adapting contract theory to fit contract farming

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ADAPTING CONTRACT THEORY TO FIT CONTRACT FARMING STEVEN Y. WU This article discusses the current state of contract theory and its usefulness for conceptualizing issues related to agricultural contracting. The paper will explore the limitations of existing theory for applied work, and what methodological improvements are needed to enhance the usefulness of the theory to agricultural economists. One pervasive problem is that the economic literature on contracts is rather fragmented and the various methodological strands are narrow in their focus. As such, agricultural economists should engage in methodological research to develop applied contracting models that can capture higher-order features of real-world agricultural contracts while delivering generalizable comparative statics predictions because contracting continues to expand along the entire modern food marketing channel. In the latter part of this article, a simple model is developed to illustrate how classic methodological approaches can be combined with recent developments in contract and game theory to construct applied theory models that are useful for capturing some important features of agricultural contracts. Key words:Agricultural contracts, contract theory, food supply chain, relational contracts. JEL codes: D43, D82, D86, Q12, Q13. According to MacDonald and Korb (2011), the use of contracts in U.S. agriculture has been increasing over the last several decades. In 1969, contracts governed only 12% of the total value of U.S. agricultural production, but this rose to 39% in 2008 and there is no evidence that this trend will decelerate because modern food marketing channels are increasingly dominated by food manu- facturers and retailers that emphasize food product innovation and food safety, both of which require a high degree of coordination between firms in different segments of the channel (Myers, Sexton, and Tomek 2010). Despite the widespread use of contracts in agriculture, it is curious that agricultural economists have not, for the most part, lever- aged the cutting-edge contract theoretic tools Steven Y. Wu is an associate professor in the Department of Agricultural Economics at Purdue University. The author gratefully acknowledges financial support provided by USDA- NIFA Award no. 2010-65400-20430, and extends thanks to James Vercammen and two anonymous reviewers for detailed comments that greatly improved the paper. Lu Liang also provided useful technical discussions regarding the model. Cor- respondence may be sent to: [email protected]. This article was subjected to an expedited peer-review pro- cess that encourages contributions that frame emerging and priority issues for the profession, as well as methodological and theoretical contributions. that have been developed in recent years. While agricultural economists were active in the late 1990s and early 2000s in lever- aging contract theory to study agricultural problems, this seems to have waned in recent years despite the rising trend of agricultural contracting. 1 Moreover, despite a long tra- dition of agricultural economists making significant methodological contributions in many areas of economics (e.g., applied econo- metrics and consumer/producer theory), this does not seem to have carried over to contracts. 2 The lack of methodological advancement in contract theory within the agricultural eco- nomics community has limited agricultural economists to providing only incomplete analyses of recent policy issues. For example, 1 For example, in the late 1990s and early 2000s, Goodhue (2000), Hueth and Ligon (1999a), Hueth et al. (1999), Hueth and Ligon (1999b, 2001), Hueth and Melkonyan (2004), Knoeber and Thurman (1995), Leegomonchai and Vukina (2005), and Tsoulouhas and Vukina (2001) all used contract theory to model specific agricultural contracting or policy issues. Since 2005, the author is only aware of the work of Lee, Wu, and Fan (2008), and Wu (2010). 2 Two exceptions include early papers by Innes (1990) and Innes and Sexton (1994). However, the author is not aware of any other papers since that time. Amer. J. Agr. Econ. 96(5): 1241–1256; doi: 10.1093/ajae/aau065 Published online August 6, 2014 © The Author (2014). Published by Oxford University Press on behalf of the Agricultural and Applied Economics Association. All rights reserved. For permissions, please e-mail: [email protected] at Serials Department on October 26, 2014 http://ajae.oxfordjournals.org/ Downloaded from

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ADAPTING CONTRACT THEORY TO FIT

CONTRACT FARMING

STEVEN Y. WU

This article discusses the current state of contract theory and its usefulness for conceptualizingissues related to agricultural contracting. The paper will explore the limitations of existing theoryfor applied work, and what methodological improvements are needed to enhance the usefulnessof the theory to agricultural economists. One pervasive problem is that the economic literature oncontracts is rather fragmented and the various methodological strands are narrow in their focus.As such, agricultural economists should engage in methodological research to develop appliedcontracting models that can capture higher-order features of real-world agricultural contractswhile delivering generalizable comparative statics predictions because contracting continues toexpand along the entire modern food marketing channel. In the latter part of this article, a simplemodel is developed to illustrate how classic methodological approaches can be combined withrecent developments in contract and game theory to construct applied theory models that areuseful for capturing some important features of agricultural contracts.

Key words: Agricultural contracts, contract theory, food supply chain, relational contracts.

JEL codes: D43, D82, D86, Q12, Q13.

According to MacDonald and Korb (2011),the use of contracts in U.S. agriculture hasbeen increasing over the last several decades.In 1969, contracts governed only 12% of thetotal value of U.S. agricultural production,but this rose to 39% in 2008 and there isno evidence that this trend will deceleratebecause modern food marketing channelsare increasingly dominated by food manu-facturers and retailers that emphasize foodproduct innovation and food safety, both ofwhich require a high degree of coordinationbetween firms in different segments of thechannel (Myers, Sexton, and Tomek 2010).

Despite the widespread use of contractsin agriculture, it is curious that agriculturaleconomists have not, for the most part, lever-aged the cutting-edge contract theoretic tools

Steven Y. Wu is an associate professor in the Departmentof Agricultural Economics at Purdue University. The authorgratefully acknowledges financial support provided by USDA-NIFA Award no. 2010-65400-20430, and extends thanks toJames Vercammen and two anonymous reviewers for detailedcomments that greatly improved the paper. Lu Liang alsoprovided useful technical discussions regarding the model. Cor-respondence may be sent to: [email protected].

This article was subjected to an expedited peer-review pro-cess that encourages contributions that frame emerging andpriority issues for the profession, as well as methodologicaland theoretical contributions.

that have been developed in recent years.While agricultural economists were activein the late 1990s and early 2000s in lever-aging contract theory to study agriculturalproblems, this seems to have waned in recentyears despite the rising trend of agriculturalcontracting.1 Moreover, despite a long tra-dition of agricultural economists makingsignificant methodological contributions inmany areas of economics (e.g., applied econo-metrics and consumer/producer theory),this does not seem to have carried over tocontracts.2

The lack of methodological advancementin contract theory within the agricultural eco-nomics community has limited agriculturaleconomists to providing only incompleteanalyses of recent policy issues. For example,

1 For example, in the late 1990s and early 2000s, Goodhue(2000), Hueth and Ligon (1999a), Hueth et al. (1999), Huethand Ligon (1999b, 2001), Hueth and Melkonyan (2004), Knoeberand Thurman (1995), Leegomonchai and Vukina (2005), andTsoulouhas and Vukina (2001) all used contract theory to modelspecific agricultural contracting or policy issues. Since 2005, theauthor is only aware of the work of Lee, Wu, and Fan (2008),and Wu (2010).

