equal to Δ0. In one of our alternative specifica-

tions, presented in the Supplementary Appendix, we assume additive error terms, instead of

multiplicative ones, and do not require a positive minimal necessary time for negotiations.

We also assume that B = v + f , where v is the unobserved base value of the captive for

the negotiating team, and f is the amount of earmarked money that we observe for released

captives. We allow these components to be correlated, for multiple reasons. First, there

could be positive correlation between v and f if the negotiating team had a preference to

release captives with characteristics that were positively correlated with the wealth of the

captive’s family. On the other hand, there could be a substitution effect between v and f ,

with families anticipating a lower v sending more of their own money to release loved ones.

We allow the mean of unobserved component to depend linearly on a set of personal

characteristics X, assumed to be observed by the seller.

We assume that the distribution of earmarked money is normal conditional on some

money having been sent. To sum up, our assumptions about total value distribution are the

27

following:

B =

⎧⎪⎨⎪⎩ υ + f

υ

pr

1− pr

(v

f) ∼ N((

μv

μf

),Λ)

μv = γX , Λ = (σv ρ

ρ σf

)

where pr is probability that some money were sent, μv and σv are the mean and standard

deviation of the general funds distribution, μf and σf are parameters of the family money

distribution and ρ is a covariance coefficient. We exogenously set pr = 0.075 in the analysis,

and estimate the rest of the parameters from the data. The data does not allow us a reliable

way to estimate pr, given that we only observe the fraction of captives with earmarked

money among rescued individuals, not among all captives that were part of the negotiations.

However, our parameter estimates presented below are not sensitive to the value assigned to

pr, as long it is from a reasonable range (0.025− 0.15).In the main body of the paper we only report our basic specification, which only includes

a constant in X, pools observations from all rescue trips to the same location, and includes

rescued captives who based on the data might have been rescued as part of bundled nego-

tiations. In the appendix, as robustness checks for our results, we report estimates from

alternative specifications. In the first one, we include age and region of origin in X.32 Al-

lowing for such differentiation slows down the computations significantly, because for each

vector of observed characteristics a separate equilibrium strategy has to be calculated. In the

32The region of origin could be revealed to the captors by various ways, for example the accent and clothingof the captive, as well as where he was captured.

28

second alternative specification we derive the time period of our data into two subperiods,

and conduct the estimation separately for those. In the third one we exclude captives who

might have been released through bundled negotiations. We also report the results from a

specification in which instead of normal, we assume that the distribution of the buyer’s eval-

uation is lognormal, thereby ruling out negative valuations.33 Finally, we report the results

from a specification in which instead of multiplicative error terms we assume additive error

terms in the data generating process. The qualitative conclusions we get from all the above

alternative specifications are very similar to those from the basic specification.

As a consistency check, we also estimate our basic specification for the Algiers data

during periods of political instability, and show that at least for the largest profession group,

estimated transaction costs and discount rates are both significantly higher during these

periods, consistent with our expectations.

4.3 Estimation procedure

The set of parameters to be identified consists of interest rate r, buyer transaction cost λ,

parameters for the buyer’s value distribution (γ,σv,μf ,σf ), and the variance of error terms

Σ. Since we observe earmarked money, parameters μf and σf can be identified from there.

Identifying the rest of the parameters is less trivial, because the model is highly non-linear

and all parameters influence all dimensions of the observed data. However, some intuition

can be provided.

As described in subsection 4.1, r−1 is a multiplier for duration of negotiations. Intuitively,

the higher the interest rate, the more costly it is for the redemptors to wait, and thus the

stronger is the signal. When interest rate is high, equilibrium duration is low. Therefore

observed negotiation durations help identify r. Short observed durations can also result from

a small variation of values. However, this also leads to small variation in observed prices,

33Note that negative evaluations do not change the qualitative features of the equilibrium, as the buyerterminates negotiations immediately both when having a negative evaluation and when having a smallpositive evaluation.

29

helping to separate the effects of the interest rate and the variation in values. The trans-

action cost parameter is identified from prices, because λ/2 enters as an additive constant

in threshold levels b and b0. Higher transaction costs lead to higher prices and a smaller

signalling region, thus to smaller variation in duration and prices. Comparing it with the

effect of interest rate, the latter influences only variation in duration, while transaction costs

influence variations both in duration and price. The mean of the unobserved component also

increases prices, but it extends the signalling region [b0, b], as opposed to shrinking it.

Formally, we use a standard maximum likelihood approach for model estimation. How-

ever, additional complexity arises because the solution for the equilibrium strategy cannot be

derived in closed form. We construct a numerical likelihood function through the following

steps.

1. First, we estimate the distribution of earmarked money using the subsample of ob-

servations with positive earmarked money. Here we deviate from the pure theory of

maximum likelihood, because we ignore information about how these parameters influ-

ence optimal strategies. However, we have enough observations to estimate it precisely,

and since only less than 10% of captives had earmarked money, its influence on the

seller’s strategy is small.

