Asymptotic Least Squares Estimators for Dynamic Games

This paper considers the estimation problem in dynamic games with …nite actions. We derive the equation system that characterizes the Markovian equilibria. The equilibrium equation system enables us to characterize conditions for identi…cation. We consider a class of asymptotic least squares estimators de…ned by the equilibrium conditions. This class provides a uni…ed framework for a number of well known estimators including Hotz and Miller (1993) and Aguirregabiria and Mira (2002). We show that these estimators di¤er in the weight they assign to individual equilibrium conditions. We derive the e¢ cient weight matrix. A Monte Carlo study compares the …nite sample performance of alternative estimators. This paper supersedes our earlier NBER working paper entitled “Identi…cation and Estimation of Dynamic Games” from May 2003. We thank the editor Bernard Salanié and an anonymous referee, Mireia Jofre-Bonet, Alexandra Miltner, seminar participants at Alicante, Brown, Columbia, Duke, East Anglia, Lancaster, Leuven, Maryland, NYU, Queen’s, UCL, Toronto, Toulouse, Yale, Washington University, the NBER summer institute for helpful comments and Ariel Pakes for discussing the paper at the 2003 NBER summer institute. Martin Pesendorfer thanks the NSF under grant SES 0214222 for …nancial support.