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LIVESTOCK DISEASE INDEMNITY DESIGN

WHEN MORAL HAZARD IS FOLLOWED

BY ADVERSE SELECTION

BENJAMIN M. GRAMIG, RICHARD D. HORAN, AND CHRISTOPHER A. WOLF

Averting or limiting the outbreak of infectious disease in domestic livestock herds is an economicand potential human health issue that involves the government and individual livestock producers.Producers have private information about preventive biosecurity measures they adopt on their farmsprior to outbreak (ex ante moral hazard), and following outbreak they possess private informationabout whether or not their herd is infected (ex post adverse selection). We investigate how indemnitypayments can be designed to provide incentives to producers to invest in biosecurity and reportinfection to the government in the presence of asymmetric information. We compare the relativemagnitude of the first- and second-best levels of biosecurity investment and indemnity payments todemonstrate the tradeoff between risk sharing and efficiency, and we discuss the implications for statusquo U.S. policy.

Key words: adverse selection, asymmetric information, indemnity design, livestock disease manage-ment, moral hazard, principal–agent model.

The outbreak of disease in domestic livestockherds is an economic problem and potentialhuman health risk. Diseases that are highlycontagious or have human health implicationsare often the target of government eradica-tion programs. Farm-level public policies un-der these programs range from bounties forinfected livestock to whole herd depopulationand farm decontamination.1

When livestock are taken by the governmentfor public health or economic reasons, the FifthAmendment of the U.S. Constitution speci-fies that just compensation must be provided

Benjamin M. Gramig is assistant professor in the Department ofAgricultural Economics at Purdue University. Richard D. Horanand Christopher A. Wolf are associate professors in the Depart-ment of Agricultural, Food, and Resource Economics at MichiganState University.

The authors gratefully acknowledge funding provided by theEconomic Research Service-USDA cooperative agreement num-ber 58-7000-6-0084 through ERS’ Program of Research onthe Economics of Invasive Species Management (PREISM),and by USDA-CSREES National Research Initiative grant no.2006-55204-17459. The authors thank Roy Black, Editor WallyThurman, and two anonymous reviewers for their many helpfulcomments and suggestions in the development of this manuscript.Any remaining errors are the authors’.

1 Off the farm, the U. S. Department of Agriculture’s Animaland Plant Health Inspection Service (APHIS) provides inspec-tion and quarantine services to prevent the introduction of diseaseacross national borders and also coordinates response to diseaseoutbreaks from within the country. Border measures that protectagainst incursion of disease are provided to protect the safety ofthe American food production system and to prevent infection ofthe domestic livestock industry.

for this private property taken for public use.This compensation takes the form of indem-nity payments. The current federal compen-sation level is defined by the Animal HealthProtection Act, Subtitle E of the Farm Secu-rity and Rural Investment Act of 2002. Thisrequires compensation to be based on the fairmarket value, as determined by the Secretaryof Agriculture, adjusted for any other com-pensation received for the event (e.g., disasterpayments or perhaps even private market in-surance). States may also offer compensationin the form of indemnities.

This article focuses on the structure of in-demnity payments, currently the primary formof public compensation, as the key mechanismfor providing farm-level incentives to investin biosecurity and to report when one’s herdbecomes infected. These actions have beenfundamental issues of concern within publicagencies responsible for livestock disease out-break response (Ott 2006). However, it is notclear that existing indemnity programs ade-quately address the issues. Existing indemnitypayments represent an implicit insurance pol-icy for livestock producers (at least with re-spect to the diseases for which indemnities arepaid), but are really more akin to ad hoc dis-aster payments due to the lack of risk clas-sification and underwriting involved. Indeed,these payments do not have the desirable risk

Amer. J. Agr. Econ. xx(x) (xxx 2009): 1–15Copyright 2009 Agricultural and Applied Economics Association

DOI: 10.1111/j.1467-8276.2009.01256.x

2 xxx 2009 Amer. J. Agr. Econ.

pooling properties associated with insurance;there are no premiums based on the risk rep-resented by an insured as part of a portfolio ofpolicies, and all taxpayers fund the indemnities.Accordingly, the current structure of indemni-ties may not generate the desired level of pri-vate risk mitigation, thereby undermining thegovernment’s livestock disease risk manage-ment objectives.

Prior economic research dealing with live-stock disease (e.g., Bicknell, Wilen, and Howitt1999; Mahul and Gohin 1999; Kuchler andHamm 2000; Horan and Wolf 2005; Hennessy2007) has also ignored incentive compatibility,at least in the presence of asymmetric infor-mation.2 We use a principal–agent model toexamine incentive compatibility in the pres-ence of information asymmetry between thegovernment and individual farmers.3 Individu-als have private information about preventivebiosecurity measures they adopt on their farmsprior to outbreak (ex ante), and following out-break (ex post) they possess private informa-tion about the disease status of their herd. Weinvestigate how indemnities can be developedto ensure incentive compatibility between thegovernment and private decision makers, andhow these incentives influence the occurrenceand magnitude of a disease epidemic. Our fo-cus is on farm-level biosecurity choices and re-porting of disease status.

A Model of On-Farm Decision Making

We develop a capital valuation model of thelivestock enterprise fashioned after that ofHennessy (2007), who adapted the efficiencywage model of Shapiro and Stiglitz (1984)to the problem of livestock disease manage-ment. Our farmer decision model departs fromHennessy (2007) by (a) introducing risk aver-sion on the part of a single farmer (onlybriefly addressed by Shapiro and Stiglitz 1984),(b) considering biosecurity and disease re-porting decisions (whereas Hennessy focused

2 Prior economic research in this area has examined producer re-sponse to prices in conjunction with a government bounty programfor scrapies in the United States (Kuchler and Hamm 2000), opti-mal actions to contain foot and mouth disease outbreak in France(Mahul and Gohin 1999), the effect of government programs toeradicate disease on prevalence level and private control efforts inNew Zealand (Bicknell, Wilen, and Howitt 1999), the dynamics ofoptimally controlling infection from a disease that is transmittedbetween wildlife and livestock (Horan and Wolf 2005), and behav-ioral incentives when there is endemic disease in a decentralizedsetting (Hennessy 2007).

3 A less formal discussion of these issues may be found in Gramiget al. (2006).

exclusively on biosecurity), and (c) by consid-ering the role of indemnity payments in farmerdecisions. A diagram of the decision-makingprocess described below is provided in figure1. The farmer is risk averse with an instanta-neous utility function U(�), where U ′ > 0 andU ′′< 0. Wealth, �, is contingent on the diseasestate and farmer choices in our model.

Let � ∈ [0, 1] be a random variable denotingthe farmer’s within-herd disease prevalencerate, defined as the proportion of animals thatwould test positive, whether clinically or sub-clinically infected. We partition the range of �to indicate that the farmer will either be sus-ceptible (noninfected, with � = 0) or infected(� > 0) at any given point in time, as the farmerwill face different choices and incentives de-pending on whether his or her herd is infectedor not. Once infected, however, the magnitudeof � matters.