2. Having set values for other parameters, we numerically solve for the seller’s optimal

first offer b using equation (3). For the normal distribution we are able to obtain closed

form solution for the integral, so optimization on this level is fast and precise.

3. We then construct a grid of unobserved valuations in the relevant region (about 1000

bins with flexible step lengths). For each B and each observation we calculate the

predicted price and duration, and compute errors.

4. After constructing the likelihood function for each value, we take expectation with

respect to B. This is a one dimensional integral, so we use Simpson’s approximation

rule rather than simulation.

30

5. Finally, we sum the likelihoods of all observations to obtain the total likelihood func-

tion.

An important feature of this problem is that the parameters of the error terms do not

influence equilibrium outcome, and thus one may optimize the objective function with respect

to Σ without reestimating the equilibrium each time. Using this inner circle makes the

optimization slower, but more robust and precise. We use this technique for all reported

tables. We calculate standard errors by a bootstrap procedure, using repeated estimation of

100 different draws from the original sample.

We conclude this subsection by formally describing the construction of the likelihood

function.

There are two types of captives: with and without earmarked money. For observations

without earmarked money probability of given realization is:

log(P (fm = 0)P (rescued = 1, pi,Δi)) =

log(1− pr) + log(∞

b0

f(εp(p,Δ), εd(p,Δ))dF (B))

,where f is pdf of N(0,Σ) and F (B) is cdf of unobserved value distribution with parame-

ters μv and σv. Here εp and εd are differences between logarithms of predicted and realized

outcomes:

εp = log(p)− log(p(B))

εd = log(Δ)− log(Δ(B, b) +Δ0)

The Jacobian of this transformation is

|∂(ξp, ξd)∂(p,Δ)

| = |1p0

0 1Δ

| = 1

pΔ

31

This term doesn’t depend on parameter values and unobserved value, so we can ignore

it in maximization. The corresponding probability for observations with earmarked money

is similar:

log(P (fm > 0)P (fmi|fm > 0)P (rescued = 1, pi,Δi)) =

log(pr) + log(ϕ(fmi − μf

σf)) + log(

∞

b0

f(εp(p,Δ), εd(p,Δ))dF (B))

,where ϕ is the pdf of the standard normal distribution and F (B) is the cdf of total

value, which is normal with parameters μv + fmi and σv. To complete the construction of

likelihood function we take into account that we observe only successful negotiation, thus to

make conditional probability we divide each probability by probability of being rescued:

log(P (observed = 1)) = log(1− Φ(b0 − μ1 − fmi

σ1))

The total log-likelihood function has the usual additive form, because we assume that ob-

servations are independent:

logL =i

logLi

4.4 Basic results

We estimate the equilibrium separately for each of the three largest recorded professions

among captives, separately for the two corsair strongholds. These professions - fishermen,

soldiers and sailors, - together constitute roughly one third of the whole sample. We exclude

all government owned captives (about 25% of rescued captives). This leaves about 1500

observations, and the average sample size for our estimations is roughly 250.

Estimation results are presented in table 3. For most professions the estimated interest

rate is twice as high in Algiers as in Tetuan. This mainly results from the fact that nego-

tiations in Algiers were shorter. However, estimated transaction costs are about the same

32

across territories and professions. The above suggest that in Algiers negotiators were more

concerned about the danger the captives faced in captivity, and about negotiations breaking

down for exogenous reasons, rather than about their own personal safety.

Estimated correlation coefficients between general fund’s money and earmarked money

for the majority of the regressions is negative and over 0.5 in absolute value. This suggests

that in most cases earmarked funds partially substituted other sources of funding. However,

the finding should be evaluated taking into account that the standard errors are very high.

Figure 1 shows equilibrium price and time to negotiation trajectories based on our esti-

mations for each profession. The first thing to notice is that equilibrium prices are higher in

Tetuan, and signaling regions are shifted to higher values.

For all four professions, on the equilibrium path an additional day of delay in Algiers

resulted in higher price discounts, because higher interest rates made signaling faster. These

graphs also reflect that observed negotiations in Tetuan were longer on average. Our esti-

mates predict a maximum duration of 20 to 35 days in Tetuan depending on profession, and

of 15 to 20 days in Algiers.

Finally, table 3 also reports the probability a negotiation was terminated. For all profes-

sions but fisherman this probability is larger in Algiers, which is in line with the available

qualitative and empirical evidence.34 Our estimates for the probability of termination are

very high, for sailors and soldiers for Algiers the estimated model predicting 70% of the

negotiations to be terminated. However, our data is not suitable for reliable estimation here.

