Private mechanisms, informal incentives, and policy intervention in agricultural contracts.

Farm advocates and policy makers have become increasingly concerned about the fairness of agricultural contracts, creating political pressure to enact new laws to regulate agricultural contracts. While some states have either enacted or proposed new legislation (e.g., the Producer Protection Act of 2000), there is currently a paucity of formal economic analysis to inform policy makers of the potential economic impacts of such interventions. In addition, the theory of contract regulation is still an evolving area (Schwartz 2002), so there is no clear consensus concerning the appropriate role of the government.

Of course, the law and economics literature offers some well-known principles concerning contracts. Most law and economics scholars focus on the regulation of incomplete contracts (ICs) or those with unenforceable components. Contracts can be incomplete for many reasons, including indescribable contingencies, prohibitive costs of writing complete contracts, and barriers to enforcement. When contracts are incomplete, an unspecified contingency might arise, creating the need for ex post renegotiation over the terms of trade and giving rise to economic distortions that may justify government intervention (Wu 2006). Thus, a central theme from the law and economics literature is that the government ought to "fill gaps" in ICs through legal rules that improve efficiency by making contracts "more complete." For example, the specification of termination damages in Section 8 of the Producer Protection Act can be interpreted as a response to a failure by parties to specify liquidated damages.

Another means by which the government might facilitate "more complete" contracts is by creating institutions or laws that improve verifiability of performance, thereby improving third-party enforcement. For example, Georgia passed HB 648 in 2004, which requires processors to provide "any statistical information and data used to determine compensation paid" at a grower's request. The government can also conduct quality grading or create institutions for measuring quality, so that conflicts over quality determination or other performance factors can be minimized. (1)

The purpose of this article is to discuss whether regulations that make contracts "more complete" are necessarily welfare improving. While conventional wisdom seems to suggest that statutorily or judicially amending contracts to make them "more complete" is desirable, a new generation of contracting models may challenge this assertion. Recent theory suggests that in a second-best world, where complete contracts are impossible to write, some parties will inevitably be left with discretion. Hence, it may be optimal for contracting parties to increase the level of incompleteness in formal contracts in order to balance discretionary powers and thus limit opportunism (Bernheim and Whinston 1998). Simple contracts that appear highly incomplete may actually be optimal in a second-best context. Moreover, when parties interact repeatedly over time, they will form relationships and these relationships can potentially deliver informal incentives that are often more effective than formal incentives at governing performance. However, the set of feasible relational contracts depends on the structure of the formal contract, which affects the amount of discretion available to parties. Thus, government attempts to make contracts more complete through regulatory intervention may have negative consequences.

Simple Contracts and Economic Efficiency

A central assumption in IC theory is that important dimensions of performance are nonverifiable by a third party. While this assumption may offer a reasonable description of real-world contracting, it does not necessarily preclude complete contracting, because parties can, in principle, design "message games" to make information verifiable (Maskin 1999). For example, a "complete" contract might ask each party to announce what they observe and, if there is disagreement, both parties would be punished: such mechanisms can induce truth-telling as a Nash equilibrium. Nonetheless, a criticism of these message games is that they are rarely observed in practice and that they are not robust to renegotiation (Hart and Moore 1999). As such, contract theorists have looked for alternatives to message games in problems with nonverifiable information.

Two related strands of research suggest that contracting parties can minimize the distortionary effects of nonverifiability even when contracts can be renegotiated. First, the work of Bernheim and Whinston (1998) on strategic incompleteness suggests that an ex ante contract can define the scope of discretionary powers available to parties; that is, less complete contracts increase discretionary latitude. Thus, an important aspect of contract design in a second-best world is to ensure a proper balance of discretionary latitude between parties so as to limit exploitation. Second, research based on mechanism design principles concludes that first-best outcomes can sometimes be achieved through simple initial contracts that are later renegotiated. (2) Even though these simple contracts have apparent "gaps" in them, they can be "optimal" in the sense that they are able to achieve first-best outcomes when combined with ex post renegotiation. Thus, any government attempts to make the initial contract more "complete" can only reduce efficiency.