2 Two exceptions include early papers by Innes (1990) andInnes and Sexton (1994). However, the author is not aware ofany other papers since that time.

Amer. J. Agr. Econ. 96(5): 1241–1256; doi: 10.1093/ajae/aau065Published online August 6, 2014

© The Author (2014). Published by Oxford University Press on behalf of the Agricultural and Applied EconomicsAssociation. All rights reserved. For permissions, please e-mail: [email protected]

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in June 2010, the USDA’s Grain Inspec-tion, Packers, and Stockyard Administration(GIPSA) proposed new rules to amend thePackers and Stockyard Act (2000), which isthe major anti-trust statute for agriculturalinput markets. One of GIPSA’s key pro-posals is that growers do not have to provecompetitive harm when suing for breach ofcontract that results only in specific harm tothe grower. However, the rules have beencontroversial, leading some U.S. Senators toquestion GIPSA’s “impartiality” (SouthernFarm Network 2011). The position takenby these senators appear to be consistentwith the findings of a number of economicstudies, which have found little evidence ofmarket power using traditional tools fromindustrial organization (U.S. GovernmentalAccountability Office 2009). However, whiletraditional tools search for evidence ofmarket power by identifying monopsonymark-downs relative to competitive pricing,contract theorists have long known that care-fully constructed contractual mechanisms canmitigate welfare losses from market power.A similar point was also made by Sexton(2013), who points out that it is difficult touse traditional oligopoly/oligopsony modelsto quantify the existence of market power infarm procurement settings involving the useof contracts. Thus, the lack of methodologicalintegration between traditional input/output(IO) models and contract theory has leftagricultural economists with very little to sayabout the potential contracting outcomes thatmay occur under the GIPSA rule.

This article discusses the usefulness of con-tract theory for conceptualizing contractingproblems in agriculture. Moreover, it add-resses the current state of the theory andpresents the author’s views on what method-ological improvements are needed for thetheory to be useful for modeling importantfeatures of agricultural contracts and formaking generalizable predictions about howpolicy interventions and other exogenousshocks might affect contracting outcomes.One possible explanation for why appliedresearchers have had difficulty making meth-odological contributions is that the gen-eral economics literature on contracts hashistorically been rather fragmented. Thisfragmentation has created methodologicaldivides where applied researchers who lever-age particular methodological approachesalso implicitly take sides in ideological deb-ates among contract theorists. Thus, the scope

of methodological contributions made byapplied researchers can be limited as themajor strands of contract theory can berather narrow in their focus in the sense thatsome methodological strands focus on tightmodeling frameworks, logical consistency,and generalizability of results, whereas otherstrands focus on real-world applicability atthe expense of generalizability and internalconsistency.

Canonical Contract Theory: The Completeand Incomplete Contracts Approaches

Since the early 1970s, contract theory hasevolved into a theoretical field within main-stream economics. Contract theorists typ-ically impose simplifying assumptions todevelop tractable models and/or make ratheridealized assumptions about what types ofcontracts are possible and how performanceis governed. Many of the assumptions aresufficiently controversial such that therehas been a methodological divide betweenthose who advocate the “complete contracts”methodology and those who advocate the“incomplete contracts” approach (Tirole1999).

The complete contracts approach hasdominated the literature and is consideredthe textbook model on contracts. Classicapplications include structuring incentivesin order to overcome asymmetric infor-mation problems such as moral hazardand adverse selection. The key assump-tion of complete contract theory is that,in a contractual relationship between twoparties, a contract governs all aspects ofperformance under all contingencies, andtherefore the key is to design an optimalstate-contingent plan. Because the contract-ing parties are able to foresee all relevantcontingencies, there should be no “surprise”contingencies that will arise. Therefore, allperformance obligations across all contin-gencies of both parties can be specified inthe initial contract. Moreover, performanceobligations under this contract can be third-party verified and enforced, and sufficientlegal penalties exist to deter each partyfrom deviating from the contract.3 Taken

3 Although hidden information such as agent effort or type isnon-verifiable, it is well-known that if there are variables thatare correlated with hidden information, a complete contract can

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together, this set of assumptions impliesthat no party to a complete contract has expost discretion to deviate from the upfrontagreement. Indeed, the presence of discre-tionary latitude to deviate from the upfrontagreement is synonymous with incompletecontracting because there are unspecified orunenforceable contingencies in a contract.

Even casual observation of real worldcontracts suggest that most are not fullystate-contingent and that at least one con-tracting party has some degree of ex postdiscretionary latitude. This discretionary lat-itude can be damaging in an efficiency sensebecause if the last mover has discretionarylatitude to deviate from the upfront agree-ment and honoring the agreement is costly,then the last mover will behave opportunis-tically (e.g., shirk on promised bonuses). Ifthe other party to the contract is forward-looking, she may anticipate this and shirkon her obligations as well. The net effectcould be that both parties will underinvest inperformance, or the parties will refuse to con-tract in the first place. Even when there is noclear last mover and/or important variablesare only contractible ex post after a state isrealized, the parties may still have to engagein ex post bargaining, which can also lead toinefficiencies.

The concern over ex post discretion wasone of the driving forces behind the “incom-plete contracts” movement, which consistsof two sub-strands: transactions cost theory(Klein and Alchian 1978; Williamson 1979)and property rights theory (Grossman andHart 1986; Hart and Moore 1990).4 However,it is important to point out that the incom-plete contracts approach is methodologicallyquite different from the complete contractsapproach in that contractual form does notendogenously emerge from an optimiza-tion problem as in the complete contractsapproach. Instead, contract structure is typi-cally arbitrarily and exogenously imposed ona problem so that the researcher can focusinstead on what types of institutions or pat-terns of asset ownership can minimize thedamage caused by unspecified contingenciesand ex post discretion.

still be specified around these variables. There will typically besome loss in efficiency due to incentive compatibility constraints,but the contract will still be fully state-contingent.

4 Please refer to Gibbons (2005) or Wu (2006) for surveys ofthis literature.

Given the methodological differencesbetween the two approaches, it is no surprisethat there has been an ideological dividewhere scholars from each side have been crit-ical of the others’ approach. One of the mostobvious criticisms of the complete contractsapproach is that many of the contracts thatemerge from constrained optimization prob-lems are overly complex and often do notmatch what is observed in practice. More-over, it is rather rare that a complete contractgoverns every aspect of performance. Inpractice, many formal contracts serve only asdefault obligations that are triggered if someinformal relational agreement breaks down.5In turn, critics of the incomplete contractsapproach often argue that the literature lacksrigorous foundations, many assumptions aread hoc, and that some of the models are inter-nally inconsistent. As an example of the lattercriticism, Tirole (1999) points out that someincomplete contracting models assume thatagents are boundedly rational, which pre-vents them from writing complete contracts,and yet the models are solved using dynamicprogramming where agents are able to per-fectly foresee their future payoffs. Anothersharp criticism described by Schmitz (2001) isthat the incomplete contracts approach oftentakes two arbitrarily defined simple contracts,say C1 and C2, that are both suboptimal, andcompares their efficiency properties. Thereis no explanation concerning how these sim-ple contracts emerged because they are notderived from first principles. Thus, one cannotknow whether there exists a third contract,say C3, that might implement first best. Theproblem with these ad hoc comparisons isthat it is difficult to know whether the analy-sis of institutions or organization form underad hoc contracts such as C1 and C2 hold onlyfor these two contracts, or hold more gen-erally. Indeed, many of the analytic modelsused in the incomplete contracts approachare motivated by very specific case stud-ies such as the classic Fisher Body/GeneralMotors vertical integration problem. Thus,many of these models appear to resemblestructured case studies.

