Sequential Estimation of Dynamic Discrete Games

Abstract

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, 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. 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 either are not available or are very imprecise, e.g., models with permanent unobserved heterogeneity. Finally, we illustrate 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. Copyright The Econometric Society 2007.

A Microeconometric Model of Firm Turnover

“…Notice that we do not include any measures of market size. This is in contrast to the studies by [1] [2] [4] where market size largely drives the empirical fit of their models. Because those studies analyze firms which operate in the retail and service sectors and serve local communities, market size is important.…”

“…This follows the empirical modeling approach of A & M [4]. Notice that we do not include any measures of market size.…”

“…As in A & M [4], we assume that a market has N representative firms who compete in quantities and reach a static equilibrium in each period. The Cournot model that we adopt specifies a market demand of the form P = α -βQ and a market supply given by Q = Nq.…”

“…To date, most studies of firm concentration have considered local markets (e.g., [1]- [4]) and as a consequence they have exploited market size as a key determinant of the number of firms. We consider instead the case of intermediate goods producers, specifically agro-food processors, whose markets may be regional, national, or even international.…”

Limit theory for panel data models with cross sectional dependence and sequential exogeneity

“…However, it also accommodates more general dynamic games where actors play stationary Markov strategies taking into account decisions of other actors. Examples of such models can be found in Rust (1994), Aguirregabiria and Mira (2007) and Bajari, Benkard and Levin (2007) who all impose the conditional independence assumption . 14 In these models σ i is the equilibrium strategy function taking into account the strategic behavior of the other agents through x t .…”