To illustrate our points, suppose that a processor and a grower can potentially trade one unit of a good, y [epsilon] {0, 1}, where 1 implies trade and 0 implies no trade. This good can also take quality levels q [epsilon] [[q.bar], [bar.q]], where q is observable but not verifiable by a third party. If trade occurs at some contractually specified price, P, the payoffs to the processor and grower are [[pi].sup.p] = R(q) - P and U = P - c(q), where the revenue function, R(q), obeys R([q.bar]) = 0, R'(q) > 0, and R"(q) [less than or equal to] 0. The cost of producing a good of quality q is given by the function c(q), where c([q.bar]) = 0, c'(q) > 0, and c"(q) > 0. Hence, the processor's and grower's profits from exchange (y = 1) are functions of the quality. If no trade occurs (y = 0), then the processor earns [bar.[pi]] and the grower earns a reservation payoff [bar.u]. Social surplus is then given by S = R(q) - c(q) - [bar.u] - [bar.[pi]]. Assume that S [greater than or equal to] 0 and R'(q) [greater than or equal to] c'(q), [angstrom]q [epsilon] [[q.bar], [bar.q]], so that y = 1 and q = [bar.q] imply social efficiency.

The timing of the relationships is as follows. At time 0, the parties may sign a contract specifying the verifiable actions and obligations. At time 1, the grower chooses q. At time 2, after q is observed, the parties may renegotiate all obligations that were not specified in the original contract or are not enforceable. We assume that the processor has full bargaining power and can make a take-it-or-leave-it offer to the grower.

In this example, a third party such as a court can verify whether trade took place (y = 1 or y = 0) and enforce the contract price, P. However, the court cannot verify q and therefore would not be able to enforce a quality-contingent price schedule. Under these assumptions, it is possible to construct contracts with varying degrees of completeness to explore the potential consequences of government intervention.

Case 1: The "Complete" Contract

We point out that limits to verifiability imply a second-best world where it would be impossible to structure a contract that fully specifies all actions. Without verifiability of q, the grower will always retain some discretion in choosing quality. However, a contract can be conditionally complete in the sense of Bernheim and Whinston (1998) if it restricts the processor's and grower's actions to the maximal extent allowable given limits to verifiability. Thus, if the government undertakes to "fill gaps" in the contract to the fullest extent possible, a "complete" contract requires enforcement of any agreement that fixes y and P so that no renegotiation of these obligations can occur. Under such a "complete" contract, the last mover in the sequential contracting game is the grower, who chooses q given y = 1 and P. Since P is fixed, the grower will set q = [q.bar], which is clearly suboptimal. Because the processor anticipates that the grower will choose q = [q.bar], it will set price [??] = c([q.bar]) + [bar.u], so that the grower's profits equal her outside payoff. Clearly, such a contract is suboptimal as it delivers only minimal quality and surplus under trade.

Case 2: An "Incomplete" Contract

We will now consider a partially incomplete option contract in the spirit of Noldeke and Schmidt (1995). In time 0, the parties specify a contract that sets P but leaves y unspecified by giving the processor the right to trade or not during the renegotiation stage. Note that for any price [P.sup.0] fixed in the initial contract, the processor will earn [[pi].sup.p] = R(q) - [P.sup.0]. Thus, the processor will exercise its option to trade only if the grower chooses [q.sup.0] such that [[pi].sup.p], = R([q.sup.0]) - [P.sup.0] [greater than or equal to][bar.[pi]]. This provides incentives for the grower to supply at least [q.sup.0] in order to induce the processor to exercise the option to trade. In fact, if [P.sup.0] is chosen carefully so that [P.sup.0] = R([bar.q]) - [bar.[pi]], then the processor will exercise the option to trade and the grower will produce first-best quality [bar.[pi]]. A fixed transfer that is not contingent on trade can also be included in the initial contract to split the surplus in any way the parties desire. The processor's discretion under the option contract offsets the grower's discretion to choose suboptimal quality. However, if the government views this partially complete contract as being "incomplete" and enforces the trading decision, y, then the processor's discretion disappears and efficiency suffers.

