Unforeseen Contingencies and Incomplete Contracts
The Review of Economic Studies
We scrutinize the conceptual framework commonly used in the incomplete contract literature. This literature usually assumes that contractual incompleteness is due to the transaction costs of describing-or of even foreseeing-the possible states of nature in advance. We argue, however, that such transaction costs need not interfere with optimal contracting (i.e. transaction costs need not be relevant), provided that agents can probabilistically forecast their possible future payoffs (even if
... yoffs (even if other aspects of the state of the nature cannot be forecast). In other words, all that is required for optimality is that agents be able to perform dynamic programming, an assumption always invoked by the incomplete contract literature. The foregoing optimality result holds very generally provided that parties can commit themselves not to renegotiate. Moreover, we point out that renegotiation may be hard to reconcile with a framework that otherwise presumes perfect rationality. However, even if renegotiation is allowed, the result still remains valid provided that parties are risk averse. 83 84 REVIEW OF ECONOMIC STUDIES a court) to motivate the restriction to a simple class of contracts such as property rights or authority. This paper is a methodological discussion of the incomplete contract literature. We question existing modelling by pointing out a tension between two important features of the literature: the postulation of significant transaction costs and the use of dynamic programming. Roughly, we argue that the rationality needed to perform dynamic programming is in standard models strong enough to ensure that transaction costs are irrelevant. More specifically, we show that even if such costs prevent agents from describing physical contingencies ex ante, and in the class of models on which the incomplete contracting literature usually focuses, they do not constrain the set of payoffs that can be reached through contracting in the absence of contract renegotiation. Thus, although we certainly acknowledge that transaction costs matter in reality, we believe that more attention needs to be devoted to the conceptual underpinnings of incomplete contract models. The basic idea behind the irrelevance theorem is very simple. If parties have trouble foreseeing the possible physical contingencies, they can write contracts that ex ante specify only the possible payoff contingencies. (After all, it is only payoffs that ultimately matter.) Then, later on, when the state of the world is realized, they can fill in the physical details. The only serious complication is incentive-compatibility: Will it be in each agent's interest to specify these details truthfully? But the techniques of the implementation literature can be used to ensure that truthful specification occurs in equilibrium.1 A rough analogy can be made with the use of securities in competitive markets. As Arrow (1953) showed, the competitive equilibrium of an economy with complete contingent markets can be replicated by having agents first trade in (a properly chosen set of) securities and then, after the state of nature is realized, conducting spot markets. The securities which can be denominated in money rather than physical goods are analogous to our payoff-denominated contracts. The spot markets correspond to "filling in the physical details." The paper is organized as follows. Section 2 lays out the classic framework of complete contracting with describable states of nature. Section 3 defines the agents' (minimal) representation of their environment in the polar case in which states of nature are indescribable, under the maintained assumption that the agents can perform dynamic programming and so are able to envision the payoff consequences of their contract and investments. Section 4 illustrates through an example the possibility that indescribability does not constrain the payoffs that can be obtained by rational parties. Then for general environments, Section 5 establishes the irrelevance theorem (Theorem 1). It shows that in the absence of contract renegotiation the indescribability of states of nature does not interfere with optimal contracting if the optimal contract when states are describable is "welfare-neutral". A contract is welfare-neutral if, whenever two states are payoff-equivalent (i.e. they are distinguishable only by features not affecting the von Neumann-Morgenstern utilities), it gives rise to the same utilities in both states; welfare-neutrality is then shown to be unrestrictive under two more primitive assumptions (Section 6): a generalization of the requirement that the ratio of the agent's marginal utilities of money be independent of the state of nature (a condition which holds for instance if preferences are quasi-linear), and the condition that the relative likelihood of two payoff-equivalent states not convey information about prior unverifiable actions, if any (Theorem 2). These two assumptions are satisfied in most incomplete contract models in the literature that we are aware of. 1. Just as we do, Wernerfelt (1989) argues that contracts can be written in terms of payoffs even when future physical contingencies are unknown. The main focus of his analysis, however, is the implementation of implicit contracts through infinitely repeated games. MASKIN & TIROLE INCOMPLETE CONTRACTS 85 Hence, the irrelevance theorem applies to these models. However, we also provide examples in which the assumptions do not hold and indescribability matters. We then show that the optimal contract can be implemented in a parsimonious way, namely through the announcement of a single action on the equilibrium path, even when states of nature are indescribable (Section 7). Section 8 examines the issue of contract renegotiation. Starting with the work of Dewatripont (1989), the economics literature has examined optimal complete contracts under the constraint that parties cannot commit not to renegotiate to their mutual advantage (see e.g. Fudenberg-Tirole (1990), Hart-Tirole (1988) and Maskin-Moore (1999). In this respect, it should be noted that this literature on complete contracts with renegotiation (CCR) adheres to the standard complete contracting methodology, and does not, directly at least, invoke indescribable contingencies. By contrast, the incomplete contracting approach, although usually allowing for renegotiation, seems at least motivationally distinct from this CCR literature. Indeed, the papers just mentioned are usually not associated with the incomplete contracting literature). First, we point out that renegotiation may be hard to reconcile with a framework that otherwise presumes perfect rationality. We suggest how rational parties could, in principle, commit themselves not to renegotiate. While, like transaction costs, renegotiation is pervasive in practice, we should devote more research toward reconciling its existence with current modelling practices. Nevertheless, we feel that exploring the implications of renegotiation for those models is worthwhile. Hence, we attempt to delineate when the indescribability of states of nature is costly given the possibility of renegotiation. In particular, we show that it is not costly in the sort of models typically considered in the literature provided that agents are at least slightly risk averse (Theorem 3). Short of a theory of bounded rationality, one can either focus on simple institutions on a priori grounds or study the implications of complete contract theory in structured environments. Section 9 discusses the implications of the irrelevance results and outlines some avenues for further research. THE COMPLETE CONTRACTING BENCHMARK There are two agents (i = 1, 2) and three dates. [Our analysis generalizes immediately to n agents.] Date 0 is the contracting date. Date 1 is the investment date; each agent i makes an ex post unverifiable investment ei E Ei. Finally, at date 2, an ex post verifiable action a is chosen. Each pair e = (el, e2) E E1 x E2 gives rise, stochastically, to a verifiable state of nature 0 characterized by: (i) a finite2 action set A0, and (ii) payoff functions u0 = (ut, ue), where ue: A0e-lR. The assumption that payoff functions themselves are verifiable ex post is obviously strong. But our goal is to show that indescribability of states by itself does not reduce welfare, and this conclusion is strengthened the more we stack the deck in favour of complete contracts. Our conclusions would continue to hold a fortiori were we to suppose that only some partial signal ze of 0 is verifiable. 2. The assumption of a finite action space for each state of nature is made for expositional and notational simplicity.