The main reason is that we do not observe failed negotiations, and we cannot identify non-

parametrically the value distribution below the threshold b0. Thus, we are left to rely purely

34To analyze this question in a reduced-form manner, we created a data set of captives for whom at leastone previous negotiation failed. The main idea here is that if the same individual appears as earmarked inseparate trips, then we know that he is alive and that negotiations failed in the previous trip. After usingextremely conservative matching criteria (detailed in the appendix) that appears to have done a good job ofminimizing type-II error (that is, only keeping individuals for whom there is a high certainty that (at least)one previous negotiation failed), we were left with 63 individuals. Of these individuals (for whom at least onenegotiation failed) 54 (85.71%) were captive in Algiers. Formal statistical tests comparing this proportionto the percentage of total rescued captives from Algiers (73%), the proportion of earmarked captives fromAlgiers (74%) or the proportion of rescued earmarked captives from Algiers (70%) all reject equality at the1% significance level. This result is consistent with a larger number of failed negotiations in Algiers.

33

on our parametric specification.

Besides parameter values estimates, it is interesting to know what part of variation in

the data we can explain with this model, a measure similar to R2 in linear regression. If the

outcome is y and its predicted value is y, this exercise would involve comparing (y− y)2 and(y − y)2. However, in our case y is not a constant, but a random variable, since underlying

value B is unknown. Thus, we use the mean of conditional distribution E[y|y] instead ofy in the formula above. For a given outcome and a prior distribution of valuations one

may calculate the posterior distribution of B given y using Bayes’ rule. The graphical

interpretation of this would be finding the closest point from the outcome (p,Δ) to the line

(p(B,Ω),Δ(B,Ω)), and taking the corresponding B as posterior estimate of B. From it

it we calculate posterior distribution for equilibrium outcome y, and compute its mean to

compare variances.

The estimated share of predicted variation in outcomes is presented in the last two rows

of the tables before the number of observations as EVduration and EVprice, which stands for

estimated variance in duration and price outcomes. These numbers are quite different for

different professions, but the average for duration is around 0.65 and for price it is 0.30.

The difference is noteworthy in the light of the error components being very similar. The

interpretation is that for plausible parameter values signaling does not give as much variation

in prices as it gives in duration of negotiations. Overall, we explain variation in the duration

of negotiations quite well, but only satisfactorily for prices.

4.5 Welfare analysis and counterfactuals

Given the estimated parameter values of the underlying model, we can calculate the equi-

librium expected division of surplus between the bargaining parties, and various sources of

losses. The total expected surplus is simply the expected buyer valuation:

Total_surplus =∞

0

BdF (B)

34

The seller surplus is already featured in the definition of equilibrium strategy:

Seller_surplus =b

b0

x(B)Be−rΔ(B,b)dF (B) + (1− F (b))x(b)b

The buyer gets the present value of his realized surplus at the time of agreement, minus

total transaction costs:

Buyer_surplus =b

b0

(1− x(B))Be−rΔ(B,b)dF (B) +∞

b

(B − x(b)b)dF (B)−

−b

b0

λ(1− e−rΔ(B,b))dF (B)

Finally, the expected social costs from various sources are:

Termination_costs =b0

0

BdF (B)

Delay_costs =b

b0

B(1− e−rΔ(B,b))dF (B)

Transaction_costs =b

b0

λ(1− e−rΔ(B,b))dF (B).

Calculation of surpluses using estimated parameters for each profession is presented in

table 4. In most cases, total surplus is much higher in Tetuan, reflecting that the estimated

mean buyer valuations tend to be higher in Tetuan. Comparison of surpluses extracted by

sellers and buyers shows that in most cases they obtained approximately equal shares of total

surplus, about 40% each. Delay costs range from 3%-5% for Sailors to 6%-7% for Fishermen

and Soldiers. Transaction costs were relatively small for all professions and all territories

and constituted about 2% of total surplus. Termination costs were also quite high: about

10% in most cases. Overall, this calculations suggest that negotiations were quite efficient,

since total costs were only about 20% of total surplus.

35

Next, we address the question that how much sellers would have gained by selling captives

in bundles, focusing only on captives for whom we can confidently rule out that they were

rescued as part of a bundle. Here we assume a bundle of 10 captives. Columns 5-8 in table

4 present our estimates. We find that selling in bundles would have mostly benefited the

seller, increasing his share from 40% to 50%-60% of total surplus. Buyers would have lost,

but not much: their average share would have fallen from 40% to 35%. One can see that all

types of costs are lower for trading in bundles, hence trading in bundles would have increased

realized social surplus.

We also examine the possibility that the seller could give a take it or leave it offer to the

buyer, or commit to leave negotiations if the initial offer is declined. The resulting estimated

distribution of surplus is presented in the last four columns (9)-(12) of table 4. As expected,

in all cases this commitment power would have benefited the seller. Since all negotiations

end immediately in this scenario, transaction and delay costs are zero. However, termination

costs are very high: 20% to 30%, leading to lower realized social surplus than in the basic

model. In all cases buyer would have been much worse off, and would have received only

25%-30% of the surplus.