Many of the criticisms of the two majorcontracting methodologies are also rele-vant for applied researchers working on

5 Dixit (2007) discusses this issue and develops some formalmodels.

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agricultural contracts. Specifically, the canon-ical complete contracts model may not beable to capture higher-ordered features ofactual agricultural contracts. On the otherhand, the more flexible incomplete contractsapproach can potentially capture higher-ordered features of agricultural contracts, butmany of the assumptions may be too ad hocto generate comparative statics predictionsthat hold beyond very specific cases.

Recent “second generation” models (e.g.,Aghion and Holden 2011) of incompletecontracts that emphasize relational contractsand endogenous incomplete contracts showsome promise for bridging the traditionaldivisions and offering applied researchersa broader range of tools. Loosely speaking,relational contracts are incomplete contractsthat govern performance via informal incen-tives, which are self-enforced via a repeatedgame; that is, it is an equilibrium outcomefor the parties to honor their agreements ifthey care sufficiently about future tradingoutcomes; Levin (2003) provides a formaldefinition. Relational contracting modelsexamine incomplete contracts derived fromfirst principles and thus have great potentialto deliver generalizable results that applyacross a variety of environments.

Important Features of Agricultural Contracts

Even casual observation of actual agriculturalcontracts reveals that many of them combinea curious mixture of very precise state-contingent terms that govern quality/defectsand very loose guidelines for other importantobligations. In particular, quantity commit-ments such as scheduling/delivery timing,volume purchased by the contractor or raisedby the grower (in production contracts),and/or changes in quantity from year-to-year/flock-to-flock are only described broadly,if at all. On the surface, this seems puzzlingbecause quantity sold in a given time frameseems to be as important as quality whendetermining grower revenue and contractorcosts. Thus, in practice most contracts do notappear to be fully state-contingent, leavingat least one party with ex post discretionarylatitude over some obligations. There is ofcourse some heterogeneity across contractsboth within and across commodities but itseems fairly clear that most contracts areincomplete and the patterns of heterogene-ity seem to be with respect to the degree of

incompleteness rather than whether contractsare complete or incomplete in an absolutesense.

Even when one contract is apparentlymore complete than another, another channelthrough which incompleteness can arise is ifit is too costly to enforce a contract (Tirole1999). For example, the typical broiler pro-duction contract is far more detailed thansay, a processing tomato marketing contract.The former can be more than 10 pages long,whereas the latter can be as short as onepage. So it appears as if the typical broilerproduction contract is more “complete”than the typical processing tomato contract.However, the institutions that verify qual-ity are very different across the two sectors.For example, a third-party entity knownas the Processing Tomato Advisory Board(PTAB), which is jointly funded by growersand processors, conducts quality grading oftomatoes, whereas performance measure-ment is conducted by the integrator in broilerproduction. Despite more detailed contracts,the lack of third-party verifiability limits theenforceability of the terms in broiler con-tracts. Without third-party enforcement, therewill exist discretionary latitude to deviatefrom the agreement since it is hard for athird-party such as a court or regulator toverify that a deviation has occurred. Somestates, such as Georgia, have passed laws toimprove the transparency of performancemeasures in broiler contracts. Footnote 1 ofWu and Roe (2007) points out that GeorgiaHouse Bill 648 requires integrators to pro-vide “any statistical information and dataused to determine compensation paid” at thegrower’s request.

Another complicating factor in pin-ning down the exact source of contractualincompleteness is that there appears to besubstantial heterogeneity in contractual struc-ture even across contractors for the samecommodity. For example, even with a cred-ible third-party that measures the qualityof processing tomatoes, some processorsin some years appear to leave out state-contingent payments for quality factors. Thisis puzzling because it is relatively inexpen-sive to condition payments on quality. This isconsistent with findings by Scott (2003), whoexamined a large number of actual businesscontracts and found that a significant numberappeared to be endogenously incompletein that they do not condition on even ver-ifiable performance measures. If contracts

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are indeed endogenously incomplete, thenmodifications must be made to both completeand incomplete contract models.

Repeat contracting is another commonfeature of agricultural contracts. Footnote 2of Wu and Roe (2007) states the following:“In personal communication, senior membersof the California Processing Tomato GrowersAssociation suggested to one of the authorsthat, in any given year, processors will re-sign90% of growers from the previous year. Thus,repeat trading is quite common.” Hamilton(2001) suggests that many broiler contractstend to continue to trade repeatedly acrossmany flocks until terminated. Leegomonchaiand Vukina (2005) make a similar point thatbroiler contracts are repeat contracts acrossmany flocks. Repeat trading is easy to handlebecause we know from the game theoretic lit-erature that repeat trading can be useful formitigating the inefficiencies that arise in one-shot games such as the Prisoner’s Dilemma.Since contracting relationships are similarto sequential Prisoner’s Dilemma games, expost discretionary latitude can be disciplinedunder repeat trading and can provide us withsome insight into why contracts might beendogenously incomplete.

The fact that many agricultural contractsare relational and therefore incompleteimplies that at least one party to the contractwill have ex post discretionary latitude. Forinstance, many agreements to buy or sell agri-cultural commodities are based on handshakeor oral agreements over the telephone.6 Thislatitude to deviate from the upfront agree-ment means that the contracting parties mustlearn to manage counterparty risk, whichrefers to the risk that one’s counterpartyto a contract will not fulfill his/her end ofthe agreement. While this risk is largelyignored in canonical contract theory, it is areal and pervasive concern in the farmingand agribusiness world (Narduzzo 2010).While there is always some counterparty riskfrom exogenous events outside of the controlof the contracting parties even under com-plete contracts, counterparty risk is magnifiedunder incomplete contracts since partieswith discretionary latitude can endogenouslychoose not to honor their obligations when itis not profitable to do so. However, classical

6 While informal agreements can be made third-party enforce-able under certain conditions, the burden of proof is higher whenthere is no written confirmation (Johnson and Gunkel 2009).

contract theory does not typically incorpo-rate counterparty risk into contract designproblems; instead, the focus is on the trade-off between risk versus incentives, where“risk” refers to randomness in translating theagent’s effort into the performance outcomethat the principal cares about. This risk islargely exogenous and can be dealt with byadjusting the power of incentives to achievesecond-best outcomes.