Repeated Interactions and Informal Incentives

When the same processor contracts with the same grower over multiple seasons or flocks, it is possible for growers and processors to govern performance using informal incentives in a relational contract. At the heart of relational contracts is the latitude to make ex post discretional adjustments in contract terms to reward or punish a trading partner's performance. A formal contract can "frame" a relational agreement by defining the scope of discretion available to contracting parties. If private parties structure formal contracts to deliver the optimal amount of discretion, then government intervention to make a contract more complete may have unintended negative consequences. We now compare the complete contract to a partially IC in order to illustrate this point.

Case 1: The Complete Contract

Recall that under a one-shot "complete" contract, the grower supplies only minimal quality, q = [q.bar]. However, if the processor and grower are involved in a repeated game, then they can use trigger strategies to sustain a subgame perfect Nash equilibrium in which the grower "cooperates" by supplying q > [q.bar]. The trigger strategy specifies that each party cooperates in each stage t so long as the parties have cooperated in all t - 1 prior stages; otherwise, the parties deviate by playing the one-shot strategies and then break off the relationship. If it is optimal for the grower to supply q, then the present value of her payoff is V = P - c(q) + [delta]V so that V = (P - c(q))/(1 - 5[delta]), where [delta] is a common discount factor. If the grower instead decides to deviate, she would earn P - c([q.bar]) in period t, but only [bar.u] thereafter so that the present value of payoffs under noncooperation is [V.sub.n] = P - c([q.bar]) + [delta][bar.u]/1-[delta]. The self-enforcement constraint for the grower to choose q is

(1) P-c(q)/1-[delta] [greater than or equal to] P - c([q.bar]) + [delta][bar.u]/1-[delta].

Solving for P yields

(2) P [greater than or equal to] c([q.bar]) + [bar.u] + c(q)-c([q.bar])/[delta].

Therefore, if the processor wants to induce the grower to cooperate, it must offer at least the one-shot price plus a premium of (c(q) - c ([q.bar]))/[delta]. A profit-maximizing processor would offer P* = c([q.bar]) + [bar.u] + (c (q) - c(q))/[delta]. This yields per-period profits for the grower of U = P* - c(q) = [bar.u] + ((1-[delta])[c(q) - c([q.bar])])/[delta], which exceeds the grower's outside payoff when [delta] < 1. We must also ensure that the processor is willing to participate, which requires that [[pi].sup.P] = R(q)- [P.sup.*] > [??] or

(3) [[pi].sup.P] = R(q) - c([q.bar]) - [bar.u] -[c(q)-c([q.bar]/[delta])] [greater than or equal to] [??]

Equation (3) implies that ([P.sup.*], q) is a subgame perfect Nash equilibrium so long as

(4) [delta] [greater than or equal to] c(q) - C([q.bar])/R(q) - c([q.bar]) - [?] - [bar.u]

If (4) holds, then the repeated interaction can generate informal incentives for the grower to supply high quality and for the processor to compensate the grower for doing so. The main claim under the complete contract is summarized below.

CLAIM 1. Assuming that (4) holds, the relational contract supported by the complete formal contract can sustain an equilibrium where q > [q.bar] and the grower earns rents" over his next best opportunity.

Case 2: A Less Complete Contract

Now consider an IC in which P is not fixed in the initial contract, analogous to the case where the government does not enforce price. For simplicity, we assume that the parties always agree to trade in the renegotiation stage. While this simplification may appear contrived, it is very much consistent with the types of relational contracts observed in the literature.

In a one-shot interaction, the outcome of this contract is rather stark; i.e., no trade takes place. To see this, first suppose that the processor and grower would like to cooperate on some informal proposal (q, P). Since the processor is the last mover after the grower produces a good of quality, q, the processor will opportunistically maximize profits and pay P = 0. Because the grower can anticipate such opportunism, which would leave her with payoffs below reservation levels, she would never enter into an agreement.

Remarkably, in a repeated trading environment, IC can potentially be better than the complete contract (C) in sustaining high levels of surplus. The ability of the processor to make discretionary price adjustments under IC offers it a discretionary instrument to incentivize grower quality. Note that within each stage game, the processor observes q before choosing P, so the processor must optimally respond to quality choices made by the grower.

