Knowledge that Transforms

In a repeated principal-agent game (supergame) in which each player's criterion is his long-run average expected utility, efficient behavior can be sustained by a Nash equilibrium if it is Pareto-superior to a one-period Nash equilibrium.Furthermore, if the players discount future expected utilities, then for every positive epsilon, and every pair of discount factors sufficiently close to unity (given epsilon), there exists a supergame equilibrium that is within epsilon (in normalized discounted expected utility) of the target efficient behavior.These supergame equilibria are explicitly constructed with simple "review strategies." 1. INTRODUCTION 1.1.Some Background IN A PRINCIPAL-AGENT SITUATION, the agent chooses an action "on behalf of" the principal.The resulting consequence depends on a random state of the environment as well as on the agent's action.After observing the consequence, the principal makes a payment to the agent according to a pre-announced reward function, which depends directly only on the observed consequence.This last restriction expresses the fact that the principal cannot directly observe the agent's action, nor can the principal observe the information on which the agent bases his action.This situation is one of the simplest examples of decentralized decisionmaking in which the interests of the decision-makers do not coincide.2If this action-reward situation occurs only once, I shall call it a short-run principal-agent relationship.The situation can be naturally modeled as a two-move game, in which the principal first announces a reward function to the agent, and then the agent chooses an action (or decision function if he has prior information about the environment).The Nash (or perfect Nash) equilibria of such a game are typically inefficient (unless the agent is neutral towards risk), in the sense that there will typically be another (but nonequilibrium) reward-decision pair that yields higher expected utilities to both players.In order to increase the efficiency of short-run equilibria, the principal could monitor (at least ex post) the information and decision of the agent.However such monitoring would tyically be costly, so that net efficiency need not be increased by monitoring.Another approach to increasing efficiency is suggested by the theory of repeated games.If a game with two or more players is repeated, the resulting situation can be modeled naturally as a game ("supergame") in which the players' actions in any one repetition are allowed to depend on the history of the previous repetitions.In the principal-agent situation, the repetition of the game would l I am grateful to R. A. Aumann, R. W. Rosenthal, and A.

The first-order approach to principal-agent problems involves relaxing the constraint that the agent choose an action which is utility maximizing to require instead only that the agent choose an action at which his utility is at a stationary point. Although more mathematically tractable, this approach is generally invalid. This paper identifies sufficient conditions-the monotone likelihood ratio condition and convexity of the distribution function condition-for the first-order approach to be valid. The Pareto-optimal wage contract is shown to be nondecreasing in output under these same conditions. MIRRLEES [5] WAS THE FIRST to point out that the standard method for analyzing the principal-agent problem is not generally correct. This method, the so-called first-order approach, involves weakening the constraint that the agent choose a utility-maximizing action to require instead only that the agent choose an action at which his utility is at a stationary point. The resulting problem is more mathematically tractable. However, as Mirrlees [5] has shown, necessary conditions for a contract to solve the first-order program are not generally even necessary conditions for the valid program. Therefore qualitative propositions about the nature of the Pareto-optimal contract derived from the first-order approach are not in general valid. This has motivated researchers to try to identify classes of cases where the first-order approach is valid.

Let S denote a set of consumers who have identical, nondecreasing, ordinal, quasiconcave utility functions u: XS(t) -* u[X (t)], where XX(t) is the vector of n goods consumed by individual s at time t. Consumers shop at different stores and hence may pay different prices for commodities.4 Let PS(t) and yS(t) denote exogenous vectors of commodity prices and income, respectively, faced by individual s at time t. This does not preclude the existence of a subset, 5, of consumers who all face the same prices, i.e., P5(t) = pS (t) for all s, s'c S. At each instant in time consumers attempt to

[This paper examines the detection of misspecification in the context of maximum likelihood models. The power properties of specification tests based on moment conditions are explicitly considered. Tests of conditional moment restrictions are also discussed and are shown to be particularly useful when exogenous variables are present. The form of optimal conditional moment tests is presented. The general results are then applied to specification tests for probit.]

This paper develops an example in which persistent deterministic business cycles appear in a purely endogenous fashion under fal.,).,~e~ oaÂ.Jte.These cycles are not attributable to exogenous 11 shocks 11 nor toThis procedure defines a function W that takes the interior of JR! into ~ itself, and it is clear that the equation qt = W(qt_ 1 ) describes the same dynamics as (2.4) through the relation qt-l = (pt-1' ... ,pt-T) for all t .1 We may in particular state for later reference LEMMA 2.2.AMu.me.(1.a),(1.c.) and (2,6).Let (pt) be. a pwocüc.1.ie.que.nc.e.06 pOJ.ii- tive.ptiic.uwilh pwod k and fe.t (pi,,.,p;)be.i:t6 onbil.Let UJ.i de.0 ine.

THE EFFECTS OF COMMODITY PRICE STABILIZATION on an individual consumer's welfare has been controversial ever since the issue was first analyzed by Waugh [15]. The early approach of Waugh, which was based explicitly on expected consumer's surplus and ignored the production side of the economy, has since been generalized in several respects. For instance, Turnovsky, Shalit, and Schmitz (hereafter T-S-S) [14] have suggested an approach that utilizes the indirect utility function of a single individual. By focusing on a single consumer and comparing risk-no risk situations where prices are random variables, they derive interesting and useful results that express conditions for the desirability of price stabilization in terms of the familiar Arrow-Pratt measure of relative risk aversion, price and income elasticities, and budget shares. Although the approach of T-S-S provides useful information about an individual's preference for or against price stability, it does not provide information about a group of heterogeneous consumers' preference for price stability. The approach of T-S-S also assumes that perfect price stabilization is possible; indeed, in many cases government policy may serve to partially stabilize prices, but not perfectly stabilize prices.2 Thus the analysis of T-S-S does not address comparisons of risk-risk situations (the comparisons of unstable versus partially stabilized prices) nor comparisons when there are heterogeneous individuals. Recently, Newbery and Stiglitz [9, 10] have used stochastic dominance rules to analyze mean preserving partial price stabilization schemes. The purpose of the present note is to extend the T-S-S and Newbery-Stiglitz analysis by providing comparisons of partial price stabilization policies that affect multiple prices in non-mean preserving ways. Since an excellent survey of the stabilization literature appears in Newbery and Stiglitz [10], we proceed with the results of our analysis.

This paper develops a continuous time general equilibrium model of a simple but complete economy and uses it to examine the behavior of asset prices. In this model, asset prices and their stochastic properties are determined endogenously. One principal result is a partial differential equation which asset prices must satisfy. The solution of this equation gives the equilibrium price of any asset in terms of the underlying real variables in the economy. IN THIS PAPER, we develop a general equilibrium asset pricing model for use in applied research. An important feature of the model is its integration of real and financial markets. Among other things, the model endogenously determines the stochastic process followed by the equilibrium price of any financial asset and shows how this process depends on the underlying real variables. The model is fully consistent with rational expectations and maximizing behavior on the part of all agents. Our framework is general enough to include many of the fundamental forces affecting asset markets, yet it is tractable enough to be specialized easily to produce specific testable results. Furthermore, the model can be extended in a number of straightforward ways. Consequently, it is well suited to a wide variety of applications. For example, in a companion paper, Cox, Ingersoll, and Ross [7], we use the model to develop a theory of the term structure of interest rates. Many studies have been concerned with various aspects of asset pricing under uncertainty. The most relevant to our work are the important papers on intertemporal asset pricing by Merton [19] and Lucas [16]. Working in a continuous time framework, Merton derives a relationship among the equilibrium expected rates of return on assets. He shows that when investment opportunities are changing randomly over time this relationship will include effects which have no analogue in a static one period model. Lucas considers an economy with homogeneous individuals and a single consumption good which is produced by a number of processes. The random output of these processes is exogenously determined and perishable. Assets are defined as claims to all or a part of the output of a process, and the equilibrium determines the asset prices. Our theory draws on some elements of both of these papers. Like Merton, we formulate our model in continuous time and make full use of the analytical tractability that this affords. The economic structure of our model is somewhat similar to that of Lucas. However, we include both endogenous production and

[It is shown that if an iterative price mechanism depends only upon a finite amount of information from the market as given by the aggregate excess demand function, then this mechanism cannot always be effective. That is, there are pure exchange economies where this mechanism will not find a price equilibrium. This statement already holds in the case of two commodities. The approach used to reach this conclusion extends to other iterative systems used to determine the zeros of a function.]