5 Conclusion

While the Barbary Corsairs have long ceased to roam the seas, the practice of ransoming

captives continues today. The empirical results presented in this paper suggest that existing

theoretical work on bargaining under asymmetric information can inform our understanding

of such ransom negotiations.

Qualitative evidence suggests the relevance of the theory by showing that the negotiating

teams’ behavior was consistent with many of the theoretical predictions. These teams worked

to conceal the identities of the captives they wanted most, and delayed the ransom of many

captives to obtain lower prices.

36

Reduced-form empirical analysis using data on ransom prices and time to rescue for

captives ransomed between 1575 and 1739 bolster this qualitative evidence in Algiers. In

particular, delay within ransoming trips led to a substantial decrease in prices, reducing

the price by an estimated 4% per each day. In Tetuan, however, we find considerably less

support for the empirical predictions.

To further investigate the differences between Algiers and Tetuan, we structurally es-

timate the model in Cramton (1991). Our estimates suggest that higher interest rates in

Algiers drive most of the observed differences in bargaining outcomes between Tetuan and

Algiers. This result, in turn, emphasizes the importance of the rate of physical decay in cap-

tivity, as well as the possibility of exogenously terminated negotiations. We use our structural

model for welfare analysis, and find that the bargaining institution was remarkably efficient,

allowing parties to realize more than 80% of total social surplus.

Our investigation also suggest avenues for future research, such as investigating the issue

of bundling in dynamic bargaining.

Finally, the historical response of many European powers to the Corsairs may provide

insights into negotiating with Somali pirates (and possibly other criminal groups). For

example, the historical preference for centralized ransoming organizations suggests that such

institutions might aid negotiations with pirates today by both enabling negotiations for

multiple cargoes at once and by reducing transaction costs (which, besides saving costs

directly, improves the bargaining power of the negotiating team).

6 References

Abramitzky, R. (2009): “The Effect of Redistribution on Migration: Evidence from the

Israeli Kibbutz,” Journal of Public Economics, 93, 498-511.

Abun-Nasr, J. (1977). A History of the Maghrib. London: Cambridge University Press.

Adams, W. and J. Yellen (1976): “Commodity bundling and the burden of monopoly,”

37

Quarterly Journal of Economics, 90, 475-498.

Admati, A. and M. Perry (1987): “Strategic delay in bargaining,” Review of Economic

Studies, 54, 345-364.

Armstrong, M. (2000): “Optimal multi-object auctions,” Review of Economic Studies, 67,

455-481.

Armstrong, M. and J. Rochet (1999): “Multi-dimensional screening: A user’s guide,”

European Economic Review, 43, 959-979.

AHN (Archivo Histórico Nacional): códices, legajos: 118, 119, 120, 121, 122, 124, 125,

126, 127, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 142, 143, 144, 145, 146,

147, 148, 149

Ausubel, L. and R. Deneckere (1994): “Separation and delay in bargaining,” mimeo,

University of Maryland.

Avery, C. and T. Hendershott (2000): “Bundling and optimal auctions of multiple

products,” Review of Economic Studies, 67, 483-497.

Ayers, I. and P. Siegelman (1995): “Race and gender discrimination in bargaining for a

new car,” American Economic Review, 85, 304-321.

BNM (Biblioteca Nacional de Madrid): mss: 2963, 2974, 3549, 3870, 3586, 3587, 3588,

3589, 3590, 3592, 3593, 3597, 3628, 3631, 3819, 3837, 3872, 4405, 4359, 4363, 4365, 4394,

6547, 6573, 7752

Bikhchandani, S. (1992): “A bargaining model with incomplete information,” Review of

Economic Studies, 59, 187-203.

Bono, S. (1998). Les Corsaires en Méditerranée. Paris: Éditions Paris-Méditerranée.

Brodman, J. (1986). Ransoming Captives in Crusader Spain. Philadelphia: University of

Pennsylvania Press.

Card, D. (1990): “Strikes and Wages: A Test of an Asymmetric Information Model,”

Quarterly Journal of Economics, 105, 625-.659.

Castillo, M., R. Petrie, M. Torero and L. Vesterlund (2011): “Gender differences

38

in bargaining outcomes: A field experiment on differential treatment,” mimeo University of

Pittsburgh.

Coindreau, R. (1948). Les Corsaires de Salé. Paris: Publications de l’Institut des Hautes

Etudes Marocaines.

Chakraborty, I. (1999): “Bundling decisions for selling multiple objects,” Economic Theory,

13, 723-733.

Cramton, P. (1991): “Dynamic bargaining with transaction costs,” Management Science,

37, 1221-1233.

Croson, R. (1996): “Information in ultimatum games: an experimental study,” Journal of

Economic Behavior and Organization, 30, 197-212.

Davis, R. (2001): “Counting European Slaves on the Barbary Coast,” Past & Present, 172,

87-124.

Davis, R. (2003). Christian Slaves, Muslim Masters. New York: Palgrave MacMillan.

