On the iterated estimation of dynamic discrete choice games

Federico Bugni and Jackson Bunting

No CWP13/18, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal Studies

Abstract: 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 de nes 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 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 K. For a specifi c 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. 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.

Keywords: dynamic discrete choice problems; dynamic games; pseudo maximum likelihood estimator; minimum distance estimator; estimation; asymptotic efficiency (search for similar items in EconPapers)
JEL-codes: C13 C61 C73 (search for similar items in EconPapers)
Date: 2018-02-16
New Economics Papers: this item is included in nep-gth and nep-ore
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Citations: View citations in EconPapers (2)

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Related works:
Journal Article: On the Iterated Estimation of Dynamic Discrete Choice Games (2021)
Working Paper: On the iterated estimation of dynamic discrete choice games (2020)
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