The grower, in turn, must respond optimally to the initial offer made by the processor. Thus, subgames across stages can be grouped into two types--those beginning after "cooperation," where the parties stick to the terms of the agreement (q, P), and those beginning after all other histories. The trigger strategy then is for the parties to cooperate if cooperation was observed in all t - 1 stages; otherwise, the parties deviate by playing the one-shot strategy and then receiving their outside payoffs thereafter. If it is optimal for the processor to honor the agreement in any given period, then the present value of its payoffs is [V.sup.P.sub.n]] = R(q) + [delta][??]/1 - [delta]. If, instead, the processor engages in opportunism, then the present value is [V.sup.P.sub.n] = R(q) + [??], so that the self-enforcement constraint becomes

(5) R(q) - P/1 - [delta] [greater than or equal to] R(q) + [delta][??]/1 - [delta].

Equation (5) also implies that R(q) - P [greater than or equal to] [??] holds in all periods, so that the processor is willing to participate in the contract. Similarly, the grower cooperates by supplying q if

(6) P - c(q).1 - [delta] [greater than or equal to] -c([q.bar]) + [delta][?]/1 - [delta]

where the r.h.s, of (6) is the present value of shirking on q. To understand (6), note that if the processor observes shirking, it responds by choosing P = 0, leaving the grower with-c([q.bar]). Then in the next period, the parties separate and earn reservation payoffs thereafter. Also, because the processor can threaten to withhold P under IC, (6) is more relaxed than (1), making it easier for the processor to induce the grower to supply high quality. The grower's participation constraint is satisfied if P - c(q) [greater than or equal to] [bar.u] in each period, or

(7) P - c(q)/1 - [delta] [greater than or equal to] [bar.u]/1 - [delta].

Note that the r.h.s, of this inequality is actually greater than or equal to the r.h.s, of (6) since-c([q.bar]) < 0 and [bar.u] [greater than or equal to] 0, so that (7) actually becomes the binding constraint rather than (6). Note also that even though (7) is tighter than (6), it is still more relaxed than (1), so that it remains easier to induce high quality under IC. Solving (7) for P yields

(8) P [greater than or equal to] [bar.u] + c(q)

which is the minimum price to induce the grower's participation. A profit-maximizing processor will offer [P.sup.**] = [bar.u] + c(q), which makes the grower's payoff just equal to her reservation payoffs. Equations (5) and (7) imply that (q, [P.sup.**]) can be sustained as a subgame perfect Nash equilibrium so long as

(9) [delta] [greater than or equal to] c(q) + bar.u]/R(q) - [??].

Note that we have assumed earlier that c([q.bar]) = 0; thus, the r.h.s, of (9) is at least as large as the r.h.s, of (4) so long as R(q) - c(q) - [??] - [bar.u] [greater than or equal to] 0, which is true by assumption. Hence, it is harder to sustain a subgame perfect Nash equilibrium under IC.

CLAIM 2. Relative to C, processors find it is easier to induce growers to supply high quality under IC. However, growers earn lower rents and self-enforcing relational agreements are harder to sustain under IC.

Comparing Claim 1 to Claim 2, it is clear that our model predicts greater rents for growers under C than under IC. However, our model makes no clear predictions about efficiency. Under IC, it is easier to motivate growers to deliver high quality in equilibrium, but this is potentially offset by the fact that a cooperative equilibrium is harder to sustain. This ambiguous prediction, combined with the fact that repeated games are typically plagued by multiple equilibria suggests that it would be instructive to conduct some empirical analysis to determine which contract is more efficient.

Experimental Evidence

In order to implement experiments testing the model just described, we parameterize it by assuming that R(q) = 10q, [??] = 0, [bar.u] equals 5 or 10, q = 1 and [bar.q] = 10. Moreover, we assume that c(q) is represented by the following schedule of quality-cost combinations: {1,0}, {2,1}, {3,2}, {4,4}, {5,6}, {6,8}, {7,10}, {8,12}, {9,15}, {10, 18} so that c(q) is increasing and convex. All "costs" and "profits" were given in experimental dollars equal to one-seventieth of an actual dollar. Trade with q = 10 is always first best, which is consistent with our analytical model. We conducted seven C sessions and twelve IC sessions. Each session had fifteen identical trading periods; thus, these are repeated games. (3) In each session, twelve human subjects were randomly assigned to be "buyers" (processors) and "sellers" (growers). In all but two sessions, we imposed market concentration in favor of buyers by assigning only five buyers and seven sellers; thus, in each period, at least two sellers were without contracts. However, in two of the twelve IC sessions, we reversed the market concentration ratio by assigning only five sellers and seven buyers. The sequence of events within each period is as follows. First, buyers make contract offers (q, P) to sellers. The offers could be "public" (any seller can accept) or "private" (offered only to specific sellers). Because all buyers' and sellers' ID numbers were fixed across periods, the option to trade privately allows parties to form long-term relational agreements. Second, after a seller accepts an offer, she chooses q. In a C session, the period ends then. In an IC session, a third stage is added where the buyer then chooses the actual P she will provide to the seller. Due to space constraints, we refer the reader to Wu and Roe (forthcoming) for the remaining details of the experiment.