Fang, H. and P. Norman (2006): “To bundle or not to bundle,” RAND Journal of

Economics, 37, 946-963.

Finkelstein, A. and K. McGarry (2006): “Multiple dimensions of private information:

evidence from the long-term care insurance market,” American Economic Review, 96, 938—

958.

Finkelstein, A., and J. Poterba (2006): “Testing for Adverse Selection with "unused

observable",” NBER Working Papers 12112. National Bureau of Economic Research, Cam-

bridge, MA.

Friedman, E. (1983). Spanish Captives in North Africa in the Early Modern Age. Madison:

The University of Wisconsin Press.

Fudenberg, D. and D. Levine (1993): “Self-confirming equilibrium,” Econometrica, 61,

523 545.

Fudenberg, D., D. Levine and P. Ruud (1985): “Strike activity and wage settlements,”

mimeo, UC Berkeley.

39

Fudenberg, D., D. Levine and J. Tirole (1985): “Infinite horizon models of bargain-

ing with one-sided incomplete information,” in A. Roth (ed.), Bargaining with incomplete

information, Cambridge University Press, Cambridge.

Fudenberg, D. and J. Tirole (1983): “Sequential bargaining under incomplete informa-

tion,” Review of Economic Studies, 50, 221-247.

Gathmann, C., and H. Hillmann (2009): “Overseas trade and the decline of privateer-

ing,” mimeo, University of Mannheim.

Garí y Siumell, J. (1873). Historia de las Redenciones de Cautivos Cristianos. Barcelona:

Imprenta de los Herederos de la Vuida Pla.

Grossman, S. and M. Perry (1986): “Sequential bargaining under asymmetric informa-

tion,” journal of Economic Theory, 39, 120-154.

Gul, F., H. Sonnenschein and R. Wilson (1986): “Foundations of dynamic monopoly

and the Coase conjecture,” Journal of Economic Theory, 39, 155-190.

Guth, W., S. Huck and W. Muller (1996): “Two-level ultimatum bargaining with

incomplete information: an experimental study,” The Economic Journal, 106, 593-604.

Guth, W., R. Schmittberger and B. Schwarz (1982): “An experimental analysis of

ultimatum bargaining,” Journal of Economic Behavior and Organization, 3, 367-388.

Jehiel, P., M. Meyer-ter-Vehn and B. Moldovanu (2007): “Mixed bundling auctions,”

Journal of Economic Theory, 134, 494-512.

Julien, C. 1970. History of North Africa. London: Routledge & Kegan Paul.

Keniston, D. (2011): “Bargaining and Welfare: A Dynamic Structural Analysis of the

Autorickshaw Market,” mimeo MIT.

Kennan, J. and R. Wilson (1989): “Strategic bargaining models and interpretation of

strike data,” Journal of Applied Econometrics, 4, S87-S130.

Leeson, P. (2007): “An-arrgh-chy: The Law and Economics of Pirate Organization” Journal

of Political Economy, 115(6), 1049-1094.

Leeson, P. (2009). The Invisible Hook. Princeton: Princeton University Press.

40

Martínez Torres, J. (2004). Prisioneros de los Infieles. Barcelona: Edicions Bellaterra.

Maziane, L. (2004). Salé et ses Corsaires (1666-1727). Caen: Presses Universitaires de

Caen.

McAfee, P., J. McMillan and M. D. Whinston (1989): “Multiproduct monopoly,

commodity bundling and correlation of values,” Quarterly Journal of Economics, 103, 371-

383.

McConnell, S. (1989): “Strikes, wages, and private information,” American Economic

Review, 79, 801-815.

CMerlo, A., F. Ortalo-Magné and J. Rust (2008): “The home selling problem: Theory

and evidence,” mimeo University of Pennsylvania.

Mitzkewitz, M. and R. Nagel (1993): “Envy, greed and anticipation in ultimatum games

with incomplete information: an experimental study,” International Journal of Game Theory,

22, 171-198.

Neelin, J.H. Sonnenschein and M. Spiegel (1988): “A further test of noncooperative

bargaining theory,” American Economic Review, 78, 824-836.

Ochs, J. and A. Roth (1989): “An experimental study of sequential bargaining,” American

Economic Review, 79, 355-384.

Palfrey, T. (1983): “Bundling decisions by a multiproduct monopolist with complete infor-

mation,” Econometrica, 51, 463-483.

Panzac, D. (2005). Barbary Corsairs: The End of a Legend 1800-1820. Boston: Brill.

Perry, M. (1986): “An example of price formation in bilateral situations: A bargaining

model with incomplete information,” Econometrica, 54, 313-321.

Rapoport, A., J. Sundali and D. Seale (1996): “Ultimatums in two-person bargaining

with one-sided uncertainty: demand games,” Journal of Economic Behavior and Organiza-

tion, 30, 173-196.

Rubinstein, A. (1982): “Perfect equilibrium in a bargaining model,” Econometrica, 50,

97-109.