Counterparty risk is pervasive in agricul-ture. Indeed, section 7 of the Iowa ProducerProtection Act states that “One of thegreatest risks for a producer in produc-tion contracting is the risk of not gettingpaid. This section establishes a first pri-ority lien for a producer for amounts dueunder a production contract involving live-stock, raw milk, or crops,” (Iowa AttorneyGeneral’s Office 2000). Thus, the counter-party risk that growers face of not gettingpaid is pervasive enough that policy mak-ers have proposed grower protection rules.Payment risk is greatest under relationalcontracts in the presence of financial stress.Boot, Greenbaum, and Thakor (1993) pointout that contractors may prefer discretionarycontracts because it leaves them with theflexibility to exchange reputational for finan-cial capital during times of financial distress.Thus, growers often face payment risk if thebuyer is facing insolvency or bankruptcy.More generally, counterparty risk need notbe limited to payment risk but can also berelated to other obligations within a contract.For example, if a supplier requires an upfrontpayment and the payment is made, then thecontractor’s counterparty risk is of receivinglow quality and/or no delivery. This might bethe case if a farmer who has already receivedpayment fails to harvest on time.

Extreme market events will naturally raisethe level of counterparty risk since contract-ing parties will have strong incentives toback out on their agreements. Parties to rela-tional contracts are particularly exposed tocounterparty risk in volatile environments.For instance, Johnson and Gunkel (2009)point out that many fertilizer contracts oper-ate on handshake agreements and that theindustry’s recent price volatility has increasedfarmer default and retailers’ counterpartyrisk.

Finally, counterparty risk increases as thelength of time between signing a contractand concluding the transaction increases. Forinstance, some biofuels contracts can extend

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up to a decade, which raises the probabilitythat the contracting parties will encounterextreme price movements or that at leastone party will face the risk of bankruptcy.For example, if a farmer has contracted togrow miscanthus but the price of alternativecrops such as corn spikes a few years later,then the farmer has a strong incentive toreplant the fields with corn to earn a higherprofit per acre (Alexander et al. 2012). Onthe other hand, if the price promised to thefarmer is indexed on corn prices, this mayreduce the risk that the farmer will back outof the agreement. Nonetheless, a price indexhas a cost in that it may increase the risk thatthe biorefinery will shirk since the biorefin-ery’s payment to farmers would spike, thusputting financial stress on the biorefinery.Therefore, there is likely to be a tradeoffbetween minimizing growers’ versus contrac-tors’ counterparty risk. In addition to marketprice movements, any exogenous shocks thataffect the payoffs of one or both parties to acontract can cause a relationship to unravelbecause the conditions under which a rela-tional contract was formed may becomeobsolete. For instance, Knoeber (2000) pointsout that the pace of technological innovationis fairly rapid in the broiler sector. Coinci-dentally, broiler grower complaints aboutcontracting seem to be more widespread thanin other agricultural sectors. One possibleexplanation is that rapid innovation maymake it harder to sustain relational contracts,which increases counterparty risk.

One last area to highlight is a feature ofthe agricultural contracting environmentthat has generated considerable controversy,that is, buyer concentration and buyer powerin agricultural procurement markets. Thisissue was the focus of Richard Sexton’s 2012Presidential Address at the AAEA meet-ings (Sexton 2013) and is also detailed inCrespi, Saitone, and Sexton (2012). Sexton(2013) emphasizes some important trends,including (but not limited to) increasingconcentration in the processing sector andincreasing the use of contracts. Indeed, theauthor poses a fundamental question: “Howdo we reconcile food industries that arestructural oligopolies/oligopsonies with highbarriers to entry, ample opportunities toobtain cooperative outcomes, and anecdotalevidence supporting little competition infarm product procurement with an exten-sive empirical literature that finds littlemarket power?” Sexton suggests that the

impact of market structure change on marketintermediaries holds the key to offering anexplanation, and provides some examplesof how large processors may not wield theirmarket power in the presence of processingcapacity constraints or fixed sales contracts.Sexton also points out that it is difficult touse traditional oligopoly/oligopsony modelsto quantify the existence of market power infarm procurement settings involving the useof contracts.

To summarize, contractual incompleteness,repeat trading, counterparty risk, and/orbuyer/market power are, in my view, some ofthe first-order features that are important tocapture when modeling agricultural contract-ing. The purpose of modeling is not to mimicthe real world, but to provide clarity aboutthe real world. This can be best achievedusing a parsimonious model that captures afew of the most important, generalizable first-order forces underlying contractual relation-ships.

Modeling First-order Features

This section illustrates how one might deve-lop a simple model for incorporating someof the first-order features discussed above,and specifically incorporates contractualincompleteness and repeat trading. Dueto space constraints, counterparty risk andbuyer/market power will not be modeled,but some discussion about how they mightbe incorporated is provided. The model willbe built in stages and divided into severalsubsections. The first subsection discussesgeneral modeling philosophy and setup, whilethe next two subsections incorporate con-tractual incompleteness and repeat trading.The final two sections include general dis-cussions about how one might incorporatecounterparty risk and buyer/market power.

What the paper presents from this pointforward are preliminary results from a work-ing paper that is currently in development(Erkal, Wu, and Roe 2014). While the resultsare preliminary and the model is not fullydeveloped here, it still might be useful topresent an abbreviated version to illustratehow one might model some first-order fea-tures of agricultural contracts. In developinga simple model, the author also attemptsto reflect recent developments in relationalcontract theory (e.g., Halac 2012; Levin 2003;MacLeod 2007) by allowing for more flexible

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contract designs that endogenously allow forboth discretionary and fixed components incontracts, which contrasts to early modelsthat assume only rigid efficiency wage-stylecontracts (e.g., Klein and Leffler 1981).The purpose here is to show how modernrelational contracting models can be use-ful for modeling many stylized features ofagricultural contracts.

Modeling Philosophy and Setup

One of the strengths of the classic “completecontracts” approach is that it is based on firstprinciples, starting with economic primitivesusing a constrained optimization frameworkin which we are clear about the constraints,the exogenous variables, and the endoge-nous variables. Relative to the incompletecontracts approach, the complete contractsapproach yields analytic results and compara-tive static predictions that tend to generalizebeyond a very specific context.