We denote the susceptible state by the sub-script S and the infected state by the subscriptI. In the susceptible state (� = 0) farmersmust choose their biosecurity effort level, b.Biosecurity reduces the probability of transi-tioning to the infected state, PSI(b), such that∂PSI(b)/∂b ≤ 0. Biosecurity also reduces theexpected magnitude of a disease outbreak,should one occur. The conditional probabil-ity density function of � is denoted g(� | b),such that G(� | b) is the twice continuouslydifferentiable conditional cumulative distribu-tion function with ∂G(� | b)/∂b ≥ 0 ∀ b. Theconditions imposed on G mean that G satisfiesfirst-order stochastic dominance in the sensethat the cumulative density for a given level ofinfection is nondecreasing (the desirable out-come) in biosecurity.4

The farmer has a baseline profit flow whendisease-free, gross of any biosecurity invest-ment, denoted by �0. Biosecurity efforts aremade at a constant per-unit cost of w. Thesecosts are incurred only in the susceptible statebecause, once infected, there is no incentive tomaintain these efforts.5 The utility of wealthin the susceptible state can therefore be ex-pressed as

US = U(�0 − bw).(1)

4 Because disease is “bad,” higher outcomes of the random vari-able are less desirable and so what we normally refer to as the“dominated” distribution is relatively more attractive for our ap-plication. For b0 < b1, G(� | b1) ≥ G(� | b0) for all b, where theinequality is strict for at least one value of b.

5 There may be instances in which biosecurity efforts continueafter infection (e.g., to prevent greater infection), but modeling thisfeature unnecessarily complicates the analysis without impactingthe qualitative results.

Gramig, Horan, and Wolf Livestock Disease Indemnity Design 3

Figure 1. Individual farmer decision tree: disease states in bold and farmer choices in dashedboxes

In the infected state (� > 0), the farmermust decide whether to report infection. Dis-ease reporting is modeled as a mixed strategy,denoted r ∈ [0, 1] (where r = 1 means alwaysreport and r = 0 means never report). Report-ing results in government testing, verificationof infection, and culling of infected animals toeradicate the disease. The farmer is compen-sated for any culled animals with a governmenttransfer denoted by �(�). Culling results in twotypes of losses for the farmer—a loss of assetvalue �G(�) (�′

G(�) > 0) associated with thelivestock itself and consequential losses frombusiness interruption � G(�) (� ′

G(�) > 0). Busi-ness interruption losses may vary widely de-pending on the characteristics of the individualoperation affected and possibly disease char-acteristics. For instance, the presence or ab-sence of breeding stock or having high fixedcosts associated with a specific capital asset(e.g., a dairy or egg-laying operation) could

contribute to the magnitude of business inter-ruption losses. The sum �G(�) + � G(�) − �(�)represents the farm’s net disease costs per unittime. The farmer’s instantaneous utility whenhe/she reports, denoted by the superscript R, istherefore given by UR

I (�0 − �G(�) − � G(�) +�(�)). The transition rate of returning to thesusceptible state is hG ≤ 1, so that cumulativeexpected indemnity payments are �(�)/hG.6

When a farmer does not report disease,then detection is still possible via govern-ment disease surveillance activities. Surveil-lance activities detect nonreported infectionwith exogenous probability q and fail to de-tect nonreported infection with probability

6 The transition rate hG is strictly less than one for diseasesthat are difficult to eradicate or that flare up, possibly due to en-vironmental contamination, even after all infected animals havebeen eliminated. Porcine reproductive and respiratory syndrome(PRRS) is an example of a disease that often flares up in this way.We are grateful to an anonymous reviewer for pointing this out.


(1 – q).7 Detection leads to government cullingof infected animals. Compensation in this caseis given by �(�) – f . The term �(�) is the sameas occurs under reporting. The term f can beviewed as a fine for not reporting. In what fol-lows, we simply refer to �(�) as the governmenttransfer and f as the fine.

If the infection goes undetected by gov-ernment surveillance, the farmer will attemptprivate culling of infected animals, with costs�F(�) < �G(�) and � F(�) < � G(�) (where�′

F(�) > 0 and � ′F(�) > 0).8 In this case there

is no indemnity payment. Rather, privatelyculled animals are sold at salvage value �(�).Whether infection is discovered by the gov-ernment or not, all infected farms that do notreport incur asset value losses and associatedconsequential losses due to culling (as occursunder reporting). We assume private culling isless effective than government culling, result-ing in a smaller transition rate to the suscep-tible state than if reporting had occurred, thatis, hF < hG.

Given this specification, the expected instan-taneous utility from not reporting is given byqUD

I (�0 − �G(�) − � G(�) + �(�) − f ) + (1 −q)UND

I (�0 − �F(�) − � F(�) + � (�)), wherethe superscript D denotes the diseased farm isdetected and the superscript ND denotes thediseased farm is not detected. The overall ex-pected utility of wealth in the infected state,conditional on the current level of infection,can therefore be expressed as

UI (r, �(�), f, �)

= rU RI (�0 − �G(�) − �G(�) + �(�))

+ (1 − r)[qU D

I (�0 − �G(�) − �G(�)

+ �(�) − f ) + (1 − q)U N DI (�0 − �F(�)

− �F (�) + �(�))].

(2)

7 Government disease surveillance is modeled as being exoge-nous to reflect the fact that ongoing surveillance activities priorto any reporting or discovery of outbreak are conducted basedon prior budgetary commitments independent of a given diseaseoutbreak.

8 Costs under reporting or detection are higher because the gov-ernment requires more stringent actions to not only cull animals,but also to clean the facilities and destroy feed and other suppliesthat might harbor the disease organism. This cleaning is expen-sive but necessary to control disease organisms that can exist forlong periods in the environment. These actions have high marginalcosts relative to the marginal benefits and private farmers wouldbe unlikely to undertake them without government intervention.Below, we show that the more stringent government requirementslead to a greater rate of transitioning to the susceptible state.

Equations (1) and (2) are individual com-ponents of a farm’s intertemporal decision-making process. In the next section, weincorporate state transition probabilities to de-rive the system of equations that represents thefull scope of the farmer’s dynamic problem.

Fundamental Asset Equations

Define VS to be the expected lifetime utility ofthe decision maker in the susceptible state. Us-ing the continuous time discount rate , we candefine VS to be the “time value” of the live-stock asset when susceptible (Hennessy 2007,p. 702). Similarly, let VI be the expected life-time utility in the infected state. This notationgives rise to the “fundamental asset equations”(Shapiro and Stiglitz 1984, p. 436)9

VS = US(b) + PSI (b)(E�[VI ] − VS)(3)

VI = UI (r, �(�), f, �)

+ PI S(r)(VS − VI )

(4)

where E� is the expectations operator withrespect to � and PIS(r) is the transition ratefrom the infected to the susceptible state.Accordingly, PI S(r) = hGr + (1 − r)[hGq +hF (1 − q)].

