Sequential Estimation of Dynamic Discrete Games

52 Pages Posted: 20 Jun 2004 Last revised: 30 Oct 2016

See all articles by Victor Aguirregabiria

Victor Aguirregabiria

University of Toronto - Department of Economics

Pedro Mira

Centro de Estudios Monetarios y Financieros (CEMFI)

Date Written: January 1, 2007


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.

Keywords: Dynamic discrete games, Multiple equilibria, Pseudo maximum likelihood estimation, Entry and exit in oligopoly markets

JEL Classification: C13, C35, C63, C73

Suggested Citation

Aguirregabiria, Victor and Mira, Pedro, Sequential Estimation of Dynamic Discrete Games (January 1, 2007). Econometrica, Vol. 75, No. 1, Available at SSRN: or

Victor Aguirregabiria (Contact Author)

University of Toronto - Department of Economics ( email )

150 St. George Street
Toronto, Ontario M5S 3G7
4169784358 (Phone)


Pedro Mira

Centro de Estudios Monetarios y Financieros (CEMFI) ( email )

Casado del Alisal 5
28014 Madrid
34 91 429 0551 (Phone)
34 91 429 1056 (Fax)

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