IDEAS home Printed from https://ideas.repec.org/a/ecm/emetrp/v75y2007i1p1-53.html
   My bibliography  Save this article

Sequential Estimation of Dynamic Discrete Games

Author

Listed:
  • Victor Aguirregabiria
  • Pedro Mira

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.

Suggested Citation

  • Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
  • Handle: RePEc:ecm:emetrp:v:75:y:2007:i:1:p:1-53
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/j.1468-0262.2007.00731.x
    File Function: link to full text
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Ariel Pakes & Michael Ostrovsky & Steven Berry, 2007. "Simple estimators for the parameters of discrete dynamic games (with entry/exit examples)," RAND Journal of Economics, RAND Corporation, vol. 38(2), pages 373-399, June.
    2. 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.
    3. V. Joseph Hotz & Robert A. Miller & Seth Sanders & Jeffrey Smith, 1994. "A Simulation Estimator for Dynamic Models of Discrete Choice," Review of Economic Studies, Oxford University Press, vol. 61(2), pages 265-289.
    4. 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, May.
    5. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    6. 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.
    7. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521471626, December.
    8. Jovanovic, Boyan, 1989. "Observable Implications of Models with Multiple Equilibria," Econometrica, Econometric Society, vol. 57(6), pages 1431-1437, November.
    9. Harsanyi, John C, 1995. "Games with Incomplete Information," American Economic Review, American Economic Association, vol. 85(3), pages 291-303, June.
    10. V. Joseph Hotz & Robert A. Miller, 1993. "Conditional Choice Probabilities and the Estimation of Dynamic Models," Review of Economic Studies, Oxford University Press, vol. 60(3), pages 497-529.
    11. William A. Brock & Steven N. Durlauf, 2001. "Discrete Choice with Social Interactions," Review of Economic Studies, Oxford University Press, vol. 68(2), pages 235-260.
    12. Tauchen, George, 1986. "Finite state markov-chain approximations to univariate and vector autoregressions," Economics Letters, Elsevier, vol. 20(2), pages 177-181.
    13. 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.
    14. Heckman, James J, 1978. "Dummy Endogenous Variables in a Simultaneous Equation System," Econometrica, Econometric Society, vol. 46(4), pages 931-959, July.
    15. 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.
    16. Rust, J., 1991. "Estimation of dynamic Structural Models: Problems and Prospects Part I : Discrete Decision Processes," Working papers 9106, Wisconsin Madison - Social Systems.
    17. Berry, Steven T, 1992. "Estimation of a Model of Entry in the Airline Industry," Econometrica, Econometric Society, vol. 60(4), pages 889-917, July.
    18. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," Review of Economic Studies, Oxford University Press, vol. 62(1), pages 53-82.
    19. Martin Pesendorfer & Philipp Schmidt-Dengler, 2003. "Identification and Estimation of Dynamic Games," NBER Working Papers 9726, National Bureau of Economic Research, Inc.
    20. 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.
    21. Kooreman, Peter, 1994. "Estimation of Econometric Models of Some Discrete Games," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 9(3), pages 255-268, July-Sept.
    22. Timothy F. Bresnahan & Peter C. Reiss, 1990. "Entry in Monopoly Market," Review of Economic Studies, Oxford University Press, vol. 57(4), pages 531-553.
    23. Paul R. Milgrom & Robert J. Weber, 1985. "Distributional Strategies for Games with Incomplete Information," Mathematics of Operations Research, INFORMS, vol. 10(4), pages 619-632, November.
    24. 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.
    25. 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.
    26. 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.
    27. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 147-165.