The time value of the susceptible livestockasset in (3) equals the sum of the instanta-neous utility in the susceptible state, US(b),and the expected capital loss if the diseasestate changes from susceptible to infected,PSI (b)(E�[VI ] − VS). Because the posttransi-tion level of infection is unknown to farm man-agers in the susceptible state, the expectedcapital loss associated with this state transitionis a function of the expectation of the lifetimestream of utility in the infected state.

Similarly, the time value of the infected live-stock asset in (4) equals the sum of the ex-pected instantaneous utility in the infectedstate, UI(r, �(�), f , �), and the expected capitalgain from transitioning to the susceptible statePI S(r)(VS − VI ). The expectations operator isnot needed in (4) because the infected farmeris assumed to know the current infection level.

9 Equations (3) and (4) are derived following Shapiro and Stiglitz(1984, p. 436). Focusing on VS, we examine expected lifetimeutility when decisions are made over small intervals of size [0,t]: (3a) VS = US(b)t + (1 − t)[PSI (b)t E� [VI ] + (1 − PSI (b)t)VS ].Note that (1 – t) ≈ e− t . Equation (3) is obtained by solving (3a)for VS and evaluating it as t → 0. Equation (4) is derived similarly.An implicit assumption in this formulation is that farm businessesare “infinitely lived entities,” as is assumed in Hennessy (2007,p. 702) and Shapiro and Stiglitz (1984, p. 435).


Equations (3) and (4) may be solved as asystem to yield

VS(b, E�[VI ]) = US(b) + PSI (b)E�[VI ] + PSI (b)

(5)

and

VI (b, r, �(�), f, �, E�[VI ])

=UI (r, �(�), f, �) + PI S(r)

[US(b)+PSI (b)E� [VI ]

+PSI (b)

] + PI S(r)

.

(6)

Equation (5) shows the lifetime expected util-ity from being in the susceptible state to be anannuity value. If there was no chance of tran-sitioning to the infected state (i.e., PSI = 0),then lifetime utility when susceptible equalsthe annuity value US/ (i.e., US is received intoperpetuity). When there is a chance of becom-ing infected (i.e., PSI > 0), the annuity valuechanges in two ways: (a) a risk premium, PSI ,is added to the risk-free rate to yield a risk-adjusted discount rate that reduces the annu-ity value associated with the susceptible stateto US/( + PSI); and (b) we must account forthe expected annuity value that accrues in theinfected state, E�[VI]/( + PSI), weighted bythe probability of transitioning to that state.

Equation (6) illustrates a similar valuationof the expected flow from the capital as-set, though conditioned on starting in theinfected state and accounting for the proba-bility of transitioning to the susceptible state.Note that the term in brackets in equation(6) represents VS(b,E�[VI]), as derived inequation (5). If there is no chance of tran-sitioning to the susceptible state (i.e., PIS =0), then lifetime utility equals the annuityvalue UI / . As with equation (5), becausethere is a chance of returning to the sus-ceptible state (i.e., PIS > 0), the discountedstream of benefits takes this into accountvia the risk-adjusted discount rate ( + PIS)and the transition probability-weighted annu-ity value that accrues in the susceptible state,PISVS(b,E�[VI])/( + PIS).

Expressions (5) and (6) are not in reducedform since they both have expected lifetimeutility from infection, E�[VI], on the right-hand side (RHS). To eliminate E�[VI] from theRHS, take the expectation of both sides of (6)with respect to �, isolate E�[VI] and substitute

the expression back into (5) and (6). The re-sulting implicit functions are

VS(b, r, f )

= (b, r)US(b) + �(b, r)E�[UI ]

(7)

VI (b, r, �(�), f, �)

= UI (r, �(�), f, �) + PI S(r)

+ PI S(r) + PI S(r)

VS(b, r, f )

(8)

where (b, r) = ( + PI S(r))/[( + PI S(r) +PSI (b))] and �(b, r) = PSI (b)/[( + PI S(r) +PSI (b))]. The term (b, r) is the risk-adjusteddiscount factor associated with the suscep-tible state, assuming the farmer is initiallysusceptible. With no risk of becoming in-fected, the discount factor would simply be1/ . This factor is adjusted by ( + PI S(r))/( + PI S(r) + PSI (b)) to account for the pro-portion of time the farmer will actually spendin the susceptible state. Similarly, the term�(b, r) is a risk-adjusted discount factor as-sociated with the infected state, assuming thefarmer is initially susceptible. If the risk of be-coming infected and then staying infected wereone, the discount factor would be 1/[(1+)]:the farmer would earn the annuity value E�[UI]/ after becoming infected, but this valuemust be discounted by 1/[1 + ] since infectionoccurs after the first period. In equation (7),the risk-adjusted discount factors (b, r) and�(b, r) weight the expected utility accruing ineach state to determine the expected presentvalue of utility when the farmer is initially sus-ceptible, VS.

Equation (8) presents the expected presentvalue of utility when the farmer is initially in-fected. The farmer initially earns UI until he orshe can transition back to the susceptible state,as reflected by the risk-adjusted discount fac-tor 1/[ + PIS(r)]. Once becoming susceptibleagain, the farmer earns the expected presentvalue VS given by equation (7). In equation(8), VS is multiplied by PIS(r) to account forthe probability of transitioning to the suscepti-ble state, and then this expected value PIS(r)VSis discounted by [ + PIS(r)] to reflect the timeit takes to become susceptible.

The general form of equations (7) and (8)is similar to the comparable equations derivedin Hennessy (2007, pp. 702–03). However, thespecific formulations are more complicatedthan in Hennessy (2007, p. 702). The level of


complexity is greater because (a) his modelincludes a single binary action while we ac-count for two separate continuous choices se-lected by the farmer, and (b) we focus on theasymmetric information problem and the de-sign of indemnification policy, which involvesbusiness interruption and consequential lossesalong with government disease surveillance,none of which are treated in the earlier work.

The Indemnity Design Problem

We use the asset value equations to solvethe overarching problem of indemnity de-sign that achieves public objectives for privatebiosecurity investment and disease report-ing behavior. In practice, we normally thinkof indemnification in connection with privateinsurance or government-subsidized risk man-agement programs like crop and flood insur-ance. Even though indemnities are requiredwhen takings occur via a government-directedcull, indemnities are also intended to serve apublic risk management function by provid-ing incentives to report infectious disease andto invest in preventive biosecurity (Ott 2006).For these reasons, we concern ourselves withthe design of an indemnification scheme thatachieves government risk management objec-tives. Later, we also discuss whether exist-ing compensation schemes are in conflict withstated risk management objectives in the pres-ence of information asymmetry.