41

Rubinstein, A. (1985): “A bargaining model with incomplete information about time

preferences,” Econometrica, 53, 1151-1172.

Schmitt, P. (2004): “On perceptions of fairness: The role of valuations, outside options,

and information in ultimatum bargaining games,” Experimental Economics, 7, 49-73.

Sieg, H. (2000): “Estimating a bargaining model with asymmetric information: Evidence

from medical malpractice disputes,” Journal of Political Economy, 108, 1006-1021.

Sobel, J. and I. Takahashi (1983): “A multistage model of bargaining,” Review of Eco-

nomic Studies, 50, 411-426.

Stewart, J. (2006). African States and Rulers. Jefferson: McFarland & Co.

Stahl, I. (1972): Bargaining theory, Stockholm: Stockholm School of Economics.

Straub, P. and J. Murnighan (1995): “An experimental investigation of ultimatum

games: Information, fairness, expectations, and lowest acceptable offers,” Journal of Eco-

nomic Behavior and Organization, 27, 345-364.

Tenenti, A. (1967). Piracy and the Decline of Venice: 1580-1615. Berkeley: University of

California Press.

Tracy, J. (1986): “An investigation into the determinants of US strike activity,” American

Economic Review, 76, 423-436.

Tracy, J. (1987): “An empirical test of an asymmetric information model of strikes,” Journal

of Labor Economics, 5, 149-173.

Waldfogel, J. (1995): “The selection hypothesis and the relationship between trial and

plaintiff victory," Journal of Political Economy, 103, 229-260.

Watanabe, Y. (2004): “Learning and bargaining in dispute resolution: Theory and evi-

dence from medical malpractice litigation,” mimeo Northwestern University.

Weiss, G. (2011). Captives and Corsairs: France and Slavery in the Early Modern Mediter-

ranean. Stanford: Stanford University Press.

42

(a) Equilibrium prices for differentprivate values

0 5 10 15 20 25 30 35 40800

1000

1200

1400

1600

1800

2000

2200

equilib

rium

pri

ce

equilibrium duration

Sailors

Algiers

non-Algiers

0 5 10 15 20 25 30 35 40600

800

1000

1200

1400

1600

1800

2000

equilib

rium

pri

ce

equilibrium duration

Fishermen

Algiers

non-Algiers

0 5 10 15 20 25 30 35 40600

800

1000

1200

1400

1600

1800

2000

equ

ilib

rium

pri

ce

equilibrium duration

Soldiers

Algiers

non-Algiers

(b) Equilibrium price-delay schedule

Figure 1: Private values, delay and pricesGraph details the equilibrium price and equilibrium time to negotiationtrajectories by profession.

Tab

le1:

Summary

Sta

tistics(forre

scued

individuals

unless

oth

erw

isenoted)

Algiers

Tetu

an

Variable

Description

Mean

St.dev.

Min

Max

NM

ean

St.dev.

Min

Max

N(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

Genera

l

YearsCaptive

Years

captive

6.10

6.45

0.02

60

7227

4.00

3.98

037

2335

Price

(SilverReales)

1658

2257

081458

7317

1973

1400

125

21439

2703

Earm

ark

ed∗

=1ifearm

arked

0.09

0.29

01

7398

0.11

0.31

01

2716

Moneysent(w

/NotRescued)

(Silver

Reales)

1224

4298

19

126440

1676

1083

1372

2515672

586

Moneysent(O

nly

Rescued)

(Silver

Reales)

1400

5299

19

126440

677

1103

1474

3415672

297

Bundled

=1ifbundled

0.43

0.50

01

7317

0.62

0.49

01

2703

Castile∗

=1iffrom

desired

areas

0.49

0.50

01

3824

0.68

0.46

01

1524

DaysE

lapsed

Daysto

agreem

ent

8.31

20.08

0272

4337

11.30

20.00

0284

2044

Govt

Captive

owned

byGov

t0.17

0.38

01

7398

0.25

0.43

01

2716

Fem

ale

∗0.05

0.22

01

7398

0.05

0.23

01

2716

Child∗

0.05

0.22

01

7253

0.08

0.27

01

2358

Age

Years

35.88

14.06

0.11

100

7253

33.68

14.21

0.83

94

2358

AgeC

apt

Agewhen

captured(Y

ears)

29.79

13.07

099.33

7185

29.97

13.66

091

2286

Pro

fession

Fisherman

0.12

0.33

01

7398

0.11

0.31

01

2716

Soldier∗

0.18

0.38

01

7398

0.17

0.37

01

2716

Majesty∗

InKing’s

Service

0.06

0.23

01

7398

0.06

0.23

01

2716

Shepherd

0.01

0.08

01

7398

0.01

0.12

01

2716

Sailor

0.06

0.23

01

7398

0.06

0.23

01

2716

Peasant

0.01

0.08

01

7398

0.02

0.14

01

2716

Indias∗

Enroute

toAmericas

0.01

0.09

01

7398

0.01

0.07

01

2716

Cleric∗

0.02

0.14

01

7398

0.01

0.12

01

2716

Other

Other

Identified

0.01

0.09

01

7398

0.02

0.12

01

2716

NI

NotIdentified

0.54

0.50

01

7398

0.54

0.50

01

2716

Notes:

∗den

otesacategory

thatwasfavoredbytheransomingmissions.