One of the most important aspects ofthe complete contracts approach is that ittreats contractual terms as endogenous sothat an optimal contractual form can emergefrom the optimization problem and is notjust imposed in an ad hoc manner. Whilethis approach will be used, a key point ofdeparture is the assumption that there isan exogenous imperfection in a contractinginstitution that acts as a barrier to completecontracting. Specifically, it is assumed that thethird-party enforcement technology is poten-tially imperfect, which reduces the set offeasible contracts available to the principal.This added constraint allows one to endog-enize incomplete contracts as a function ofan exogenous friction in a contracting insti-tution. Assuming that there are exogenous(to the contracting parties) imperfections inthe enforcement technology is quite com-mon in the recent contracting literature (e.g.,Bernheim and Whinston 1998; Levin 2003;Dixit 2007; MacLeod 2007), although it is notthe only way to model exogenous imperfec-tions in contracting institutions. For example,Battigalli and Maggi (2002; 2008) assumethat there are exogenous costs to describingall relevant contingencies, which ultimatelylimits fully state-contingent contracts.7 The

7 In addition, if one is modeling the design of contractinginstitutions, then obviously one could not treat the enforce-ment technology as exogenous. Thus, it is important to matchassumptions with the problem at hand.

important point is that the modeler has someflexibility in defining the source of exogene-ity, although an applied researcher mustbe careful to ensure that the maintainedassumptions are consistent with stylized factsand real world institutions. Moreover, it iscrucial that the maintained assumption istruly exogenous and does not create internalinconsistencies within the model.

The model starts with a principal (e.g.,a processor) who contracts with an agent(e.g., a farmer) in order to produce somecommodity for which quality is important.Quantity considerations are omitted to focuson quality incentives.8 Exogeous uncertaintyand asymmetric information issues are alsoavoided since they often distract readersfrom the most basic definition of a contract,which is that a contract is simply an agree-ment that is meant to be enforced.9 Instead,focus will be placed on enforcement limitsthat may leave at least one party with discre-tionary latitude to deviate from the upfrontagreement.10

Under a contract, each party has obli-gations to take actions consistent with theagreement. We can specify the principal andagent’s actions generically as ai ∈ Ai, where

8 It would not be difficult to relax this assumption and considerboth quality and quantity considerations. In fact, one couldcombine the two by using a multitask principal-agent model inthe spirit of Holmstrom and Milgrom (1991).

9 In the author’s experience, researchers who do not specializein contract theory often think of contracts as being synonymouswith models of asymmetric information. While contracts cancertainly be used to mitigate asymmetric information and are infact introduced this way in most textbooks, moral hazard andadverse selection are simply special cases of a broader class ofproblems within contract theory. While the tradeoff between riskand incentives (moral hazard problems) and nonlinear pricing(adverse selection) are certainly interesting, perhaps even morefundamental in practice are the incentive problems associated withgetting parties to honor their promises. This is often abstractedaway in textbook treatments where there is an implicit assumptionthat a perfect legal system and omniscient third-party exists toverify and enforce contracts. Similarly, those familiar with theincomplete contracts literature may wonder why the author doesnot pay more attention to the hold-up problem. Again, the hold-up problem is only relevant in very specific contexts, namely,when (1) ex ante investments are non-verifiable, and (2) there issome ex ante bounded rationality about the nature of trade. Manymajor investments made by producers are far from non-verifiable(e.g., investment in new housing facilities is highly verifiable) andmost trading parties generally have a good idea of the qualityspecifications, the timing of deliver, etc., ex ante. This is notto say hold-up is completely irrelevant in agriculture. However,the author attempts to cover first order features that tend togeneralize across most agricultural contracting environments.

10 The three classes of information problems within the contracttheory literature are moral hazard, adverse section, and theavailability of public information for a third-party to enforce acontract.While the first two types of information problems are well-known, the third type is less well-known outside the incompletecontracts and relational contract literature. Dixit (2007) providesa thorough discussion of the importance of public information.

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i = A, P. A key assumption is that there is anagency conflict so that the two parties haveconflicting of objectives.

Assumption 1. An agency conflict existsin that for aA′ > aA′′ and ap′ > ap′′ , we have:πP(aP , aA′) > πP(aP , aA′′); πP(aP′ , aA)<πP(aP′′ ,aA); πA(aP , aA′) < πA(aP , aA′′); and πA(aP′ ,aA) > πA(aP′′ , aA).

In other words, all else being equal, theprincipal always prefers that the agentincreases his actions while minimizing herown actions. The opposite is true for theagent. For example, the agent’s obligationmight be to deliver some quality level, q ≥ Q,where capital Q refers to the quality levelspecified in the contract, and q refers to theactual quality delivered. The principal’s obli-gation is w = p + b ≥ W , where w is totalactual payment and W is the promised pay-ment in the contract. The total payment wcan also be decomposed into a base price,p, and a bonus payment b. Capitalized Pand B are used for the contractually speci-fied fixed and bonus payments, respectively.The payoff functions for the two parties areπP = r(q) − p − b and πA = p + b − c(q),where r′ > 0, r′′ ≤ 0, c′ > 0, and c′′ ≥ 0. Notethat the principal always prefers higher qual-ity, all else being equal, and the agent alwaysprefers a higher payment.

Exogenous imperfections are modeled inthe enforcement technology in the sense ofBernheim and Whinston (1998).

Assumption 2. Assume that the enforce-ment technology can be represented by anordered partition of Ai, Ei = {ei1, . . . , eiNi},where each subset of the partition is left closedand each party i prefers smaller actions inEi and party j prefers higher actions. A thirdparty cannot distinguish any two actions thatbelong to the same subset ein, but can dis-tinguish two actions that belong to differentsubsets of the partition, eik and eil , where k �= l.

By assumptions 1 and 2, only ein = inf einfor all n are contractible (i.e., third-partyenforceable). That is, only the smallestaction in each subset of the partition canbe enforced. Moreover, finer partitions of Eiimply better enforcement technology since itincreases the number of enforceable actions.

To illustrate, suppose that the good canonly take three quality levels AA = {low,medium, high}. An example of a perfectenforcement technology is EA = {eA1, eA2,eA3} = {{low}, {medium}, {high}}. Note thateach element of the partition is a singleton,

so a third-party can perfectly distinguishevery quality level. An example of imper-fect enforcement is EA = {eA1, eA2} = {{low},{medium, high}}. Here, a third party knowswhen low quality has occurred but can-not distinguish medium from high quality.Thus, the contractible set is EA = {eA1, eA2} ={low, medium}. Finally, if EA = {eA1} = {{low,medium, high}}, then only low quality istrivially contractible.

Using the Model to Conceptualize ContractualIncompleteness

The enforcement technology machinery deve-loped in the previous subsection provides aprecise method of defining an incompletecontract. Continuing with our example withthree different quality levels, note that undera perfect enforcement technology, EA ={eA1, eA2, eA3} = {{low}, {medium}, {high}}, it ispossible to write a fully complete contract.This complete contract can either specifyQ = high in exchange for a price P or it canprovide a set of state-contingent prices, Pl ,Pm, and Ph to be paid under each qualityrealization without demanding a specificquality level. In the former contract, a third-party directly enforces Q and P, whereasin the latter, a third party enforces the con-tingent payments, Pl , Pm, and Ph. As longas the contingent payments are chosen toensure incentive compatibility of producinghigh quality, the two contracts are outcome-equivalent as they both implement Q = high,though the latter contract tends to be moreeffective when there is randomness in trans-lating an agent’s action into a quality realiza-tion, so the agent cannot guarantee a specificquality level. However, since randomness hasnot been introduced in the model, focus willbe placed on the former type of contract.

