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Sequential Estimation of Dynamic Discrete Games

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Author Info
Victor Aguirregabiria
Pedro Mira

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Abstract

This paper studies the estimation of dynamic discrete games of incomplete information. Two main econometric issues appear in the estimation of these models: the indeterminacy problem associated with the existence of multiple equilibria and the computational burden in the solution of the game. We propose a class of pseudo maximum likelihood (PML) estimators that deals with these problems, and we study the asymptotic and finite sample properties of several estimators in this class. We first focus on two-step PML estimators, which, although they are attractive for their computational simplicity, have some important limitations: they are seriously biased in small samples; they require consistent nonparametric estimators of players' choice probabilities in the first step, which are not always available; and they are asymptotically inefficient. Second, we show that a recursive extension of the two-step PML, which we call nested pseudo likelihood (NPL), addresses those drawbacks at a relatively small additional computational cost. The NPL estimator is particularly useful in applications where consistent nonparametric estimates of choice probabilities either are not available or are very imprecise, e.g., models with permanent unobserved heterogeneity. Finally, we illustrate these methods in Monte Carlo experiments and in an empirical application to a model of firm entry and exit in oligopoly markets using Chilean data from several retail industries. Copyright The Econometric Society 2007.

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File URL: http://hdl.handle.net/10.1111/j.1468-0262.2007.00731.x
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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 75 (2007)
Issue (Month): 1 (01)
Pages: 1-53
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Handle: RePEc:ecm:emetrp:v:75:y:2007:i:1:p:1-53

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  1. Martin Pesendorfer & Philipp Schmidt-Dengler, 2003. "Identification and Estimation of Dynamic Games," NBER Working Papers 9726, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  2. Ariel Pakes & Michael Ostrovsky & Steve Berry, 2004. "Simple Estimators for the Parameters of Discrete Dynamic Games (with Entry/Exit Samples)," NBER Working Papers 10506, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
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  3. McKelvey, Richard D. & McLennan, Andrew, 1996. "Computation of equilibria in finite games," Handbook of Computational Economics, in: H. M. Amman & D. A. Kendrick & J. Rust (ed.), Handbook of Computational Economics, edition 1, volume 1, chapter 2, pages 87-142 Elsevier. [Downloadable!] (restricted)
  4. repec:att:wimass:19916 is not listed on IDEAS
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  6. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Blackwell Publishing, vol. 70(1), pages 147-165, January.
  7. Victor Aguirregabiria & Pedro Mira, 2002. "Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models," Econometrica, Econometric Society, vol. 70(4), pages 1519-1543, July. [Downloadable!] (restricted)
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  8. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
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  9. Ariel Pakes & Paul McGuire, 1997. "Stochastic Algorithms for Dynamic Models: Markov Perfect Equilibrium, and the 'Curse' of Dimensionality," Cowles Foundation Discussion Papers 1144, Cowles Foundation, Yale University. [Downloadable!]
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  11. Andrea Moro, 2003. "The Effect Of Statistical Discrimination On Black-White Wage Inequality: Estimating A Model With Multiple Equilibria," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(2), pages 467-500, 05. [Downloadable!] (restricted)
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  15. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-59, July. [Downloadable!] (restricted)
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  16. Janet S. Netz & Beck A. Taylor, 2002. "Maximum Or Minimum Differentiation? Location Patterns Of Retail Outlets," The Review of Economics and Statistics, MIT Press, vol. 84(1), pages 162-175, February. [Downloadable!] (restricted)
  17. Ericson, Richard & Pakes, Ariel, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Blackwell Publishing, vol. 62(1), pages 53-82, January. [Downloadable!] (restricted)
  18. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, 09. [Downloadable!] (restricted)
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  19. Ariel Pakes & Paul McGuire, 1994. "Computing Markov-Perfect Nash Equilibria: Numerical Implications of a Dynamic Differentiated Product Model," RAND Journal of Economics, The RAND Corporation, vol. 25(4), pages 555-589, Winter. [Downloadable!] (restricted)
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  20. Jovanovic, Boyan, 1989. "Observable Implications of Models with Multiple Equilibria," Econometrica, Econometric Society, vol. 57(6), pages 1431-37, November. [Downloadable!] (restricted)
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  21. Hotz, V Joseph & Robert A. Miller & Seth Sanders & Jeffrey Smith, 1994. "A Simulation Estimator for Dynamic Models of Discrete Choice," Review of Economic Studies, Blackwell Publishing, vol. 61(2), pages 265-89, April. [Downloadable!] (restricted)
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  22. Bresnahan, Timothy F & Reiss, Peter C, 1991. "Entry and Competition in Concentrated Markets," Journal of Political Economy, University of Chicago Press, vol. 99(5), pages 977-1009, October. [Downloadable!] (restricted)
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  23. Berry, Steven T, 1992. "Estimation of a Model of Entry in the Airline Industry," Econometrica, Econometric Society, vol. 60(4), pages 889-917, July. [Downloadable!] (restricted)
  24. Hotz, V Joseph & Miller, Robert A, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," Review of Economic Studies, Blackwell Publishing, vol. 60(3), pages 497-529, July. [Downloadable!] (restricted)
  25. Bresnahan, Timothy F. & Reiss, Peter C., 1991. "Empirical models of discrete games," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 57-81. [Downloadable!] (restricted)
  26. Toivanen, Otto & Waterson, Michael, 2000. "Empirical research on discrete choice game theory models of entry: An illustration," European Economic Review, Elsevier, vol. 44(4-6), pages 985-992, May. [Downloadable!] (restricted)
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