SMU SOE Seminar (Mar 9, 2018): On the Iterated Estimation of Dynamic Discrete Choice Games

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TOPIC:

ON THE ITERATED ESTIMATION OF DYNAMIC DISCRETE CHOICE GAMES

ABSTRACT This paper investigates 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 ∈ ℕ 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 ∈ ℕ. This complements ndings 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 fixed K ∈ ℕ. For a specific choice of the weight matrix, the K-MD estimator has the same asymptotic distribution as the K-ML estimator. Our main result provides an optimal sequence of weight matrices for the K-MD estimator and shows that the optimally weighted K-MD estimator has an asymptotic distribution that is invariant to K. This new result is especially unexpected given the findings in Aguirregabiria and Mira (2007) for K-ML estimators. Our main result implies two new and important corollaries about the optimal 1-MD estimator (derived by Pesendorfer and Schmidt-Dengler (2008)). First, the optimal 1-MD estimator is optimal in the class of K-MD estimators for all K ∈ ℕ. In other words, additional policy iterations do not provide asymptotic efficiency gains relative to the optimal 1-MD estimator. Second, the optimal 1-MD estimator is more or equally asymptotically efficient than any K-ML estimator for all K ∈ ℕ. Keywords: Dynamic Discrete Choice Problems, Dynamic Games, Pseudo Maximum Likelihood Estimator, Minimum Distance Estimator, Estimation, Asymptotic Efficiency. JEL Classification: C13, C61, C73 Click here to view the paper. Click here to view the CV.
		PRESENTER Federico Bugni Duke University
		RESEARCH FIELDS Theoretical and Applied Econometrics
		DATE: 9 March 2018 (Friday)
		TIME: 4pm - 5.30pm
		VENUE: Meeting Room 5.1, Level 5 School of Economics Singapore Management University 90 Stamford Road Singapore 178903

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