Table 1 provides the main results. Row 1 reports the highest possible aggregate surplus across all sessions of a specific contract type, where all sellers supply q = 10. Thus, it represents a "surplus frontier." While our analytical model did not provide unambiguous predictions about which contract would yield higher surplus, the results in row 2 suggest that the IC contract would bring the economy much closer to the frontier. Subjects achieved around 72-73% of full efficiency under IC regardless of whether concentration favored buyers or sellers. In contrast, the C subjects reached only 49% of the frontier. Note also that our experiments yielded results remarkably consistent with some predictions of our analytical model. For instance, row 5 reports the percentage of private trades (i.e., self-enforcing relational agreements) that took place under each contract type. Note that a much higher percentage of trades took place within relational agreements under C, which is consistent with our analytical claims. While a higher percentage of trades took place within self-enforcing relational agreements under C, sellers supplied higher quality (as indicated by higher aggregate surplus), on average, under IC, which is consistent with the prediction that it is easier to induce sellers to supply high quality under IC. The main point of these results is that it is possible for less complete contracts to facilitate more efficient trading so that government intervention to make a contract more complete may reduce efficiency.

With regard to distribution, rows 3 and 4 reveal that sellers earned more under C than under IC, which is also consistent with theoretical predictions. Reversing market concentration in favor of sellers under IC increased sellers' share of surplus, but sellers still earned less than they did under C. Moreover, less than 1% of trades under C resulted in sellers earning profits below reservation levels, whereas this jumped to 21% under IC. Thus, the degree of contractual completeness will likely have both efficiency and distributional consequences.

Conclusion

A widely accepted principle in the law and economics literature is that government efforts to "fill gaps" or take other legislative actions to make contracts "more complete" is generally efficiency enhancing. In this article, we discuss this principle in light of recent developments in contract theory and argue that regulatory efforts to make simple contracts more "complete" may, in some circumstances, be welfare reducing. Our analysis presumes that in a second-best world where there are barriers to complete contracting, people are able to devise private mechanisms to overcome potential losses from contractual incompleteness. Some of these private mechanisms involve the use of simple contracts combined with ex post discretionary adjustments to terms to overcome barriers to enforcement. However, because simple contracts may be apparently incomplete, it might be tempting for lawmakers to try to make these contracts more "complete," which would create unintended negative consequences. This suggests that, in a second-best world, the determination of efficient policies to regulate agricultural contracts becomes dramatically more difficult and complex. Standardized policy proposals that do not account for industry- or relationship-specific realities have little hope of achieving efficiency.

If our claims are correct, policy makers should be judicious in imposing contracting restrictions using what Ayres and Gertner (1989) call "immutable rules." These are rules that cannot be changed by contractual agreement. For example, Section 10 of the Producer Protection Act makes the Act immutable by not permitting parties to contract around rights and obligations specified in the Act. Ayres and Gertner (AG) suggest that immutable rules should be used only when parties cannot protect themselves due to the presence of contracting externalities, duress, or fraud. In the absence of these considerations, AG suggest that default rules, which can be contracted around by prior agreement, are preferred. The logic is that if lawmakers choose the wrong default rules, private parties can still contract around them and achieve a reasonable level of efficiency.

References

Ayres, I., and R. Gertner. 1989. "Filling Gaps in Incomplete Contracts: An Economic Theory of Default Rules.'" Yale Law Journal 99(1):87-130.

Bernheim, D.B., and M.D. Whinston. 1998. "'Incomplete Contracts and Strategic Ambiguity." American Economic Review 88:902-32.