Recall that our proposed payment structurepays one amount, �(�), to an infected farmerwho reports, and a lesser amount, �(�) – f(which may be negative), to an infected farmerwho does not report and is caught. As we de-scribe in detail below, our proposed indem-nity structure uses government transfers �(�)to address ex ante moral hazard (biosecurityactions) and fines f to address ex post adverseselection (disease reporting). We begin ouranalysis with the reporting problem, in whicha fine is imposed in response to a given report-ing strategy, r: f = 0 when � = 0 or when � >0 and the farmer’s strategy is r = 1; f > 0 oth-erwise when the farmer is caught.10 This struc-ture, which involves one value of f for each

10 We have modeled this as an adverse selection problem basedon the assumption that farmers know their infection level prior togovernment detection. In reality, there may be instances in whichneither party knows about the infection prior to government test-ing. This could perhaps be modeled by endogenizing the informa-tion set available to each party, an issue that we leave for futurework.

action—reporting or not, given � > 0— is anal-ogous to how adverse selection problems havebeen addressed in the literature (Rothschildand Stiglitz 1976). The fines mimic a “menuof contracts,” which induce the agent to re-veal private information. We introduce finesbecause reporting, which yields social bene-fits, is outside the scope of constitutionally re-quired compensation for takings. In the nextsection, we propose a method for setting thefine so that it achieves the desired reportingbehavior.

The moral hazard problem is addressed bysetting the transfer, �(�). Here the govern-ment’s transfer to the farmer is based on �,which is observed (verified as a result of test-ing) after infection is discovered or reported.The transfer influences the farmer’s incentivesto take biosecurity actions because the likeli-hood of becoming infected is influenced by b.We might therefore expect a lower marginalpayment for larger infection rates. This wouldmimic the risk sharing property of deductiblesor co-pays commonly used to address moralhazard problems in the principal–agent lit-erature (Laffont and Martimort 2002), thecrop insurance literature (Chambers 1989),and the broader insurance literature (Arrow1963; Raviv 1979).

In the presence of both adverse selectionand moral hazard, some combination of the in-struments used to address both types of infor-mation problems individually can be expectedto induce the desired biosecurity investmentand reporting behaviors from the agent in thecurrent application. However, to simplify theexposition, we discuss the different compo-nents of the indemnity rule (�(�) and f ) in-dividually. We proceed by addressing each ofthe two parts of the information problem in re-verse chronological order. That is, we proposea way to solve for the indemnification schemethat will (a) lead the farmer to report any in-fected animals to the government, thereby re-vealing his/her hidden information, and (b)create incentives for the government’s desiredlevel of biosecurity investment, thereby miti-gating the hidden action problem.

The Adverse Selection Problem—Reporting

Reporting is assumed to be socially desirable(all other things equal) because early detec-tion of infection limits the duration of a dis-ease outbreak event and has been found tobe the most important factor in minimizing to-tal economic damages from a livestock disease


( |b)

r

VI

r 1lim

0

f = f* along solid curve, where f*

selected so that (f*)=0

f = 0 along dashedcurve, such that

(0) is notconstrained to be

non-negative

Figure 2. Fines f are set to ensure positive marginal incentives to report for all prevalencelevels �

epidemic (UN-FAO 2002). The government’sobjective is to set fines in such a way thatreporting of suspected disease always occurs.The farmer is the agent in our principal–agentframework and we assume he/she chooses a re-porting strategy, r ∈ [0, 1], to maximize his/herdiscounted utility stream in the infected state,given by (8). This means that the marginal in-centive to report (positive, negative, or zero) isgiven by the sign of ∂VI(b, r, �(�), f , �)/∂r, andthe associated Kuhn–Tucker conditions implythe optimal private reporting strategy.

The principal wants to set the fine so that theagent always finds reporting to be privately op-timal. The difficulty is that the marginal incen-tives to report will differ depending on bothb and �, each of which are unobservable tothe principal. The principal must therefore seta single fine such that the agent finds it opti-mal to report regardless of the values of b and�. Specifically, the fine is set so that reportingoccurs even when the marginal incentives toreport are at their minimum value. The mini-mum value of the marginal incentives to reportare given by the expression

( f ) = min∀b,�

[limr→1

(∂VI (b, r, �(�), f, �)

∂r

)].

(9)

Choosing f such that (f ) ≥ 0 for all values ofb and � ensures that the farmer always has anonnegative marginal incentive to report. Thatis, as long as the agent, when operating at themargin, is indifferent between increasing anddecreasing his/her reporting strategy, then thefarmer will have a positive incentive to reportfor any value of � > 0. This concept is depicted

graphically in figure 2.11 Here, b is taken asgiven and the dashed curve indicates that thefarmer will not have a positive incentive to re-port disease for all levels of � when f = 0.We denote by f ∗ the fixed fine that achieves(f ∗) = 0 and ensures a nonnegative marginalincentive to report over the range of �.

The Moral Hazard Problem—BiosecurityInvestment

Given that f ∗ ensures reporting, we now turn tothe government’s problem of designing trans-fer payments, �(�), that provide incentives forbiosecurity investment. As indicated above inrelation to deductibles or co-pays used to ad-dress moral hazard problems, some amount ofrisk sharing between the government and thefarmer will be necessary to solve the hiddenaction problem. This can be seen by a compar-ison of the instantaneous utility of wealth inthe susceptible state and in the infected state(when r = 1) for the special case in which thefarmer is fully indemnified against all losses:�(�) = �G(�) + � G(�). In this case, utility wheninfected reduces to UI = U(�0), which is notdependent on biosecurity and is strictly greaterthan utility when susceptible if there is any pos-itive investment in biosecurity US = U(�0 −bw). In this situation, it is not clear why any-one would biosecure and it suggests that farm-ers will need to bear some share of the risk ofdisease-related losses for there to be incentiveto invest in biosecurity. The question we turn

11 Figure 2 does not reflect the shape of any particular functionalform for VI , rather it is provided to shore up the intuition associatedwith the proposed method for setting fines so that reporting occurs.


to now is how the government should struc-ture indemnities to facilitate risk sharing in aconstrained-efficient manner (i.e., an indem-nity that is second best due to asymmetric in-formation regarding the biosecurity action).

Assume the government takes into accountthe private net benefits of livestock produc-tion, VS(b,1, f ∗), the expected external dam-ages associated with the disease,

�(b)

(∫ 1

0D(�)g(� | b) d�

)

and the expected social cost of governmenttransfers,

�(b)�

(∫ 1

0�(�)g(� | b) d�

).

The function D(�) (with D′(�) > 0) repre-sents external damages due to infection.12

Damages are multiplied by the risk-adjusteddiscount factor �(b) = �(b, 1) = PSI (b)/[( +PI S(1) + PSI (b))] (with �′ < 0) to account forthe fact that damages only arise and govern-ment transfers are only made if the systemtransitions to the infected state, and that thistransition can occur numerous times in the fu-ture. The coefficient � > 0 represents the con-stant marginal cost of diverting funds to theindemnity program, which may include trans-actions costs (Alston and Hurd 1990).

