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Sequential Estimation of Dynamic Discrete Games

  • Victor Aguirregabiria

    (Boston University)

  • Pedro Mira

    (CEMFI)

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, though 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 feasible for some models and data; 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 are either not available or very imprecise, e.g., models with permanent unobserved heterogeneity. Finally, we illustrate these methods in Montecarlo experiments and in an empirical application to a model of firm entry and exit in oligopoly markets using Chilean data from several retail industries.

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File URL: http://econwpa.repec.org/eps/io/papers/0406/0406006.pdf
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Paper provided by EconWPA in its series Industrial Organization with number 0406006.

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Length: 38 pages
Date of creation: 17 Jun 2004
Date of revision:
Handle: RePEc:wpa:wuwpio:0406006
Note: Type of Document - pdf; pages: 38
Contact details of provider: Web page: http://econwpa.repec.org

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  1. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
  2. Bresnahan, T.F & Reiss, P.C., 1989. "Entry And Competition In Concentrated Markets," Papers 151, Stanford - Studies in Industry Economics.
  3. Hotz, V.J. & Miller, R.A., 1991. "Conditional Choice Probabilities and the Estimation of Dynamic Models," GSIA Working Papers 1992-12, Carnegie Mellon University, Tepper School of Business.
  4. J. Levin & P. Bajari, 2004. "Estimating Dynamic Models of Imperfect Competition," 2004 Meeting Papers 579, Society for Economic Dynamics.
  5. Hotz, J.V. & Miller, R.A. & Sanders, S. & Smith, J., 1992. "A Simulation Estimator for Dynamic Models of Discrete Choice," GSIA Working Papers 1992-13, Carnegie Mellon University, Tepper School of Business.
  6. 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.
  7. Martin Pesendorfer & Philipp Schmidt-Dengler, 2003. "Identification and Estimation of Dynamic Games," NBER Working Papers 9726, National Bureau of Economic Research, Inc.
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  9. Kooreman, Peter, 1994. "Estimation of Econometric Models of Some Discrete Games," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(3), pages 255-68, July-Sept.
  10. Jovanovic, Boyan, 1989. "Observable Implications of Models with Multiple Equilibria," Econometrica, Econometric Society, vol. 57(6), pages 1431-37, November.
  11. Bresnahan, Timothy F. & Reiss, Peter C., 1991. "Empirical models of discrete games," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 57-81.
  12. Alberto Bisin & Andrea Moro & Giorgio Topa, 2006. "The Empirical Content of Models with Multiple Equilibria," 2006 Meeting Papers 660, Society for Economic Dynamics.
  13. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 70(1), pages 147-165, January.
  14. 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.
  15. 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.
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  17. James J. Heckman, 1977. "Dummy Endogenous Variables in a Simultaneous Equation System," NBER Working Papers 0177, National Bureau of Economic Research, Inc.
  18. Paul Milgrom & Robert Weber, 1981. "Distributional Strategies for Games with Incomplete Information," Discussion Papers 428R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  19. Newey, Whitney K. & McFadden, Daniel, 1986. "Large sample estimation and hypothesis testing," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 36, pages 2111-2245 Elsevier.
  20. Brock, William A & Durlauf, Steven N, 2001. "Discrete Choice with Social Interactions," Review of Economic Studies, Wiley Blackwell, vol. 68(2), pages 235-60, April.
  21. Victor Aguirregabiria & Pedro Mira, 1999. "Swapping the Nested Fixed-Point Algorithm: a Class of Estimators for Discrete Markov Decision Models," Computing in Economics and Finance 1999 332, Society for Computational Economics.
  22. 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.
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  24. Bresnahan, Timothy F & Reiss, Peter C, 1990. "Entry in Monopoly Markets," Review of Economic Studies, Wiley Blackwell, vol. 57(4), pages 531-53, October.
  25. 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 for Research in Economics, Yale University.
  26. Ericson, Richard & Pakes, Ariel, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Wiley Blackwell, vol. 62(1), pages 53-82, January.
  27. Ariel Pakes & Paul McGuire, 1992. "Computing Markov perfect Nash equilibria: numerical implications of a dynamic differentiated product model," Discussion Paper / Institute for Empirical Macroeconomics 58, Federal Reserve Bank of Minneapolis.
  28. repec:att:wimass:9106 is not listed on IDEAS
  29. 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.
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  31. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
  32. Berry, Steven T, 1992. "Estimation of a Model of Entry in the Airline Industry," Econometrica, Econometric Society, vol. 60(4), pages 889-917, July.
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