Knowledge that Transforms

This paper considers a general equilibrium model of an economy where some firms may exhibit increasing returns to scale or more general types of nonconvexities. The firms are instructed to follow the standard marginal cost pricing rule or to fulfill the first-order necessary conditions for profit maximization. A general existence theorem of equilibria is proved in the case of an arbitrary number of firms. No assumption is made to imply the aggregate productive efficiency of equilibria, a condition that must be excluded in the nonconvex case. Copyright 1990 by The Econometric Society.

This paper proposes a new approach to the study of economic problems that have hitherto been modeled as games with discontinuous payoffs. Typically, the discontinuities arise from indeterminacies in the underlying problem. The authors' point of departure from the conventional approach is to view the sharing rules that resolve these indeterminacies as part of the solution rather than as part of the description of the model. A solution to the authors' model is a sharing rule, together with a profile of (mixed) strategies that satisfies the usual (Nash) best response criterion. Their main result is that such a solution always exists. Copyright 1990 by The Econometric Society.

MCKELVEY AND PAGE (1986) proved a remarkable theorem on common knowledge. Suppose n individuals start with a common prior and then form conditional probabilities of some event of interest based on their different information. If a stochastically monotone aggregate of the n conditional probabilities is common knowledge, then the assessments must be identical. We show that the aggregation of individual assessments allowed for in the theorem admits an elementary characterization: a function is stochastically monotone if and only if it is additively separable into strictly increasing components

This paper is an empirical investigation of equilibrium restrictions on household consumption and male labor supply. It exploits a simple factor structure, rationalized by two assumptions, that household allocations are Pareto optimal and that the labor market is competitive. The paper estimates household preferences, and tests how well this parsimonious factor structure represents panel data on married couples and time series data on asset returns. Most of the estimates are roughly comparable to those found in previous work; no evidence against the simple factor representation is found and the intertemporal capital asset pricing model is not rejected. Copyright 1990 by The Econometric Society.

The authors study a rich class of noncooperative games that includes models of oligopoly competition, macroeconomic coordination failures, arms races, bank runs, technology adoption and diffusion, R&D competition, pretrial bargaining, coordination in teams, and many others. For all these games, the sets of pure strategy Nash equilibria, correlated equilibria, and rationalizable strategies have identical bounds. Also, for a class of models of dynamic adaptive choice behavior that encompasses both best-response dynamics and Bayesian learning, the players' choices lie eventually within the same bounds. These bounds are shown to vary monotonically with certain exogenous parameters. Copyright 1990 by The Econometric Society.

Using the Eaton and Lipsey mode, one shows that a hierarchical system of central places is socially optimal: firms having less frequent purchases are clustered with firms having more frequent purchases in any configuration minimizing total transport and production costs

EMPIRICAL STUDIES OF TWO SIDED MATCHING have so far concentrated on markets in which certain kinds of market failures were addressed by resorting to centralized, deterministic matching procedures. Loosely speaking, the results of these studies are that those centralized procedures which achieved stable outcomes resolved the market failures, while those markets organized through procedures that yielded unstable outcomes continued to fail.2 So the market failures seem to be associated with instability of the outcomes. But many entry-level labor markets and other two-sided matching situations don't employ centralized matching procedures, and yet aren't observed to experience such failures. So we can conjecture that at least some of these markets may reach stable outcomes by means of decentralized decision making. And decentralized decision making in complex environments presumably introduces some randomness into what matchings are achieved. However, as far as we are aware, no nondeterministic models leading to stable outcomes have yet been studied. The present paper demonstrates that, starting from an arbitrary matching, the process of allowing randomly chosen blocking pairs to match will converge to a stable matching with probability one. (This resolves an open question raised by Knuth (1976), who showed that such a process may cycle.) Furthermore, every stable matching can arise

In the general structural equation model only the direction of the vector of coefficients of the endogenous variables is determined.The traditional normalization rule defines the coefficients that are of interest but should not be embodied in the estimation procedure: we show that the properties of the traditionally defined ordinary least squares and two stage least squares estimators are distorted by their dependence on the normalization rule.Symmetrically normalized analogues of these estimators are defined and are shown to have essentially similar properties to those of the limited information maximum likelihood estimator.

IN NONLINEAR MODELS the power function is often approximated by asymptotic methods. The most common approach is to consider the asymptotic local power function. The local power function is monotonic and it has essentially the same shape as the power function in the classical normal linear regression model. However, the accuracy of the approximation can be poor at nonlocal alternatives. This note examines the exact powers of the Wald test in the case of a one parameter nonlinear regression model with normal errors. The model is based on the exponential response function f( x, O) = exp( Ox). The results show that the exact power function of the Wald statistic can be nonmonotonic. For selected designs the exact powers of the Wald test first increase and then eventually decline as the distance between the hypothesized and the true values of the parameter increases. The exponential structure appears in many nonlinear models; see Gallant (1975, 1987) and Bates and Watts (1988). This suggests that nonmonotonicity of the Wald test is a feature of a wide class of nonlinear models. Indeed, Nelson and Savin (1988) show that it arises in standard logit, probit, and Tobit models as well. The focus here on the nonlinear regression model is for expository convenience. While the existence of nonmonotonic power is not new, the surprising results are that this phenomenon occurs in very simple nonlinear models and that it can be quite severe. In such cases the asymptotic local power approximation provides a very poor guide to the performance of alternative tests.