Knowledge that Transforms

This paper studies the estimation of dynamic discrete games of incomplete information. Two main econometric issues appear in the estimation of these models: the indeterminacy problem associated with the existence of multiple equilibria, and the computational burden in the solution of the game. We propose a class of pseudo maximum likelihood (PML) estimators that deals with these problems and we study the asymptotic and finite sample properties of several estimators in this class. We first focus on two-step PML estimators which, though attractive for their computational simplicity, have some important limitations: they are seriously biased in small samples; they require consistent nonparametric estimators of players’ choice probabilities in the first step, which are not always feasible for some models and data; and they are asymptotically inefficient. Second, we show that a recursive extension of the two-step PML, which we call nested pseudo likelihood (NPL), addresses those drawbacks at a relatively small additional computational cost. The NPL estimator is particularly useful in applications where consistent nonparametric estimates of choice probabilities are either not available or very imprecise, e.g., models with permanent unobserved heterogeneity. Finally, we illustrate these methods in Montecarlo experiments and in an empirical application to a model of firm entry and exit in oligopoly markets using Chilean data from several retail industries.

Earlier version: June 16, 2004; Revision: June 22, 2006

Consider a Bayesian collective decision problem in which the preferences of agents are private information. We provide a general demonstration that the utility costs associated with incentive constraints become negligible when the decision problem is linked with a large number of independent copies of itself. This is established by defining a mechanism in which agents must budget their representations of preferences so that the frequency of preferences across problems mirrors the underlying distribution of preferences, and then arguing that agents' incentives are to satisfy their budget by being as truthful as possible. We also show that all equilibria of the linking mechanisms converge to the target utility levels. The mechanisms do not require transferable utility or interpersonal comparisons of utility, and are immune to manipulations by coalitions.

In this paper, we consider the nonparametric identification and estimation of the average effect of a dummy endogenous regressor in models where the regressors are weakly but not additively separable from the error term. The model is not required to be strictly increasing in the error term, and the class of models considered includes limited dependent variable models such as discrete choice models. Conditions are established conditions under which it is possible to identify the average effect of the dummy endogenous regressor in a weakly separable model without relying on parametric functional form or distributional assumptions and without the use of large support conditions.

We report recent advances concerning the package allocation problem, in which traders seek to buy or sell combinations of goods. The problems are most difficult when some goods are not substitutes. In that case, competitive equilibrium typically fail to exist but the core is non-empty and comprises the competitive solutions. Also in that case, the Vickrey auction fails to select core allocations and yield revenues that are less than competitive. The Ausubel-Milgrom auction generally selects core allocations and, when goods are substitutes, prescribes the Vickrey allocation. We also evaluate the problems and promise of mechanisms for the package exchange problem.

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This paper analyzes equlibrium and welfare for a tractable class of economies (games) with externalities, strategic complementarity or substitutability, and heterogenous information. First, we characterize the equilibrium use of information; complementarity heightens the sensitivity of equilibrium actions to public information, raising aggregate volatility, whereas substitutability heightens the sensitivity to private information, cross-sectional dispersion. Next, we define and characterize an efficiency benchmark designed to address whether the equilibrium use of information is optimal from a social perspective; the efficient use of information reflects the social value of aligning choices across agents. Finally, we examine the comparative statics of equilibrium welfare with respect to the information structure; the social value of information is best understood by classifying economies according to the inefficiency, if any, in the equilibrium use of information. We conclude with a few applications, including production externalities, beauty contests, business cycles, and large Cournot and Bertrand games.

This paper develops a theoretical framework for studying contract and enforcement in settings with nondurable trading opportunities and complete but unverifiable information. The framework explicitly accounts for the parties' individual trade actions. The sets of implementable state-contingent payoffs, under various assumptions about renegotiation opportunities, are characterized and compared. The results indicate the benefit of modeling trade actions as individual, rather than as public, and they highlight the usefulness of a structured game-theoretic framework for applied research.

This paper examines changes in the distribution of wages using bounds to allow for the impact of nonrandom selection into work. We show that worst case bounds can be informative. However, because employment rates in the United Kingdom are often low, they are not informative about changes in educational or gender wage differentials. Thus we explore ways to tighten these bounds using restrictions motivated from economic theory. With these assumptions, we find convincing evidence of an increase in inequality within education groups, changes in educational differentials, and increases in the relative wages of women.

Does individual behavior in a laboratory setting provide a reliable indicator of behavior in a naturally occurring setting? We consider this general methodological question in the context of eliciting risk attitudes. The controls that are typically employed in laboratory settings, such as the use of abstract lotteries, could lead subjects to employ behavioral rules that differ from the ones they employ in the field. Because it is field behavior that we are interested in understanding, those controls might be a confound in themselves if they result in differences in behavior. We find that the use of artificial monetary prizes provides a reliable measure of risk attitudes when the natural counterpart outcome has minimal uncertainty, but that it can provide an unreliable measure when the natural counterpart outcome has background risk. Behavior tended to be moderately risk averse when artificial monetary prizes were used or when there was minimal uncertainty in the natural nonmonetary outcome, but subjects drawn from the same population were much more risk averse when their attitudes were elicited using the natural nonmonetary outcome that had some background risk. These results are consistent with conventional expected utility theory for the effects of background risk on attitudes to risk.