ORDINARY LEAST SQUARES ESTIMATION OF A DYNAMIC GAME MODEL

• Author: Sorawoot Srisuma,Fabio A. Miessi Sanches,Daniel Junior Silva
• Date: 01 May 2016
• DOI: http://doi.org/10.1111/iere.12170
• Published date: 01 May 2016

INTERNATIONAL ECONOMIC REVIEW

Vol. 57, No. 2, May 2016

ORDINARY LEAST SQUARES ESTIMATION OF A DYNAMIC GAME MODEL∗

BYFABIO A. MIESSI SANCHES,DANIEL JUNIOR SILVA,AND SORAWOOT SRISUMA1

University of S˜

ao Paulo, Brazil; University of Warwick, U.K.; University of Surrey, U.K.

Estimation of dynamic games is known to be a numerically challenging task. A common form of the payoff functions

employed in practice takes the linear-in-parameter specification. We show a least squares estimator taking a familiar

OLS/GLS expression is available in such a case. Our proposed estimator has a closed form. It can be computed without

anynumerical optimization and always minimizes the least squares objective function. We specify the optimally weighted

GLS estimator that is efficient in the class of estimators under consideration. Our estimator appears to perform well in

a simple Monte Carlo experiment.

1. INTRODUCTION

We consider the computational aspect for estimating a popular class of dynamic games in an

infinite time horizon, where players’ private values enter the payoff function additively and are

independent across players, under the conditional independence framework. Recent surveys

for such model can be found in Aguirregabiria and Mira (2010) and Bajari et al. (2012). A

variety of methods have been proposed to estimate these games in recent years; examples

are given below. However, a common component of the methodologies in the literature is a

nonlinear optimization problem that may act as a considerable deterrent for applied researchers

to estimate dynamic games due to involved programming needs and/or long computational

time.

In this note, we propose a simple class of least squares estimators that have closed form

when the payoffs have a linear-in-parameter specification. Our estimator takes a familiar or-

dinary least squares (OLS) expression in the simplest case, and the efficient version has the

generalized least squares (GLS) form. The linear parameterization can be quite general. In

games with finite states linear-in-parameter payoff can be interpreted as nonparametric; oth-

erwise it can generally represent any nonlinear (basis) functions of observables. In any case,

payoff with the linear-in-parameter structure is the leading specification employed in empirical

work.

Estimation of dynamic games can be challenging. Games with multiple equilibria give rise

to incomplete models, where each parameter corresponds to multiple probability distributions

(Tamer, 2003). Even without the multiplicity issue, a full solution approach is computationally

demanding since the game has to be solved for every parameter value (Rust, 1994). A popular

approach to estimate dynamic games is to perform a two-step estimation procedure. Its origin

can be traced back to the novel work of Hotz and Miller (1993) in a single agent setting, whose

insight is to perform inference on a model that is generated using the empirical decision rule

that can be estimated in the first step from the observed choice and transition probabilities.

∗Manuscript received June 2014; revised January 2015.

1We are grateful to Martin Pesendorfer for encouragement and support. We thank a coeditor and an associate editor

and anonymous referees for suggestions that helped improve the article. We also thank Joachim Groeger, Emmanuel

Guerre, Oliver Linton, Robert Miller, Pasquale Schiraldi, Richard Smith, and Dimitri Szerman for useful advice and

comments. Please address correspondence to: Sorawoot Srisuma, School of Economics, University of Surrey, Guildford,

Surrey, GU2 7XH, U.K. E-mail: s.srisuma@surrey.ac.uk.

623

C

(2016) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association