    28. Bresnahan, Timothy F. & Reiss, Peter C., 1991. "Empirical models of discrete games," Journal of Econometrics, Elsevier, vol. 48(1-2), pages 57-81.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Aguirregabiria, Victor & Nevo, Aviv, 2010. "Recent developments in empirical IO: dynamic demand and dynamic games," MPRA Paper 27814, University Library of Munich, Germany.
    2. Jason R. Blevins & Ahmed Khwaja & Nathan Yang, 2018. "Firm Expansion, Size Spillovers, and Market Dominance in Retail Chain Dynamics," Management Science, INFORMS, vol. 64(9), pages 4070-4093.
    3. Paul B. Ellickson & Sanjog Misra, 2011. "Structural Workshop Paper --Estimating Discrete Games," Marketing Science, INFORMS, vol. 30(6), pages 997-1010, November.
    4. Joao Macieira, 2010. "Oblivious Equilibrium in Dynamic Discrete Games," 2010 Meeting Papers 680, Society for Economic Dynamics.
    5. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    6. Wang, Jin, 2021. "Do birds of a feather flock together? Platform’s quality screening and end-users’ choices theory and empirical study of online trading platforms," International Journal of Industrial Organization, Elsevier, vol. 75(C).
    7. Aradillas-Lopez, Andres, 2012. "Pairwise-difference estimation of incomplete information games," Journal of Econometrics, Elsevier, vol. 168(1), pages 120-140.
    8. Liu, Nianqing & Vuong, Quang & Xu, Haiqing, 2017. "Rationalization and identification of binary games with correlated types," Journal of Econometrics, Elsevier, vol. 201(2), pages 249-268.
    9. Paul Ellickson & Sanjog Misra, 2012. "Enriching interactions: Incorporating outcome data into static discrete games," Quantitative Marketing and Economics (QME), Springer, vol. 10(1), pages 1-26, March.
    10. Paul L. E. Grieco, 2014. "Discrete games with flexible information structures: an application to local grocery markets," RAND Journal of Economics, RAND Corporation, vol. 45(2), pages 303-340, June.
    11. Kyoo il Kim, 2006. "Semiparametric Estimation of Signaling Games," Working Papers 19-2006, Singapore Management University, School of Economics.
    12. Davis, Peter, 2006. "Estimation of quantity games in the presence of indivisibilities and heterogeneous firms," Journal of Econometrics, Elsevier, vol. 134(1), pages 187-214, September.
    13. Maruyama, Shiko, 2014. "Estimation of finite sequential games," Journal of Econometrics, Elsevier, vol. 178(2), pages 716-726.
    14. Hu, Yingyao & Shum, Matthew, 2012. "Nonparametric identification of dynamic models with unobserved state variables," Journal of Econometrics, Elsevier, vol. 171(1), pages 32-44.
    15. Aguirregabiria, Victor & Mira, Pedro, 2010. "Dynamic discrete choice structural models: A survey," Journal of Econometrics, Elsevier, vol. 156(1), pages 38-67, May.
    16. Tomlin, Ben, 2014. "Exchange rate fluctuations, plant turnover and productivity," International Journal of Industrial Organization, Elsevier, vol. 35(C), pages 12-28.
    17. A. Ronald Gallant & Han Hong & Ahmed Khwaja, 2012. "Bayesian Estimation of a Dynamic Game with Endogenous, Partially Observed, Serially Correlated State," Working Papers 12-01, Duke University, Department of Economics.
    18. Allan Collard-Wexler, 2006. "Plant Turnover and Demand Fluctuations in the Ready-Mix Concrete Industry," Working Papers 06-08, Center for Economic Studies, U.S. Census Bureau.
    19. Xiao, Mo & Orazem, Peter F., 2011. "Does the fourth entrant make any difference?: Entry and competition in the early U.S. broadband market," International Journal of Industrial Organization, Elsevier, vol. 29(5), pages 547-561, September.
    20. Michaela Draganska & Sanjog Misra & Victor Aguirregabiria & Pat Bajari & Liran Einav & Paul Ellickson & Dan Horsky & Sridhar Narayanan & Yesim Orhun & Peter Reiss & Katja Seim & Vishal Singh & Raphael, 2008. "Discrete choice models of firms’ strategic decisions," Marketing Letters, Springer, vol. 19(3), pages 399-416, December.

    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ecm:emetrp:v:75:y:2007:i:1:p:1-53. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley Content Delivery). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.