Contract enforcement, social efficiency, and distribution: some experimental evidence.

We follow the basic design of Brown, Falk, and Fehr (BFF) and two of our treatments are identical to theirs. In addition, we add a third treatment, which is unique to our study. In this treatment, we let buyers make discretionary ex post adjustments in compensation. Hamilton (2001) points out that some contractors can make unilateral adjustments in payments ex post, so this allowance is consistent with agricultural contracting. Further, parties can track the reputations of past trading partners and have discretion to renew or dissolve existing relationships based on past performance. This creates the possibility of relational contracting where the promise of future relationship-specific gains from trade can be used to provide informal incentives to discipline current behavior.

In each experiment subjects are partitioned into two groups: buyers and sellers. (4) All trading takes place on networked computers enclosed in cubicles to eliminate between-subject visual contact. Moreover, anonymity is preserved by assigning all subjects identification (ID) numbers. Each experiment has two trading sessions featuring distinct contract enforcement regimes. Each session has 17 trading rounds--two practice rounds and 15 "live" rounds that may determine eventual cash payment. ID numbers are fixed across rounds, which allows subjects to develop and track reputations.

Within each trading round, buyers offer contracts to sellers specifying a price--quality combination for a unit of an abstract good, where quality can be thought to embody all costly performance factors. Sellers can only accept or reject offers. A buyer can make as many offers as desired in each round, but once one offer is accepted, all other offers are withdrawn and no additional offers can be made. Similarly, once a seller accepts an offer, no other offers can be entertained. In short, each buyer and seller can conclude at most one trade per round. No buyers (sellers) are obligated to make (accept) offers in any round.

Buyers can extend two types of offers: public and private. Public offers are displayed on the computer screens of all sellers and buyers; any seller can accept any public offer. Private offers are extended by entering a specific seller's ID number into the computer. Only the seller identified sees the offer and only he can choose to accept it. Private offers enable long-term relationships, which lie at the core of relational contracting theory. For example, if a buyer predicts benefits from contracting with a specific seller (i.e., can earn relationship-specific rents) and wants to establish a long-term relationship, the buyer can make a single, private offer to that seller in each round rather than venturing into the open market and hoping that that seller is the first to accept the offer. (5) Had we not incorporated private trading, it would have been difficult for parties to establish relational agreements that persisted over time as buyers would have had to hope that their targeted sellers accepted their public contracts before any other sellers did so.

Every round features the same five buyers and seven sellers. Fewer buyers than sellers create buyer concentration because at least two sellers do not trade in each round. This forces sellers to compete for a limited number of contracts, which tilts bargaining power in favor of buyers. (6) Excess demand for contracts is consistent with stylized facts in some sectors. For example, according to Mitchell (2004), most chicken processors have waiting lists for those who want to become growers and some existing growers want to add capacity to expand contract production. Our subjects maintained the same role (e.g., buyer) during both sessions in an experiment and no subject participated in more than one experiment (two sessions).

In order to test the impact of third-party enforcement on efficiency and surplus, we examine three enforcement regimes. First, in the "complete contract" (C) treatment, the computer fully and perfectly enforces all contractual components. That is, sellers must supply the quality stipulated in the contract, and buyers must pay the agreed upon price. In the second treatment, called "Relational Contract 1" (RC1), the computer only enforces contractual price, so that discretionary price adjustments are made illegal. Quality is unenforceable, that is, sellers can supply quality that differs from contractual specifications. This treatment mimics situations where neither input quality nor output measurement (e.g., weighing of birds) is verifiable by a third-party. In this case, measured performance is unenforceable by a third-party because when quality is low, both parties can blame each other (e.g., growers can claim poor quality inputs and processors can claim grower torpor) and verifiability is costly. Our C and RC1 treatments are identical to BFF's. The third treatment, called "Relational Contract 2" (RC2), is unique to our study. This treatment is similar to RC1 except that the buyer can make expost adjustments to the promised price; that is, after observing the seller's delivered quality, the buyer can choose a price that deviates from contract specifications. Our RC2 treatment allows for the examination of a broader range of informal incentive mechanisms used to regulate trading. We show that our RC2 treatment can provide significant new insights into the nature of relational contracting relative to the findings of BFF.

Round specific payouts are determined for buyers as follows:

(1) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where [[pi].sub.b] is the buyer's profit, Q is the actual quality chosen by the seller, and P is the actual price received by the seller. All payments are given in experimental points where subjects earn 1 dollar for 70 points.

The seller's profit is

(2) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where r is a reservation payoff in the absence of trade (5 or 10 depending on the session). We impose positive reservation payoffs for sellers to ensure that they earn some money during the experiment. Varying reservation payoffs should only induce buyers to change their price offers to ensure that sellers' reservation payoffs are covered, but efficiency should not be affected. During the experiment, Q is an integer in the set {1, 2, ...,10} and P is an integer in the set {0, 1, ..., 100}. The cost function, c(Q), is fully 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. Note that marginal cost never exceeds 3 and that a buyer's marginal benefit always exceeds 3 so that first best is achieved if the seller delivers maximum quality. At the end of each round, each subject is informed of her own payoff and her trading partner's payoff.

We conducted thirteen experiments. Each experiment included two of the treatments (C, RC1, or RC2). Each subject participated in both treatment sessions during an experiment, which means that order effects might arise. Hence, the design counterbalances the order of appearance for each of the three enforcement regime sessions. (7) Before subjects were paid, they provided demographic information. (8) There were a total of 156 subjects in twenty-six sessions (two in each of the thirteen experiments) where thirteen were C treatments, seven were RC1 treatments, and six were RC2 treatments. Subjects made 1,903 out of a total of 1,950 possible trades across all sessions. Table 1 provides a summary of treatments, sessions, participants, rounds, and trades. The experimental economy was programmed using Z-TREE software (Fischbacher 1999). For five C treatments, r = 10, and for the others, r = 5; r = 5 for all RC1 and RC2 sessions. See Wu and Roe (2006) for additional details of the experiment, including subject instructions.

Predictions

In this section, we provide theoretical predictions for each treatment. Like BFF, we use the theory of repeated games to generate predictions. We focus on the case where the seller's reservation payoff is set at r = 5, but the case where r = 10 is analyzed similarly.

In treatment C, the sequence of events within a round is as follows. First the buyer offers a contract, which specifies the desired P and Q. If a seller accepts, payoffs are determined and the round ends. Note that Q and P specified in an agreement are third- party enforced, that is, neither party can deviate from contracted Q and P. Thus, the buyer's profit-maximizing contract choice is determined by solving the problem

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

Substituting the binding constraint into the objective function yields

(4) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

which gives the first-order condition

(5) 10 - c'(Q) = 0.

As noted above, marginal cost never exceeds 3 so the buyer should implement maximum quality, [Q.sup.*] = 10. With [Q.sup.*] in hand, it is easy to solve for [P.sup.*] = 23 from the participation constraint to ensure that the seller will accept. Because both parties can earn at least as much when trading, we predict that all five buyers will make offers and that five sellers will accept them. Hence, in equilibrium, five trades occur in the round and joint surplus is given by

(6) [S.sup.C] = [[pi].sub.b] + [[pi].sub.s] - r = 77.

Due to perfect third-party enforcement, sellers and buyers have no incentive to deviate from this prediction in any round of the session.