On the iterated estimation of dynamic discrete choice games

We study the asymptotic properties of a class of estimators of the structural parameters in dynamic discrete choice games. We consider K-stage policy iteration (PI) estimators, where K denotes the number of policy iterations employed in the estimation. This class nests several estimators proposed in the literature. By considering a "maximum likelihood" criterion function, our estimator becomes the K- ML estimator in Aguirregabiria and Mira (2002, 2007). By considering a "minimum distance" criterion function, it defines a new K-MD estimator, which is an iterative version of the estimators in Pesendorfer and Schmidt-Dengler (2008) and Pakes et al. (2007). First, we establish that the K-ML estimator is consistent and asymptotically normal for any K. This complements findings in Aguirregabiria and Mira (2007), who focus on K = 1 and K large enough to induce convergence of the estimator. Furthermore, we show that the asymptotic variance of the K-ML estimator can exhibit arbitrary patterns as a function K. Second, we establish that the K-MD estimator is consistent and asymptotically normal for any K. [...]