Given this specification, the government’sobjective function in setting transfers to inducebiosecurity effort is

max�(�),b

VS(b, 1, f ∗)

−�(b)

(∫ 1

0[D(�) + ��(�)]g(� | b) d�

)

s.t. b ∈ arg maxb

VS(b, 1, f ∗)

(10)

12 The damage function is meant to capture disease spread exter-nalities without explicitly modeling the spreading process, as thiswould include multiple agents. Because ours is a model of a singleagent, we are essentially assuming that damages by one farmer areindependent of those caused by other farmers. Cross-farm impactson infection transition rates may also be important but are not mod-eled. The model could be expanded to account for these issues, aswell as market or social benefits associated with private livestockproduction, but with significant added complexity. For instance,Segal (1999, 2003) addresses contracting problems involving ex-ternalities in a different context. We view the present model as afirst step toward understanding the broader problem of livestockdisease management in a multiagent setting.

where the use of fine f ∗ drives r to 1, the agent’sunobservable choice of biosecurity effort con-strains the principal, and “argmax” denotes theset of arguments that maximize the objectivefunction that follows. The term VI does notappear as a separate argument in (10) because(a) the biosecurity choice is relevant when thefarm is currently susceptible, and (b) VI has al-ready been accounted for in setting the fine f toensure reporting occurs. Also note that E�[VI]is implicit in VS.

The term VS(b, 1, f ∗) can be written as fol-lows by evaluating equation (7) at r = 1 andf ∗:

VS(b, 1, f ∗)

= US(b)(b)

+ �(b)∫ 1

0U R

I (1, �(�), �)g(� | b) d�.

(11)

Equation (11) is the focus of farmer decisionmaking in the susceptible state. By the rev-elation principle (Dasgupta, Hammond, andMaskin 1979; Myerson 1979), the constraintin (10) ensures the agent’s optimal choiceof biosecurity effort b is constrained to beb, the government’s desired level of invest-ment. The regulator chooses �(�) to maximizefarmer utility while taking into account thecost of indemnities, monitoring, and responseto outbreak required to implement the chosendisease risk management policy. The agent’sfirst-order condition (FOC) with respect to bimplies the optimal private choice. We substi-tute the agent’s FOC for the constraint in prob-lem (10) so that it can be written as

max�(�),b

VS(b, 1, f ∗)

− �(b)E�[D(�) + ��(�)]

s.t.∂VS(b, 1, f ∗)

∂b= 0.

(12)

The approach of substituting the farmer’s FOCin for the constraint is called the first-order ap-proach (FOA) (see, e.g., Ross 1973; Harris andRaviv 1979; Holmstrom 1979; Rogerson 1985;Hyde and Vercammen 1997; Mirrlees 1999).The FOA is valid as a general solution methodfor problem (10) when the convexity of the dis-tribution function condition (CDFC) and themonotone likelihood ratio condition (MLRC)are satisfied (Rogerson 1985; Mirrlees 1999).We assume both of these conditions are sat-isfied in what follows. The CDFC is satisfied


by ∂2G(� | b)/∂b2 ≥ 0. The conditional prob-ability density function of disease satisfies theMLRC if gb(� | b)/g(� | b) is nonincreasing in� (Milgrom 1981).13 Whitt (1980) proved thatthe MLRC implies first-order stochastic domi-nance (FOSD), and is actually a much strongercondition than FOSD.

Because it may be hard to garner intu-ition from gb(� | b)/g(� | b), Milgrom (1981)provides an alternative explanation of therelevance of the MLRC in terms of the gov-ernment’s ability to infer the agent’s hiddenactions from the observation of �. He describesthe MLRC in terms of a principal who has aprior over the agent’s choice of effort (b), ob-serves the outcome realized (�), and then up-dates her prior to calculate a posterior on thebiosecurity effort choice. Denote the posteriorprobability distribution of b given observedoutcome � by F(b | �). Using Milgrom’s (1981)results, the nature of disease is such that theMLRC is equivalent to �0 ≤ �1 ⇒ F(b | �1) ≥F(b | �0)∀b, where �0 is a more favorable signalthan �1 that the agent exerted the desired levelof biosecurity effort.14 The importance of theassumptions about the nature of the MLRCwill become clearer when the conditions for di-vergence from the first-best indemnity and theimplications of the model for indemnity designare considered below.

Using the FOA, the Lagrangian for the gov-ernment’s problem is

L = VS(b, 1, f ∗) − �(b)E�[D(�) + ��(�)]

+

(∂VS(b, 1, f ∗)

∂b

)(13)

where is the shadow value of the constraint.The existence of the constraint, due to thefarmer’s freedom to make their own biosecu-rity decision, renders this a second-best prob-lem. In the appendix, we illustrate that > 0because the government would like the farmerto increase his/her investment in biosecuritygiven the optimal indemnity payment. That is,the optimal indemnity here is only second best

13 Milgrom (1981) finds the term should be nondecreasing in �,but in his model the action has the opposite effect on the distribu-tion as our action b. Accordingly, the sign is reversed here.

14 It should be noted that the interpretation of the MLRC inthe current context of a malady is different than the examplesmost often found in the literature because lower realized values ofthe random variable prevalence represent the desirable outcome,whereas in the typical wage contract example higher values of therandom variable output are desirable and signal greater effort.

due to the information problem; a first-best in-demnity, implemented in conjunction with re-quirements on the choice of b, could be usedto attain greater welfare in the absence of in-formation asymmetry (in which case wouldoptimally vanish). Holmstrom (1979) also findssuch a result.

Following Holmstrom (1979), pointwise op-timization with respect to �(�) yields the fol-lowing necessary condition, which must holdfor all �

∂U RI (1, �(�), �)

∂�(�)− �

= − ∂2VS(b, 1, f ∗)

∂b2

= − ∂U R

I (1, �(�), �)∂�(�)

[�′(b)�(b)

+ gb(� | b)g(� | b)

].

(14)

Condition (14) implicitly defines � SB(�), thesecond-best indemnity as a function of �.Specifically, condition (14) can be used to de-rive

� SB(�) = �G(�) + �G(�) − �0

+ U ′−1

�

1 + [

�′(bSB )�(bSB ) + gb(� | bSB )

g(� | bSB )

]

(15)

where bSB is the second-best value of b. Thistransfer payment compensates the farmer forasset and business interruption losses, net ofdisease-free profits, plus a positive inversemarginal utility term that arises due to riskaversion. Substituting this expression into UR

I ,we find that instantaneous wealth in the in-fected state equals the final term in (15). Thisterm ensures that the farmer’s utility in the in-fected state depends on the level of infection—that is, the farmer bears some risk for his/herbiosecurity choices. The level of risk borne bythe farmer depends on the argument of U ′−1.

