We are thankful for comments from a co-editor, four anonymous referees, Pat Bajari, Victor Chernozukov, Phil Haile, Igal Hendel, Han Hong, Ken Judd, Mike Keane, Bob Miller, Ariel Pakes, Martin Pesendorfer, Matt Shum, Steven Stern, Eli Tamer, Ken Wolpin, and seminar participants at Amsterdam (Tinbergen), Universidad Carlos III, Carnegie–Mellon, CEMFI, Duke, Harvard, MIT, Minnesota, New York University, Princeton, Queen's, Stanford, Texas–Austin, Toronto, Toulouse, Virginia, and Wisconsin–Madison. The first author thanks the National Science Foundation for financial support (Grant SES-0241943). The second author acknowledges support from the Ministerio de Educacion y Ciencia (Grant BEC2002-02773). We thank Gustavo Vicentini for his excellent research assistance. We also thank Hernan Roman for providing the data that we used in the empirical application.
Sequential Estimation of Dynamic Discrete Games
Version of Record online: 29 JAN 2007
Volume 75, Issue 1, pages 1–53, January 2007
How to Cite
Aguirregabiria, V. and Mira, P. (2007), Sequential Estimation of Dynamic Discrete Games. Econometrica, 75: 1–53. doi: 10.1111/j.1468-0262.2007.00731.x
- Issue online: 29 JAN 2007
- Version of Record online: 29 JAN 2007
- Manuscript received March, 2005; final revision received September, 2006.
- Dynamic discrete games;
- multiple equilibria;
- pseudo maximum likelihood estimation;
- entry and exit in oligopoly markets
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.