Imposing Equilibrium Restrictions in the Estimation of Dynamic Discrete Games

48 Pages Posted: 7 Oct 2019

See all articles by Victor Aguirregabiria

Victor Aguirregabiria

University of Toronto - Department of Economics

Mathieu Marcoux

University of Montreal

Date Written: September 2019

Abstract

Imposing equilibrium restrictions provides substantial gains in the estimation of dynamic discrete games. Estimation algorithms imposing these restrictions -- MPEC, NFXP, NPL, and variations -- have different merits and limitations. MPEC guarantees local convergence, but requires the computation of high-dimensional Jacobians. The NPL algorithm avoids the computation of these matrices, but -- in games -- may fail to converge to the consistent NPL estimator. We study the asymptotic properties of the NPL algorithm treating the iterative procedure as performed in finite samples. We find that there are always samples for which the algorithm fails to converge, and this introduces a selection bias. We also propose a spectral algorithm to compute the NPL estimator. This algorithm satisfies local convergence and avoids the computation of Jacobian matrices. We present simulation evidence illustrating our theoretical results and the good properties of the spectral algorithm.

Keywords: convergence, Convergence selection bias, Dynamic discrete games, Nested pseudo-likelihood, Spectral algorithms

JEL Classification: C13, C57, C61, C73

Suggested Citation

Aguirregabiria, Victor and Marcoux, Mathieu, Imposing Equilibrium Restrictions in the Estimation of Dynamic Discrete Games (September 2019). CEPR Discussion Paper No. DP14007, Available at SSRN: https://ssrn.com/abstract=3464536

Victor Aguirregabiria (Contact Author)

University of Toronto - Department of Economics ( email )

150 St. George Street
Toronto, Ontario M5S 3G7
Canada
4169784358 (Phone)

HOME PAGE: http://individual.utoronto.ca/vaguirre/

Mathieu Marcoux

University of Montreal ( email )

C.P. 6128 succursale Centre-ville
Montreal, Quebec H3C 3J7
Canada

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