The final term in equation (15) is a diminish-ing function (due to risk aversion) of its argu-ment, which is a ratio of the marginal cost ofdiverting funds to indemnities to the marginalinformation costs arising from the hidden ac-tion. If the government was not constrained bythe farmer’s biosecurity choice, then = 0 andthe argument would equal the marginal costof diverting funds to indemnities. With > 0,


the term �′/� + gb/g reflects a tradeoff be-tween the farmer’s ability to withhold privateinformation and the government’s ability to ac-cess this information. By maintaining privateinformation about his/her level of biosecurityeffort, the farmer is the sole provider of biose-curity protection in its bilateral relationshipwith the government and thus can operate as amonopolist who exerts information power. Al-ternatively, accessing this private informationallows the government to exert monopsonypower as the sole purchaser of biosecurity ef-forts (via the incentives provided by the in-demnity payment). Information is thereforethe key to exerting each of these powers, whichultimately determines the amount of risk thegovernment can induce the farmer to bear andthe information rents the farmer can earn as aresult of hidden action.

Though the government cannot observe bdirectly, it can make inferences about thechoice of b by observing the realized value of�. These inferences are made based on knowl-edge of the term gb/g, as indicated above inour discussion of the MLRC, and also the term�′/�. Holmstrom (1979, p. 79) points out thatthe term gb/g is simply the derivative of thelikelihood function ln[g(� | b)], when b is takenas an unknown variable, and suggests that gb/gmeasures how strongly one is inclined to inferfrom � that the agent did not undertake theassumed action. The larger is gb/g, the morewilling the government is to believe the farmertook the required actions and is therefore will-ing to increase the payment � SB(�). Essen-tially, the farmer is able to take advantage ofhis/her information power for larger values ofgb/g.

Now consider the term �′/�. This term canbe written as �′/� = (/[bSB])εPSI,b, whereεPSI,b = P′

SI(bSB)bSB/PSI(bSB), and measureshow responsive the transition probability tothe infected state is to biosecurity efforts. Thelarger is |�′/�| (since �′/� < 0), the less likelyis a transition to the infected state. If |�′/�| islarge and an infection occurs (which the gov-ernment will know about due to reporting),the government can infer that the farmer likelydid not undertake sufficient biosecurity efforts.Accordingly, the government reduces � SB(�)when |�′/�| is known to be large, thereby ex-erting information power in response to farmerreporting. This means that farmers bear morerisk in situations where their biosecurity effortsare more likely to prevent infection.

Finally, the following adjoint equation alsois necessary

∂L

∂b= ∂VS(b, 1, f ∗)

∂b

− ∂{�(b)E�[D(�) + ��(�)]}∂b

+

{∂2VS(b, 1, f ∗)

∂b2

}= 0.

(16)

Condition (16) determines while the con-straint in (12) (the agent’s FOC) determinesbSB. Using the agent’s FOC, condition (16) canbe used to solve for

= ∂{�(b)E�[D(�) + ��(�)]}∂b

×{

∂2VS(b, 1, f ∗)∂b2

}−1

.

(17)

The shadow value reflects the marginal impactof biosecurity on the sum of expected dam-ages and indemnity costs. This term is a com-ponent of the indemnity defined by (15), sothat the farm’s marginal external impacts areaccounted for indirectly through the use of theindemnity. The indemnity is required to dealwith both the insurance problem and the exter-nality problem because asymmetric informa-tion about the farm’s biosecurity investmentsprevents direct targeting of b to internalize thefarm’s marginal external impacts. Tinbergen(1952) finds that a single instrument cannotgenerally be used to address multiple problemsefficiently, and so the indemnity is second best.We describe how the farm’s external impactsinfluence the indemnity, and the implicationsfor biosecurity investment, in greater detail aswe compare the first-best and second-best pro-grams.

First Best Versus Second Best

How do second-best outcomes compare to thefirst-best outcomes? The first-best choice ofbiosecurity is the one that the governmentwould choose to make on its own, not havingto rely on the farmer to make the choice. Ac-cordingly, the first-best outcome arises whenthere are no constraints on the government’sproblem—that is, the regulator is neither con-strained by the farmer’s first-order conditionnor is truthful disclosure an issue, so that thereis neither an ex post adverse selection nor anex ante moral hazard problem. In this case, =0 so that condition (16) becomes


∂VS(b, 1, f ∗)∂b

= ∂{�(b)E�[D(�) + ��∗(�)]}∂b

= �′(b)∫ 1

0[D(�) + ��∗(�)]g(� | b) d�

+ �(b)∫ 1

0[D(�) + ��∗(�)]gb(� | b) d�

(18)

where �∗(�) is the first-best indemnity sched-ule. Condition (18) implicitly defines the first-best level of biosecurity, b∗. This conditionindicates that b∗ equates the marginal ex-pected private costs of biosecurity with themarginal impact of biosecurity on the sum ofexpected damages and indemnity costs. Thefirst RHS term after the second equality is neg-ative since �′ < 0. The final RHS term is alsonegative since both D and �∗ are increasingin � (we show �∗′(�) > 0 in equation (20) be-low) and since G exhibits FOSD with respectto b. Accordingly, ∂VS(b, 1, f ∗)/∂b < 0 in thefirst-best outcome. As ∂VS(b, 1, f ∗)/∂b = 0 inthe second-best case (in which the farmer’s re-sponse to the indemnity matters), condition(18) indicates that b∗ > bSB: the governmentwould ideally have the farmer invest more inbiosecurity than the farmer would choose forhim or herself. The first-best strategy involvesrequiring farmers to adopt b = b∗ (which isverifiable with no hidden action) in order tobe eligible for an indemnity payment of �∗(�)if they become infected. If farmers adopt b <b∗, then no indemnity payment would be madepostinfection.

Now consider how the first-best and second-best indemnities compare. The first-best in-demnity, �∗(�), is the special case of (15) inwhich = 0 and b is evaluated at b∗. Assum-ing bSB ≈ b∗, then we find that the followingmust hold15

(19a) � SB(�)

{<

>�∗(�)

⇔ gb(� | bSB)g(� | bSB)

+ �′(bSB)�(bSB)

{<

>0 .

(19b)

15 As noted above, bSB < b∗. However, we make the assumption,here and in what follows, that bSB ≈ b∗ to simplify the presentation.This does not affect the qualitative results, but would affect thequantitative results (e.g., such as the level of � where � SB(�) =�∗(�)). The sign of (19a) and (19b) follow from the derivative rulefor inverse functions and the risk aversion of the farmer.

Condition (19) indicates that farmers receiveinformation rents relative to the first-best case,under the conditions defined by (19b), whilethe government reduces payments below thefirst-best level under the conditions definedby (19a). The relative payment levels in (19)are a result of the same tradeoffs that arosein the second-best payment levels defined by(15): they depend on the realized value of �,which the government views as evidence of thefarmer’s unobservable biosecurity effort.

