Efficient and Convergent Sequential Pseudo-Likelihood Estimation of Dynamic Discrete Games

Adam Dearing and Jason R. Blevins.

Abstract. We propose a class of sequential pseudo-likelihood estimators for structural economic models with an equality constraint, with particular focus on dynamic discrete games. We show that under some regularity conditions, all estimates in the sequence are asymptotically efficient and that the sequence converges to the true parameter values with probability approaching one as the sample size grows. The key insight is to apply a single Newton iteration to the fixed point equation in estimation. We show that the nested pseudo-likelihood (NPL) estimator of Aguirregabiria and Mira (2002; 2007) is a special case of our sequential estimator in single-agent models but not in dynamic games. Furthermore, we show that a change of variable in the equilibrium fixed point equation results in an estimator that is no more computationally burdensome than NPL when flow utility is linear in parameters.

Keywords: dynamic discrete games, dynamic discrete choice, nested pseudo likelihood.