Sequential estimation of dynamic discrete games

This paper studies the estimation of dynamic discrete games of incomplete informa-tion. Two main econometric issues appear in the estimation of these models: the inde-terminacy problem associated with the existence of multiple equilibria and the compu-tational 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 asymp-totic and finite sample properties of several estimators in this class. We first focus on two-step PML estimators, which, although they are 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 available; and they are asymptotically inefficient. Sec-ond, 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 con-sistent nonparametric estimates of choice probabilities either are not available or are very imprecise, e.g., models with permanent unobserved heterogeneity. Finally, we il-lustrate these methods in Monte Carlo experiments and in an empirical application to a model of firm entry and exit in oligopoly markets using Chilean data from several retail industries