Knowledge that Transforms

A new framework for games in continuous time is proposed. The continuous-time model conforms as closely as possible to the conventional discrete-time framework. Indeed, continuous time is viewed as "discrete time, but with a grid that is infinitely fine." The paper presents several examples illustrating the difficulties that arise in continuous-time game theory. Theorems relate the equilibria of continuous time games to the equilibria of approximating discrete time games. A variety of industrial organization applications are studied, yielding sharp predictions. Applications include continuously repeated games, preemption models, and patent races. Copyright 1989 by The Econometric Society.

We consider the null hypothesis that a time series has a unit root with possibly nonzero drift against the alternative that the process is «trend-stationary». The interest is that we allow under both the null and alternative hypotheses for the presence for a one-time change in the level or in the slope of the trend function. We show how standard tests of the unit root hypothesis against trend stationary alternatives cannot reject the unit root hypothesis if the true data generating mechanism is that of stationary fluctuations around a trend function which contains a one-time break

A general central limit theorem is proved for estimators defined by minimization of the length of a vector-valued, random criterion function. No smoothness assumptions are imposed on the criterion function in order that the results might apply to a broad class of simulation estimators. Complete analyses of two simulation estimators, one introduced by A. Pakes (1986) and the other by D. McFadden (1989), illustrate the application of the general theorems. These examples illustrate how simulation can be used to circumvent two computational problems that arise frequently in applied econometrics: evaluating intractable aggregation formulae and evaluating discrete response probabilities. Copyright 1989 by The Econometric Society.

In this paper, we develop a classical approach to model selection. Using the Kullback-Leibler Information Criterion to measure the closeness of a model to the truth, we propose simple likelihood-ratio based statistics for testing the null hypothesis that the competing models are equally close to the true data generating process against the alternative hypothesis that one model is closer. The tests are directional and are derived successively for the cases where the competing models are non-nested, overlapping, or nested and whether both, one, or neither is misspecified. As a prerequisite, we fully characterize the asymptotic distribution of the likelihood ratio statistic under the most general conditions. We show that it is a weighted sum of chi-square distribution or a normal distribution depending on whether the distributions in the competing models closest to the truth are observationally identical. We also propose a test of this latter condition.

This paper presents an analysis of the structure of competitive equilibrium in a smooth, exchange economy where there are incomplete markets in financial instruments whose overall payoffs (both prices and yields) are fixed in units of account. The main result establishes that such market incompleteness generates a comparable degree of allocation indeterminateness. It is also shown how this real indeterminacy may increase when prices and yields are treated as variables rather than parameters. Copyright 1989 by The Econometric Society.

A concept of an egalitarian solution is developed within the framework of cooperative game theory. The solution is designed to capture the interplay between social values (in this case, egalitarianism) and individual behavior. Both the final outcomes possible coalitional deviations are constrained by these social norms. The authors' main result: despite using a partial order (the Lorenz criterion) to compare allocations, their solution concept yields at most one allocation for each game. The concept is illustrated by a detailed study of convex games, and by a number of examples and applications. Copyright 1989 by The Econometric Society.

The past decade has seen the econometric implementation of macroeconomic multi-market fix-price models for a number of European countries. The procedure in use, the full information maximum likelihood (FIML) method, unfortunately becomes very cumbersome and seems out of reach when additional features are incorporated in the model (disaggregation into micro markets, opinion surveys,...). One purpose of the present work is to prove the fruitfulness of the following estimation strategy: use Monte-Carlo simulations to compute the first and second order moments of the endogenous variables, and maximize a resulting pseudo likelihood function to estimate the parameters. We first describe the PML method in the context of the so-called canonical disequilibrium model. We then apply it to a small aggregated macroeconomic model previously studied under FIML by Artus, Avouyi-Dovi, Laroque (1985), where we allow for a disaggregation into micro markets. The results we obtain are strikingly similar to theirs. This both demonstrates in this example the robustness of the FIML procedure to the introduction of micro markets and stresses the usefulness of the PML method in obtaining reliable estimates at a smaller cost.

A single, long-run player plays a simultaneous-move stage game against a sequence of opponents who only play once, but observe all previous play. If there is a positive prior probability that the long-run player will always play the pure strategy he would most like to commit himself to (his Stackleberg strategy), then his payoff in any Nash equilibrium exceeds a bound that converges to the Stackleberg payoff as his discount factor approaches one. When the stage game is not simultaneous move, this result must be modified to account for the possibility that distinct strategies of the long-run player are observationally equivalent. Copyright 1989 by The Econometric Society.