Under a regime such as EA = {eA1, eA2} ={{low}, {medium, high}}, which is imperfect, itis still possible to write a complete contractby specifying Q = medium in exchange fora fixed payment P. Since medium is in thecontractible set, a third-party can enforceand sanction deviations from medium. More-over, a fixed payment is always enforceable.Therefore, neither the principal nor theagent have discretion to deviate from theupfront agreement. Notice that with imper-fect enforcement, it is now impossible towrite a complete contract that specifiesQ = high. Thus, enforcement limits reduce theset of available enforceable contracts.

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What does an incomplete contract look likeunder the same regime? There are numerousways of specifying incomplete contracts, butone example is provided to illustrate. Sup-pose a contract specifies Q = high, a fixedpayment P, and a bonus B if the agentdelivers q = high. Because Q = high isnot contractible, it follows that the agentalways has ex post discretion to deviate fromQ = high; that is, the agent can choose q < Q.Additionally, because B is contingent onQ = high, it is also not contractible and istherefore a discretionary bonus. In otherwords, both parties have ex post discretion todeviate from the upfront agreement.

One can easily see that an incompletecontract would lead to efficiency losses.Note first that the principal would offer acontract that just satisfies the agent’s parti-cipation and incentive compatibility con-ditions. A binding participation constraintrequires πA = P + B − c(high) = u, where uis the agent’s reservation utility or outsideoption. A binding incentive compatibilitycondition requires B = c(high) − c(low). Sub-stituting the latter into the former yieldsP = u + c(low). Since this is a sequen-tial game where the principal is the lastmover, a rational principal would not payan unenforceable bonus. Therefore, theagent would only receive P − c(high) = u +c(low) − c(high) < u by producing high qual-ity. A forward-looking agent would anti-cipate this and choose q = low, which wouldensure him u. Backward-inducting one morestage, the principal should anticipate thatthe best she can hope for is r(low) − P =r(low) − u − c(low), so only low quality getstraded.11 This efficiency loss is the crux ofclassic arguments about the undesirability ofincomplete contracts.

It is now useful to introduce some addi-tional notation. Let πf and uf denote thepayoffs obtained from using the completecontract that generates the highest jointsurplus. To illustrate this, we return to ourexample where AA = {low, medium, high} andassume that joint surplus r(Q) − c(Q) − π −u is monotonically increasing in quality.12

11 Even if the principal were to write a contract based on aminimum quality of Q = medium, the outcome would still be lessthan Q = high, so efficiency losses would still occur.

12 The assumption of monotonicity is made only to keep thisexample simple. Monotonicity need not be true in general. Forexample, for a continuous quality space, there could be an optimallevel of quality. Going beyond that level may reduce joint surplusas marginal returns may be less than the marginal costs.

Then, in the EA = {eA1, eA2}={{low}, {medium,high}} regime, the enforceable contract thatspecifies Q = medium in exchange for afixed payment P is the complete contractthat yields the highest surplus. A completecontract for Q = high is not possible anda complete contract for Q = low does notyield as high of a surplus as the Q = mediumcontract. Thus, we have πf = r(medium) − Pand uf = P − c(medium).13 The most efficientquality level in the contractible (enforceable)set is denoted as Qf . In this example, we haveQf = medium.

Incorporating Repeat Trading

Now that a formal way of conceptualizingincomplete contracts has been specified, thesecond major feature will be incorporated,which is repeat trading. Such trading actuallycomplements incomplete contracts becauserepeat trading provides parties a way to self-enforce agreements that are not third-partyenforceable. In fact, a relational contract is anincomplete contract, though the reverse is notnecessarily true. The anticipation of futurerewards and punishments via repeat businesscan be a powerful motivator for people notto use their ex post discretion opportunis-tically. This section will illustrate that if thethird-party enforcement technology is weakwhile parties value repeat business, then aninformal agreement can potentially imple-ment higher quality than a formal contract.Informal agreements based on repeat tradingare known as relational contracts.

Relational contracting has been one ofthe most active areas of research in con-tract theory in recent years (Bernheim andWhinston 1998; Levin 2003; Brown, Falk, andFehr 2004; MacLeod 2007; Kvaløy and Olsen2009; Halac 2012). Indeed, there has beensignificant advancement in the tools availablefor analyzing trade under incomplete con-tracts and repeat trading. The basic premiseof a relational contracting model is that theperformance outcome (in this case quality q)is not public information and is therefore dif-ficult for a third-party to enforce.14 Therefore,

13 At this point, the size of P is irrelevant because it is simplya transfer from the principal to the agent and is therefore purelydistributional and does not affect efficiency.

14 Thus, relational contracts are fundamentally dealing witha verifiability problem rather than an asymmetric informationproblem. While moral hazard and adverse selection are notnecessary ingredients of a relational contract, one can still study

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the contracting parties must self-enforce theiragreement through repeat trading.

Following Erkal, Wu, and Roe (2014), theimperfect enforcement apparatus is nowcombined with a relational contracting modelto show how an incomplete contractual formcan be endogenized. Let the agent’s actionset (quality choice) be denoted by AA =[q, q] ⊂ R+ where the enforcement tech-nology, EA, (see assumption 2) is a partitionof AA. The payoffs πf and uf are the payoffsfor the principal and agent, respectively, fromusing the optimal complete contract givenenforcement limits. The contracting timelinefollows the typical textbook principal-agentsequence:

1. The principal offers a relational contractwhich is a triplicate (P, B, Q).

2. The agent decides whether to acceptor reject. If rejected, the principal andagent default to the best formal contractif uf + πf ≥ u + π and to their outsideoptions, which yield payoffs u and π,otherwise. To account for this, a binaryvariable is defined as α ∈ {0, 1}, whereα equals 1 if uf + πf ≥ u + π, and 0otherwise.

3. If accepted, the agent chooses actualquality q.

4. The principal observes q and choosesactual bonus b.

The optimal relational contract is obtained bysolving:

maxQ,P,B

(1 − δ)[r(Q) − P − B] + δV[C] s.t.(1)

(1 − δ)[r(Q) − P − B] + δV[C](2)

≥ απf + (1 − α)π

(1 − δ)[P + B − c(Q)] + δU[C](3)

≥ αuf + (1 − α)u

(1 − δ)[r(Q) − P − B] + δV[C](4)

≥ (1 − δ)[r(Q) − P]+ δ[απf + (1 − α)π]

relational contracting with the addition of asymmetric information.See Levin (2003) and Halac (2012) for examples.

and

(1 − δ)[P + B − c(Q)] + δU[C](5)

≥ (1 − δ)[P − c(q)]+ δ[αuf + (1 − α)u].

