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

TL;DR

This paper introduces a new efficient and convergent sequential pseudo-likelihood estimator for dynamic discrete games, improving computational stability and asymptotic properties, and demonstrating strong finite-sample performance.

Contribution

The paper develops the k-EPL estimator that considers joint behavior of players, reformulates the problem in value function space, and proves its efficiency and convergence properties.

Findings

k-EPL is consistent and asymptotically efficient at each iteration.

The estimator converges almost surely to the maximum likelihood estimator.

Monte Carlo simulations show strong finite-sample performance.

Abstract

We propose a new sequential Efficient Pseudo-Likelihood (k-EPL) estimator for dynamic discrete choice games of incomplete information. k-EPL considers the joint behavior of multiple players simultaneously, as opposed to individual responses to other agents' equilibrium play. This, in addition to reframing the problem from conditional choice probability (CCP) space to value function space, yields a computationally tractable, stable, and efficient estimator. We show that each iteration in the k-EPL sequence is consistent and asymptotically efficient, so the first-order asymptotic properties do not vary across iterations. Furthermore, we show the sequence achieves higher-order equivalence to the finite-sample maximum likelihood estimator with iteration and that the sequence of estimators converges almost surely to the maximum likelihood estimator at a nearly-superlinear rate when the data are generated by any regular Markov perfect equilibrium, including equilibria that lead to inconsistency of other sequential estimators. When utility is linear in parameters, k-EPL iterations are computationally simple, only requiring that the researcher solve linear systems of equations to generate pseudo-regressors which are used in a static logit/probit regression. Monte Carlo simulations demonstrate the theoretical results and show k-EPL's good performance in finite samples in both small- and large-scale games, even when the game admits spurious equilibria in addition to one that generated the data. We apply the estimator to study the role of competition in the U.S. wholesale club industry.