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

Adam Dearing and Jason R. Blevins.
The Ohio State University, Department of Economics
Working Paper.

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Abstract. We propose a new sequential Efficient Pseudo-Likelihood (k-EPL) estimator for dynamic discrete choice games of incomplete information. 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.

Keywords: dynamic discrete games, dynamic discrete choice, multiple equilibria, pseudo maximum likelihood estimation.

JEL Classification: C57, C63, C73, L13.

BibTeX Record:

@TechReport{dearing-blevins-2021,
  author       = {Adam Dearing and Jason R. Blevins},
  title        = {Efficient and Convergent Sequential Pseudo-Likelihood Estimation of Dynamic Discrete Games},
  year         = {2021},
  type         = {Working Paper},
  institution  = {The Ohio State University}
}