The symbol δ is the discount factor.15

Inequalities 2 and 3 are the participationconstraints and 4 and 5 are dynamic incentivecompatibility constraints or self-enforcementconstraints. Note that B is missing from theright-hand-side of equation 5 because theprincipal moves last and always observes qbefore choosing b. Thus, if the agent shirks,then the principal will not pay a bonus. Thevariables V(C) and U(C) are the flow (one-period stage-game) continuation payoffsstarting in state “C,” which is the coopera-tive state in which relational contracting issuccessful.16

To understand these flow payoffs, let � bethe set of contracts, where a typical elementis (P, B, Q). Letting “F” denote “formal con-tract,” � can be partitioned as C ∪ F = � andC ∩ F = ∅. Then, either (P, B, Q) ∈ C or F ,where the “C” contracts are relational con-tracts. The flow payoffs, V(C) and U(C), aretherefore just the per-period payoffs fromthe optimal relational contract (P, B, Q) ∈ C.If either party shirks on the relational con-tract, then the parties respond by refusingto engage in a relational contract in thefuture, and either rely on formal contractsor break off trade and earn their outsideoptions. Furthermore, to simplify the analysis,it is assumed that contracts are stationaryin that the same (optimal) incentive schemeis offered every period. Levin (2003) hasshown that, under the assumption of riskneutrality, if an optimal relational contractexists, then there are stationary contracts thatare optimal. Since exogenous risk has notbeen imposed on the model, focus can beplaced on stationary contracts, which has thebenefit of greatly simplifying the analysis. Inparticular, V(C) and U(C) are now constantacross periods so the principal’s objectivefunction can be written in present value formas maxQ,P,B[r(Q) − P − B] + δ

1−δV[C]. Fol-

lowing convention from both the repeated

15 One can think of the discount factor as a parable for howmuch people value future payoffs.

16 In general, these per-period flow payoffs need not be constantacross periods. However, under the assumption of stationarity,they are constant across periods.

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Wu Adapting Contract Theory to Fit Contract Farming 1251

game and relational contracting literatures,the objective function is multiplied by (1 − δ)to express payoffs as a per-period average,which yields 1.17 Because the same compen-sation plan is offered every period, problem1 becomes essentially a static optimizationproblem.

Note that 4 and 5 can be combined toobtain:

δ

1 − δ[V(C) − απf − (1 − α)π](6)

≥ B ≥ [c(Q) − c(q)]

− δ

1 − δ[U(C) − αuf − (1 − α)u].

This provides a very intuitive look at theself-enforcement conditions. Essentially, equ-ation 6 says that the promised unenforceablebonus has to be large enough to prevent theagent from shirking; that is, it must coverthe cost difference between honoring theagreement by producing Q and the mostprofitable shirk, which is to produce min-imum quality q minus future discountedsurplus that the agent obtains from the rela-tionship. Conversely, for the promised bonusto be credible, it cannot be so large that itexceeds the discounted rents that the prin-cipal receives from the relationship. If thepromised bonus is not credible, the agent willnot believe that it will be paid. Equation 6can also be used to solve for δ, which yields:

δ ≥ δ(Q) = c(Q) − c(q)

r(Q) − c(q) − α[πf + uf ]− (1 − α)[π + u]

(7)

= c(Q) − c(q)

r(Q) − c(q) − α[r(Qf ) − c(Qf )]− (1 − α)[π + u]

.

The critical value δ(Q) is the cutoff pointfor the informal contract to be self-enforcing,and depends on Q. If δ drops below 7, thenthe contracting parties do not place enoughvalue on future payoffs for the relationalcontract to be self-enforcing. Thus, δ ≥ δ(Q)is a necessary condition for self-enforcement.

17 See Gibbons (1992) for a detailed discussion of why mul-tiplying through by (1 − δ) transforms a present value into anaverage per-period payoff.

Additionally, if the principal wants to con-tract for a more efficient Q, this puts pressureon the self-enforcement constraint. Thus,the self-enforcement constraint can limit thelevel of quality that can be sourced. However,the self-enforcement constraint also dependson δ and the payoffs uf and πf , which in turn,depends on the quality of the enforcementtechnology. Thus, there is an interactionbetween contractual incompleteness, contractstructure, and the enforcement technology.

To see this interaction, note that if Qf isthe third-party enforceable quality level thatyields the highest joint surplus, then the Qf -based complete contract specifies mutualobligations (Qf , P), where both Qf and Pare third-party enforced. This contract yieldspayoffs πf = P − c(Qf ) and uf = P − c(Qf ).Substituting these payoffs into the middleterm in condition 7 yields the last term in7. Condition 7 thus provides the minimumthreshold for the discount factor that makesit worthwhile for the parties to endogenouslychoose to use an informal relational contractthat implements some Q that yields a highersurplus than Qf . Notice that there is a sim-ple comparative static prediction embeddedhere: if the enforcement technology improves(e.g., EA becomes a more refined partitionof AA), then gross surplus r(Qf ) − c(Qf )would increase. This would weakly raise theright-hand-side of equation 7, which makes itharder for the parties to sustain a relationalcontract. This increases the incentive forparties to use a formal contract.

Due to space constraints, the optimal con-tract will not be derived using the full setof Kuhn-Tucker conditions; the reader israther referred to Erkal, Wu, and Roe (2014).Before stating the key result, note that jointsurplus is S(Q) = r(Q) − c(Q) − π − u. Theresult is stated as follows:

Proposition 1. Let Qf .b. be the first bestquality level such that Qf .b. ∈ arg maxQ {S(Q)}.Then if there exists Q such that S(Qf .b.) ≥S(Q) > S(Qf ) and δ ≥ δ(Q), an incompletecontract that implements Q is preferred overthe best complete contract.

In other words, if there is enough imper-fection in the enforcement technology so thatthere exists some Q that yields joint surplusthat is strictly greater than what is obtain-able from the best formal contract, and Qcan be self-enforced (people care sufficientlyabout the future), then the parties will use

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an incomplete contract. Intuitively, Q yieldshigher joint surplus than any formal contractso that there is more surplus to be shared.

Note that as the enforcement technologyimproves, the contractible set EA will approx-imate AA.18 In the limit, the most efficientcontractible quality level Qf → Qf .b. so theparties will increasingly gravitate towardcomplete contracts. However, if the enforce-ment technology is poor enough, then Qfwill yield relatively low surplus and theparties will rely on a relational contract toimplement Q > Qf .