From (15), larger marginal external impacts(a larger ) have the effect of: (a) reducing� SB relative to �∗ when � SB < �∗, and (b) in-creasing � SB relative to �∗ when � SB > �∗. Thatis, marginal external impacts create a wedgebetween the first-best and second-best indem-nities, driving � SB and �∗ farther apart for eachvalue of � except �T . The effect is to generategreater incentives, in the second-best case, forfarmers to consider the effects of their choiceof b on ex post levels of �: when marginal exter-nal impacts are high, the farmers stand to gainmore when � is low and to lose more when �is high. In this respect, the indemnity workssimilarly to a pollution abatement subsidy, inwhich polluters are paid less when they pollutemore (Baumol and Oates 1988). First-best in-demnities do not need to provide such incen-tives because the level of b is observable andcould therefore be targeted with a separate in-strument such as a mandate (e.g., indemnitiesmight only be paid if the farmer adopted therequired level of biosecurity).

Though the externalities drive a wedge be-tween the first-best and second-best indem-nities, there will be one value of � at whichthe two are equivalent. Define the thresholdlevel of infection at which � SB(�) = �∗(�)as �T , such that gb(�T | bSB)/g(�T | bSB) +�′(bSB)/�(bSB) = 0. This means that � SB(�) <�∗(�) for � > �T , and � SB(�) > �∗(�) for � <�T .16 How small is �T? It should be small

16 An anonymous reviewer points out that � SB(�) > 0 as � → 0and asks whether the farmer would have incentives to intentionallyinfect his/her herd to collect the indemnity payment. If bSB > 0,which must be the case when there is an incentive to invest inbiosecurity, then VS(bSB, 1, f ∗) > VS(0, 1, f ∗) and the farmer wouldnot want to increase PSI by decreasing b to zero. But PSI < 1 whenb = 0. What if the farmer could costlessly increase PSI to one?Denote the net present value of being susceptible in that case (i.e.,when b = 0 yields PSI = 1) by VS(0, 1, f ∗)|PSI=1 . We can show thatVS(0, 1, f ∗) > VS(0, 1, f ∗)|PSI=1 when US(0, 1) >E� [UI ], whichmust hold when it is optimal to invest at the level bSB > 0. Hence,by transitivity, VS(bSB , 1, f ∗) > VS(0, 1, f ∗)|PSI=1 : the indemnitypayment should not encourage purposeful infection. Purposefulinfection may be optimal if the farmer could ensure that the diseasedoes not spread too much within his/her herd, so as to ensure alarger indemnity. We note that: (a) it may not be easy to ensurean outcome with low prevalence, particularly for nonendemic and


*

ˆ

SB1

SB2

SB3

T0

Figure 3. Possible shapes for the first-best indemnity payment schedule, � ∗(�), and the second-best indemnity payment schedule, � SB(�)

enough to infer that sufficient biosecurity ef-forts have been undertaken. In particular, �T issmaller than the value of �, denoted �, at whichgb(� | b) = 0. This point in the distribution is ofinterest because for � < � the marginal benefitof biosecurity, in terms of reducing the cumu-lative density of prevalence, is increasing. Asmaller � yields even larger marginal benefitsof biosecurity.

By structuring indemnities according to(19), the government provides very strong in-centives for a farmer to undertake significantbiosecurity efforts. If the government observes� > � it will pay farmers for culled animals ata lower rate than it would if it could observebiosecurity actions directly; this is because arelatively high level of infection suggests asmall likelihood of private biosecurity effort.Even for observed levels of infection �T < � <�, the level of effort inferred by the govern-ment is still sufficiently low that the farmercannot extract information rents from the gov-ernment. Only if the level of observed infectionfalls below the critical value �T will the govern-ment be convinced that the agent has investedin biosecurity at a high enough level to give upinformation rents to the farmer.

The relationship between the prevalencelevel and size of indemnities is also of greatinterest. To evaluate the slope of � SB(�),

highly contagious diseases, and (b) we would have to analyze such astrategy as a repeated game because the government would likelygrow weary of paying indemnities to the same individuals timeafter time.

differentiate condition (15) with respect to �to get

� ′(�) = �′G(�) + � ′

G(�)

+(

U ′

−U ′′

)

∂

(gb(� | bSB )/g(� | bSB )

)∂�(

1 + [

gb(� | bSB )g(� | bSB ) + �′(bSB )

�(bSB )

])

(20)

where U ′ = ∂URI /∂� and U ′′ = ∂2UR

I /∂�2. Thefirst two RHS terms are positive and equal theslope of the first-best indemnity �∗(�) (since = 0 in the first-best case). The third termarises in the second-best case, and the sign ofthis term depends on the value of �. In thethird RHS term, (U ′/(−U ′′)) > 0 for a risk-averse agent, the numerator is negative bythe MLRC, and the sign of the denominatoris determined by the sign of � = gb(� | bSB)/g(� | bSB) + �′(bSB)/�(bSB) and the relativemagnitude of terms, which for a given b de-pends on �.

Several different possibilities for the shapeof � SB(�) relative to that of �∗(�) are depictedin figure 3. For very low levels of �, � SB(�) >�∗(�). The second-best indemnity may be ini-tially increasing or decreasing based on thesign of equation (20). This is because � > 0 forlow values of �, making the third RHS termin (20) negative and the sign of � ′(�) ambigu-ous. The negative third term means the slope of� SB(�) is initially less than the slope of �∗(�),so that these curves eventually intersect and


become equal at �T . When � > �T , then � < 0and the denominator of the third RHS term isof ambiguous sign. Denote � (with � > �T) tobe the value of � such that the denominator ofthe third RHS term vanishes; the slope of thesecond-best indemnity goes to –∞ and thereis a discontinuity in the graph of � SB(�). Thismeans the slope of � SB(�) becomes negativeprior to �. If � < 1, this suggests that for anyobserved prevalence �T < � < �, the second-best indemnity should be paid at a level belowthe first-best level to maintain the appropriateincentives to invest in b.17

While it is mathematically possible for theslope of the second-best indemnity functionto be positive and/or negative over the rangeof �, an indemnity schedule that is mono-tonically decreasing in the prevalence level,such as � SB

1 (�), would provide the strongestincentives for biosecurity.18 In such cases, theinformation rents paid to the farmer would bestrictly decreasing with prevalence up until � =�T . Beyond this point, the reduction in pay-ments relative to the first-best case would beincreasing. Biosecurity incentives would seemto be weaker under the curves labeled � SB

2 and� SB

3 , which seem contrary to the government’sobjective.

The extent to which observed prevalence isan accurate signal of actual preventive biose-curity effort is clearly important for imple-menting the indemnity schedule, � SB(�). Itis conceivable that for diseases that are ex-tremely contagious (i.e., foot and mouth dis-ease, highly pathogenic avian influenza, exoticNewcastle’s disease, or classical swine fever)an individual’s herd could become infected re-gardless of the extent of biosecurity measurestaken ex ante. For this reason, a “one size fitsall” policy that only pays indemnities on thebasis of observed prevalence levels is likely tobe problematic in practice.