Theva

riable

Day

sElapsedis

equalto

0thefirstday

an

agreem

entis

reach

ed.See

textfordetails.

Tab

le2:

Reduced-F

orm

Estim

atesbyLocation

Algiers

Algiers

Algiers

Tetu

an

Tetu

an

Tetu

an

(1)

(2)

(3)

(4)

(5)

(6)

PanelA:Pricesand

Delay(dep

endentvariable

is100*logarithm

ofransom

price)

Delay(D

ays)

-3.93

-3.77

-1.98

0.01

-0.07

0.03

(0.85)

(0.84)

(0.60)

(0.10)

(0.07)

(0.14)

N308

130

2893

015

0512

9852

6

PanelB:Pricesand

Private

Inform

ation(dep

endentvariable

is100*logarithm

ofransom

price)

Earm

ark

ed35.04

36.26

33.05

33.96

32.44

28.42

(4.83)

(4.38)

(5.22)

(4.84)

(4.27)

(6.37)

N308

130

2893

015

0512

9852

6

PanelC:Delayand

Private

Inform

ation(dep

endentvariable

isdelay

inday

s)Earm

ark

ed-0.38

-0.39

-0.13

-0.59

-1.19

-2.04

(0.17)

(0.19)

(0.10)

(1.19)

(1.27)

(1.31)

N314

330

8693

915

1413

0352

8

PanelD:Delayand

Uncertainty

(dep

endentvariable

isdelay

inday

s)S.D

./M

ean

0.36

0.42

0.57

-0.20

-0.05

-0.18

(0.13)

(0.17)

(0.28)

(1.95)

(2.08)

(2.16)

Mean/100

0.00

0.01

-0.03

0.23

0.28

1.85

(0.00)

(0.01)

(0.02)

(0.14)

(0.15)

(1.69)

N306

030

0590

114

8212

7351

7

Con

trols

No

Yes

Yes

No

Yes

Yes

Sample

All

All

Non-D

elayed

All

All

Non-D

elayed

Notes:

Delay

measuresthenumber

ofday

selapsedsince

thestart

ofnegotiations.

Earm

arked

isanindicatorvariable

equalto

oneifthecaptivehadmoney

sentfrom

Spain

thatwasearm

arked

forhis

rescue.

S.D

./M

eanis

thecoeffi

cien

tofva

riationofthe

amountofearm

arked

money

bycalculated

byprofession.

Mea

n/100is

themean

ofthesamequantity

divided

by100(and

isgiven

inconstantsilver

reales).N

isthenumber

ofobservations.

Controls

includeacaptive’stimein

captivity,

ageatcaptivity,

agen

der

dummy,

adummyeq

ualto

oneifthecaptivewasyounger

than16when

ransomed

andprofessiondummies(thesedummies

are

omittedin

panel

D).

The“Non-D

elay

ed”sample

consistsofallcaptives

whowereransomed

onthefirstobserved

ransoming

exped

itionfollow

ingtheircapture.Standard

errors

clustered

byransomingtrip

are

inparentheses.

Tab

le3:

Structu

ralEstim

atesbyPro

fession,Location

Sailors,

Sailors,

Sailors,

Fisherm

en,

Fisherm

en,

Fisherm

en,

Soldiers,

Soldiers,

Soldiers,

Tetu

an

Algiers

Diff

erence

Tetu

an

Algiers

Diff

erence

Tetu

an

Algiers

Diff

erence

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

λ1128

471

657

681

365

315

669

425

244

(120)

(44)

(128)

(234)

(62)

(242)

(88)

(58)

(105)

μv

1803

118

168

519

6014

8847

211

9662

1134

(710)

(439)

(834)

(914)

(264)

(951)

(830)

(593)

(1020)

σv

2280

1634

646

1970

944

1026

2295

1989

306

(638)

(247)

(687)

(610)

(149)

(628)

(477)

(294)

(560)

μf

985

925

6098

592

560

985

925

60(173)

(114)

(207)

(173)

(114)

(207)

(173)

(114)

(207)

σf

763

658

105

763

658

105

763

658

105

(102)

(80)

(130)

(102)

(80)

(130)

(102)

(80)

(130)

ρ0.54

-0.79

1.33

-0.65

-0.48

-0.17

-0.78

-0.85

0.07

(0.62)

(0.44)

(1.19)

(0.65)

(0.22)

(0.67)

(0.62)

(0.39)

(0.73)

r0.015

0.028

-0.013

0.027

0.042

-0.015

0.017

0.031

-0.014

(0.004)