What follows is some general discussionconcerning how the form of an incompletecontract might differ from a complete con-tract. It is important to note that a contractis simply an agreement between the princi-pal and agent that the parties intend to beenforced. Here “enforced” refers to eitherthird-party or self-enforcement.19 Under acomplete/formal contract, a third-party isperfectly able to enforce actions directly(e.g., quality of the agent and payment ofthe principal). Hence, the agreement is justthe pair (Pf ,Qf ); that is, the agent agrees toproduce Qf and the principal agrees to payPf for Qf .20 In contrast, if Qf does not yieldvery high surplus, the parties might decide tomake an informal agreement (P, B, Q). Here,the agreement is that the agent will producesome Q (that yields higher surplus than Qf ).The principal agrees to pay a small fixed feeP (an upfront payment) and a discretionarybonus B to complete payments once Q isdelivered. Note that B is not enforceableby a third-party because it depends on Q.However, it is self-enforcing if the partiescare strongly enough about the prospect offuture business together. It should be notedthat no agreement about B is needed in theformal contract because a third-party directlyenforces Qf , so B plays no incentive role.21

18 The author uses approximate rather than converge herebecause EA can only be made countably infinite, whereas AA isa subset of real numbers. Therefore, AA will always have greatercardinality. Nonetheless, EA is dense in AA since every point inAA is either in EA or can be made arbitrarily close to a memberEA if the partition is made fine enough.

19 Perhaps another way to think of it is that the agreementmust be “credible.”

20 The size of Pf depends on relative bargaining power but isconstrained by the participation constraints of the principal andagent.

21 It is also possible to specify a relational contract (P, Q) withthe bonus omitted, which is an efficiency wage contract. However,

An explicit formal agreement differs fromthe relational agreement both in form andin intention. In other words, under the rela-tional contract, parties are not just explicitlyagreeing to the best formal contract and thenperforming beyond its terms. The intentionunder the formal contract is for the parties toimplement Qf . But the intention of the rela-tional contract is to implement Q. This is whyin practice, many non-verifiable performancefactors are omitted from written agreements;that is, there is no point to a written agree-ment that specifies Qf if the parties intend toimplement Q. In practice, however, there arecases where parties build a relational contracton top of a written contract. However, inthese cases, the written contract is not meantto govern performance, but rather to serveas a fallback position in the case of a legaldispute. Hence, there is interaction with con-tract law. An analysis of these issues wouldbe beyond the scope of this paper, but Dixit(2007) touches on some of them.

The above framework allows us to deriveendogenous incomplete contracts from anoptimization problem. Thus, it can serve as afoundation for incorporating other first orderfeatures of agricultural contracts. Due tospace constraints, counterparty risk or buyerpower were not formally integrated into themodel.

Counterparty Risk

As mentioned earlier, counterparty risk isheightened under relational contracts andin environments that are volatile. This sug-gests that a potential avenue of research is tofocus on how various hedges against marketvolatility affect counterparty risk. Alexanderet al. (2012) point out that index contractstied to input prices or prices of alternativecrops can reduce the probability that farmerswill refuse to honor their commitments. How-ever, index contracts increase the probabilitythat extreme price movements can increasefinancial stress on the contractor, which raisescounterparty risk for the farmer. A fruitfuldirection then might be to develop a theoryof optimal price indexing to minimize jointcounterparty risk.

such a contract is suboptimal. On the other hand, a completecontract of the form (Pf , Qf ) is optimal.

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Wu Adapting Contract Theory to Fit Contract Farming 1253

Buyer/Market Power

There are two possible approaches to incor-porating buyer power. First, one can ask howan increase in the agent’s bargaining power,say, through collective bargaining, mightaffect contracting outcomes. One would haveto combine the relational contracting modelwith a formal bargaining model, such as Nashbargaining or alternating offers. This is usefulfor modeling an environment where a prin-cipal no longer makes a take-it-or-leave itoffer to an agent but rather negotiates con-tract terms with the agent. Many Californiaproduce sectors use collective bargaining tonegotiate contracts so this might be an appro-priate approach for these sectors. The secondapproach is to assume that the principal con-tinues to make take-it-or-leave-it offers butthe level of competition in the market placechanges. For example, if there is an increasein competition, growers may still receivetake-it-or-leave-it offers from contractorsbut have more alternative outlets for theirproducts. This approach might better captureinteractions in, say, the broiler sector.

One caveat is that modeling competitionand endogenous contracting outcome in ageneral equilibrium environment with mul-tiple buyers and multiple sellers can leadto quite a complex game. Moreover, it mayinvolve matching and search mechanisms.At this point in time, even the theoreticalliterature on general equilibrium with con-tracts is still in its infancy. As such, an appliedeconomist would be hard pressed to developa coherent model of general equilibriumcontracting. An alternative possibility is toexplore these issues using experimental eco-nomics, where a laboratory economy can beset up to explore contracting outcomes undervarious treatments, where each treatmentinvolves different degrees of competition.

Experimental economics has become quiteuseful for studying applied problems thatdo not have clear theoretical implications.For instance, it is difficult to generate unam-biguous predictions for real world marketoutcomes since outcomes are highly sensi-tive to institutions, norms, and trading rules.Thus, the field of Market Design uses exper-imental economics to test how sensitiveoutcomes are to variations in matching rulesand procedures.

Along these lines, MacDonald and Wu(2014) use economic experiments to exam-ine how varying the level of competition

in markets where multiple buyers maketake-it-or-leave-it offers to multiple sell-ers affect relational contracting outcomes.These authors’ preliminary results suggestthat, with concentration, agents are morewilling to accept contracts that leave buy-ers with more discretion. With respect tothe model in this paper, this implies a lowerP and higher B. These contracts providehigher-powered incentives to sellers, andreduce the cost of incentives to buyers. Thisreduction in contracting costs for buyerscan potentially cause buyers to expand pur-chases. Thus, the favorable impact (to buyers)of market concentration on agency costscan work in the opposite direction of thevolume, depressing the impact of monop-sony/oligopsony power. The net effect is thatthe traditional welfare loss triangle frommarket power might be mitigated. Theseresults can potentially explain why growercomplaints about contracts can co-exist withlittle empirical evidence of market power.From a policy perspective, this suggests thatthe 2010 GIPSA rule that relaxes the tradi-tional court requirement that growers alsohave to prove competitive harm when suingfor breach of contract that results only inpersonal harm might make some economicsense.

One caveat is that, while the MacDonaldand Wu paper suggests that concentrationincreases the potential for opportunism bycontractors, it is not clear how prevalentopportunism is in practice. Sexton (2013)points out that if processors know that theyneed to provide some minimum compen-sation to ensure long-term supply, this maydiscipline the degree to which processorsbehave opportunistically. Sexton’s pointwould be consistent with a high discountfactor within the context of the relationalcontracting framework developed in thispaper.

Conclusion

This paper provides a discussion and over-view of methodological issues in canonicalcontract theory that limit the ability of thetheory to adequately model important fea-tures of agricultural contracts. It also showshow recent developments from contractand game theory can buttress canonicalapproaches to facilitate the development

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of a relational contracting model that cancapture some important features of the agri-cultural contracting environment. The authorwould like to caution that the model devel-oped in this paper is rather preliminary andrepresents only one approach to modelingagricultural contracts. Moreover, the authorhas not discussed empirical strategies fortesting contract theories and predictions.Hopefully this paper will stimulate moreagricultural economists to make contribu-tions to applied contracting methodology, anddevelop innovative empirical tools for testingcontract theory to answer important policyquestions.

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