Brown, M., A. Falk, and E. Fehr. 2004. "'Relational Contracts and the Nature of Market Interactions." Econornetrica 72:747-80.

Hart, O., and J. Moore. 1999. "Foundations of Incomplete Contracts." Review of Economic Studies 66:115-38.

Maskin, E. 1999. "Nash Equilibrium and Welfare Optimality." Review of Economic Studies 66:23-38.

Noldeke, G., and K. Schmidt. 1995. "Option Contracts and Renegotiation: A Solution to the Hold-Up Problem." Rand Journal of Economics 26:163-79.

Schwartz, A. 2002. "Contract Theory and Theories of Contract Regulation." In E. Brousseau and J.M. Glachant, eds. The Economics of Contracts. Cambridge, UK: Cambridge University Press, pp. 59-71.

Wu, S. 2006. "Contract Theory and Agricultural Policy Analysis: A Discussion and Survey of Recent Developments." Australian Journal of Agricultural and Resource Economics, December.

Wu, S., and B. Roe. Forthcoming. "Contract Enforcement, Social Efficiency, and Agent Welfare: Some Experimental Evidence." American Journal of Agricultural Economics, in press.

(1) For example, one rarely hears about disputes related to quality measurement in the processing tomato industry, where a third-party institution called the Processing Tomato Advisor Board, which is jointly funded by processors and growers, undertakes quality measurement.

(2) Mechanism design is a branch of contract theory or game theory that is concerned with the design of rules or contracts that can elicit information revelation by parties that have private information.

(3) A question that might arise is whether a finitely repeated game is adequate for testing predictions from an infinitely repeated model. We claim that a finitely repeated game does not significantly alter results in a laboratory setting. To explain this claim, it is well known that an infinitely repeated game can be interpreted as a finitely repeated game that has a random termination date. However, one can substitute the probability of random termination with the probability that a player will be matched with another player who has nonself-regarding social preferences and may therefore play cooperatively even in the final round of the finite game. This assumption is reasonable because numerous game theory experiments have shown that most subject pools tend to be very heterogeneous with many people exhibiting social preferences for cooperation, Indeed, experiments by Brown, Falk, and Fehr (2004) show that, because of the existence of subjects with social preferences, finitely repeated contracting games can lead to cooperative outcomes that look similar to what might be expected under infinitely repeated games.

Jack Schieffer and Steven Wu are graduate student and assistant professor, respectively, in the Department of Agricultural, Environmental, and Development Economics, The Ohio State University.

The authors gratefully acknowledge funding from the USDA/NRICGP program for Markets and Trade or Rural Development, Sponsor ID (40040100): 2005-35400-15963, Award No. GRT00001044/60003271.

This article was presented in a principal paper session at the AAEA annual meeting (Long Beach, CA, July 2006). The articles in these sessions are not subjected to the journal's standard refereeing process. Table 1. Results from the Relational Contracting Experiments

Partially

Incomplete Buyer Trading Outcomes Complete (C) Concentration (IC-1) 1. Efficient aggregate surplus 40,400 52,250 2. Aggregate surplus 19,899 41,362

(49.3%) (a) (73.5%) 3. % aggregate surplus to 0.99 0.16

sellers 4. Seller surplus per trade $21 $11 5. % of private trades 0.55 0.31 6. % of trades seller surplus 0.002 0.21

below reservation

Partially

Incomplete Seller Trading Outcomes Complete (C) Concentration (IC-2) 1. Efficient aggregate surplus 40,400 10,800 2. Aggregate surplus 19,899 7,795

(49.3%) (a) (72.2%) 3. % aggregate surplus to 0.99 0.33

sellers 4. Seller surplus per trade $21 $19 5. % of private trades 0.55 0.19 6. % of trades seller surplus 0.002 0.19

below reservation (a) Numbers in parentheses in row 2 are the percentages of efficient aggregate that the dollar For $19.899 is 49.3% of. surplus (row 1) figures represent. example, $19,899 is 49.3% of $40,400. Notes: All dollars figures are in cxperintcntal units. Buyer concentration has five buyers and seven sellers in each experiment. The ratio is reversed in the seller concentration experiments. There were 512 observations for C. 740 observations for IC-I. and 148 observations for IC-2.