(0.004)

(0.005)

(0.013)

(0.006)

(0.014)

(0.002)

(0.007)

(0.007)

c17.12

13.40

3.72

18.28

15.24

3.04

11.67

13.36

-1.69

(3.87)

(1.21)

(4.04)

(4.89)

(1.02)

(5.00)

(1.38)

(2.46)

(2.82)

pr t

erm

ination

0.53

0.70

0.43

0.28

0.57

0.70

EVduration

0.74

0.82

0.53

0.85

0.75

0.53

EVprice

0.26

0.19

0.38

0.26

0.30

0.18

N93

146

149

359

211

454

Notes:

λisthemonetary

equivalentoftransactioncostsper

day

(given

inconstantsilver

reales).μvisthemeanofthedistribution

ofmoney

whichcould

bepaid

from

thegen

eralfundsforacaptive(given

inconstantsilver

reales).σvis

thestandard

dev

iation

ofthis

distribution(given

inconstantsilver

reales).μfis

themeanofthedistributionofearm

arked

fundssentforaparticular

captive(given

inconstantsilver

reales).σfis

thestandard

dev

iationofthis

distribution(given

inconstantsilver

reales).ρis

the

covariance

betweenearm

arked

andgen

eralfunds.

ris

theinterest

rate.cis

themonetary

equivalentoftransactioncostsper

day

(given

inconstantsilver

reales).pr t

erm

inationis

theprobabilitythenegotiationwasterm

inated.EVdurationgives

thepercentof

thevariationin

durationsthatissuccessfullyex

plained

bythemodel

andEVpric

egives

thepercentofvariationin

pricesex

plained

.N

gives

thenumber

ofobservationsusedin

estimation.Standard

errors

inparentheses.

Tab

le4:

Distribution

ofSurp

lusbetw

een

theCorsairsand

theRanso

mingTeam

Estim

ated

Ifbundled

in10

Takeit

orleaveit

Tetu

an

Algiers

Tetu

an

Algiers

Tetu

an

Algiers

Values

Share

Values

Share

Values

Share

Values

Share

Values

Share

Values

Share

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

PanelA:Sailors

Sellersurplus

931

0.43

299

0.40

1295

0.59

422

0.54

992

0.46

326

0.44

Buyersurplus

821

0.38

282

0.38

651

0.30

243

0.31

595

0.27

205

0.27

Delay

costs

67

0.03

37

0.05

33

0.01

60.01

00.00

00.00

Transactioncosts

31

0.01

14

0.02

21

0.01

40.01

00.00

00.00

Terminationcosts

328

0.15

117

0.16

183

0.08

110

0.14

590

0.27

217

0.29

Totalcosts

425

0.20

168

0.22

237

0.11

120

0.15

590

0.27

217

0.29

Total

217

71

749

121

821

785

121

771

749

1PanelB:Fisherm

en

Sellersurplus

919

0.42

684

0.44

1218

0.56

861

0.55

1023

0.47

779

0.50

Buyersurplus

846

0.39

620

0.40

768

0.35

595

0.38

615

0.28

410

0.26

Delay

costs

140

0.06

115

0.07

106

0.05

85

0.05

00.00

00.00

Transactioncosts

44

0.02

32

0.02

42

0.02

25

0.02

00.00

00.00

Terminationcosts

234

0.11

117

0.07

59

0.03

50.00

545

0.25

380

0.24

Totalcosts

418

0.19

265

0.17

207

0.09

114

0.07

545

0.25

380

0.24

Total

2183

115

681

2193

115

701

2183

115

681

PanelC:Soldiers

Sellersurplus

682

0.41

329

0.39

931

0.54

465

0.52

755

0.45

372

0.44

Buyersurplus

650

0.39

333

0.39

574

0.34

298

0.33

484

0.29

245

0.29

Delay

costs

104

0.06

60

0.07

56

0.03

18

0.02

00.00

00.00

Transactioncosts

34

0.02

18

0.02

28

0.02

10

0.01

00.00

00.00

Terminationcosts

214

0.13

114

0.13

120

0.07

104

0.12

443

0.26

237

0.28

Totalcosts

351

0.21

192

0.22

204

0.12

132

0.15

443

0.26

237

0.28

Total

168

31

854

117

091

896

116

831

854

1

Notes:

Sellersu

rplusis

expectedvalueofthetransactionto

seller.Buyer

surp

lusis

expectedva

lueofthetransactionto

buyer.

Delaycostsis

expecteddep

reciationofthecaptiveduringnegotiationprocess.Tra

nsa

ction

costsare

expectedcostsofwaiting

fornegotiationsto

finishfortherescueteam.Termination

costsis

expectedva

lueofcaptives

forwhichnegotiationsterm

inated

withouttransactionto

takeplace.Totalcostsis

thesum

ofDelaycosts,

Tra

nsa

ctioncostsandTermination

costs.

Allva

lues

are

given

inconstantsilver

reales.