17 It should be noted that for � > � the slope of the second-bestindemnity is expected to be +∞ as you approach � from the right.This suggests that it is possible that the first- and second-best in-demnities cross again at another point � > �, but it does not seemlikely that an information reward would be optimal at high levelsof �. Moreover, whether or not � falls within the unit interval isunknown.

18 For � < �T , the condition required for a monoton-ically decreasing second-best indemnity schedule like � SB

1(�) in figure 3 is �′

G (�) + � ′G (�) < |[U ′/(−U ′′)] [∂(gb(� | b)/

g(� | b))/∂�]/(1 + �)|. This condition may be reasonable inpractice because �′

G (�) + � ′G (�) is likely a very small positive

quantity at lower values of �. Alternatively, the condition thatgives rise to the increasing segments of � SB

2 and � SB3 over the

relevant range of � is �′(�) + � ′(�) > |[U ′/(−U ′′)] [∂(gb(� | b)/g(� | b))/∂�]/(1 + �)| for that range of �.

Policy Implications

Our model uses two distinct mechanisms toprovide incentives for biosecurity and truthfuldisclosure: (a) indemnities to achieve desiredlevels of biosecurity, and (b) fines that in-duce disclosure of disease status (alternatively,these mechanisms can be viewed as a differ-ential indemnity schedule based on whetheran infected farmer reports or not). By usingtwo distinct policy instruments, individuallydesigned with each information problem inmind, it is possible to create clear incentivesfor farmers to behave in a manner that is con-sistent with government risk management ob-jectives.

Status quo indemnification for livestock dis-ease losses by U.S. Department of Agricul-ture (USDA) has paid producers on the basisof “compensation value” equal to “fair mar-ket value assuming disease-free status” (Ott2006, p. 72). This amount is necessarily greaterthan the true market value of diseased ani-mals culled by the government and is intendedto create incentives for reporting. The govern-ment has also recognized that unless farmersface some uncompensated losses as a result ofoutbreak they cannot be expected to take pre-ventive biosecurity measures and thus does notcompensate farmers for consequential losseswhen issuing indemnities. Animal health au-thorities have relied on a single mechanism—indemnities—to facilitate both ex ante biose-curity effort and ex post reporting. By using asingle mechanism to induce biosecurity and re-porting simultaneously, the incentives for eachindividual private action are not clear.

Direct comparison of the relative magnitudeof status quo indemnities and the second-bestindemnities implied by our analysis is not pos-sible, but the major difference is the shape ofthe indemnity schedules implied by the differ-ent policies. Status quo policy suggests the in-demnity schedule is strictly increasing in � (justlike the first-best indemnity, �∗(�), depictedin figure 3), while the second-best indemnityimplied by condition (19) is declining over atleast some segment of the range of � . It is notat all clear how the incentives created by thestatus quo policy facilitate the government’sjoint objectives. An upward sloping indemnityschedule, in the absence of any penalty for notreporting, may actually create incentives for in-fection when you consider that the status quohas sought to use indemnities based on thedisease-free fair market value of livestock as


a means of resolving the ex post adverse selec-tion problem.

In an effort to induce early reporting,Belgium and the Netherlands, in the case ofepidemic livestock diseases, no longer com-pensate producers for dead animals and onlypartially compensate them for diseased stock(Horst et al. 1999). This approach, arrived atas a result of these countries’ experiences withclassical swine fever and foot and mouth dis-ease, shares some important elements with oursecond-best indemnities. First, while there isnot an explicit fine for not reporting, there isa penalty to waiting to report since dead ani-mals fetch no payment. This feature can help toachieve incentive compatibility with reducedor eliminated monitoring costs. Second, par-tial compensation for already-infected animalsshifts some of the risk to farmers, as do our pay-ments. An indemnity plan that does not shiftrisk in this fashion may actually create incen-tives for infection, which could be one problemassociated with status quo U.S. policy.

The discussion of incentive compatibility ap-plies not only to public policy, but also to thedevelopment of private insurance for livestockdisease protection. If private coverage is avail-able to farmers, the incentives provided bylivestock insurance contracts could potentiallybe in competition with the objectives of pol-icy while satisfying the individual objectivesof producers (i.e., income smoothing as riskmanagement). Careful consideration in the de-sign of private market coverage for livestockdisease losses is required in order to ensurethat public policy and private risk manage-ment products are jointly incentive compati-ble. Also, design of public policy should takeinto account the role that private coveragecould play in achieving public policy objectivesand how government decisions may hinder orbolster private markets for insurance. If thisis not the case, then the constrained efficientresult analyzed here will not be achievable.

There are a few limitations and possible ex-tensions to this work that are worth noting. Thefirst limitation is the political feasibility of thefine approach to force reporting. Provided � –f > 0, we believe reducing indemnities for dis-eased animals is consistent with the notion of“fair market value” and therefore satisfies anyconstitutional requirement to compensate fortakings. Indeed, the “fair market value” of dis-eased animals is likely zero or a salvage value atbest (not the disease-free value of the infectedanimals as in the status quo policy). Consti-tutional inconsistencies may arise, however, if� – f < 0. More research would be needed

to know whether such an outcome is actuallya concern, but it could be an issue for somefarms since information asymmetry results inuniform application of f —meaning f might beof reasonable magnitude for some farms butcould be relatively large for others.

Second, our model does not consider the ex-ternalities that occur because of private report-ing and biosecurity decisions. It is clear thatone farm’s decision to biosecure is likely influ-enced by perceptions about the likelihood ofinfection dependent on their neighbor’s biose-curity choices. Reporting infectious disease onone farm will result in a quarantine of sur-rounding farms and impose potentially largeand widespread costs. The effect of these ex-ternalities on indemnities relates to the liter-ature on contracting with externalities (e.g.,Segal 1999, 2003) and is likely a fruitful avenuefor future work.

Finally, we did not consider multiperiod in-teractions and intertemporal correlations ofagents. These considerations could conceiv-ably lead to different auditing implications aswas found in Sheriff and Osgood (2008).

[Received February 2008;accepted November 2008.]

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Appendix

Generalize the farmer’s FOC, which is the con-straint in problem (12), to be

∂VS

∂b= c(A.1)

where c is a constant. Here, c = 0 for the farmer’sproblem, while we indicated in condition (18) thatc = c∗ < 0 for the first-best outcome. Using thisnotation, the Lagrangian is

L = VS(b, 1, f ∗) − �(b)E�[D(�) + ��(�)]

+

(∂VS

∂b− c

).

(A.2)

From (A.2), we can derive − = ∂L/∂c. Clearly,∂L∂c |c=0 < 0: an increase in c when c = 0 means thesolution moves farther away from the first-best out-come of c∗ < 0, implying a reduction in welfare.Hence, > 0.

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