IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/101968.html
   My bibliography  Save this paper

Testing for equilibrium multiplicity in dynamic Markov games

Author

Listed:
  • Otsu, