We analyze equilibria in exchange economies following the approach taken by Borch and Wilson. We correct Wilson's main result by showing that linear contracts are sufficient but not necessary for the existence of syndicates under heterogeneous beliefs. We introduce the concept of the decomposability of syndicates and demonstrate that linear contracts are necessary only for arbitrarily decomposable syndicates. This implies that groups that form syndicates under an arbitrary set of beliefs must also employ linear contracts.

This paper, which in part serves as a common introduction to the two papers following in this issue, attempts to define the meaning of the interpretability of a parameter in a system of simultaneous linear relationships. It attempts, moreover, to expound a basis for interpreting the parameters of a nonrecursive or interdependent system causally. This is done in terms of an underlying causal chain system to which the interdependent system is either an approximation or a description of the equilibrium state. OVER THE PAST fifteen years there has been an extended discussion of the meaning and applicability of nonrecursive as distinct from recursive systems in econometrics, and throughout this discussion there has been a marked divergence of views as to the merits of the two types of models. It is not the purpose of this note to extend that controversy further, but rather to attempt a constructive statement of the relationship betweenthe two approaches and the circumstances under which each is applicable. We assume that the reader is generally familiar with the past discussion' and that it will suffice here simply to recall that a recursive, or causalchain, system has the formal property that the coefficient matrix of the non-lagged endogenous variables is triangular (upon suitable ordering of rows and columns) whereas a nonrecursive, or interdependent, system is one for which this is not the case. While the triangularity of the coefficient matrix is a formal property of recursive models, the essential property is that each relation is provided a causal interpretation in the sense of a stimulus-response relationship. The question of whether and in what sense nonrecursive systems allow a causal interpretation is the main theme of this paper.

This paper is concerned with the use of spectral analysis to analyze data generated by computer simulation experiments with models of economic systems. An example model serves to illustrate two different applications of spectral analysis. First, spectral analysis is used to construct confidence bands and to test hypotheses for the purpose of comparing the results of the use of two or more alternative economic policies. Second, spectral analysis is employed as a technique for validating an econometric model.

We study mixed hitting-time models that specify durations as the first time a Lévy process-a continuous-time process with stationary and independent incrementscrosses a heterogeneous threshold.Such models of substantial interest because they can be deduced from optimal-stopping models with heterogeneous agents that do not naturally produce a mixed proportional hazards structure.We show how strategies for analyzing the identifiability of the mixed proportional hazards model can be adapted to prove identifiability of a hitting-time model with observed covariates and unobserved heterogeneity.We discuss inference from censored data and give examples of structural applications.We conclude by discussing the relative merits of both models as complementary frameworks for econometric duration analysis.

Consider a two-player discounted infinitely repeated game. A player's belief is a probability distribution over the opponent's repeated game strategies. This paper shows that, for a large class of repeated games, there are no beliefs that satisfy three properties: learnability, a diversity of belief condition called CSP, and consistency. Loosely, if players learn to forecast the path of play whenever each plays a strategy that the other anticipates (in the sense of being in the support of that player's belief) and if the sets of anticipated strategies are sufficiently rich, then neither anticipates any of his opponent's best responses. This generalizes results in Nachbar (1997).

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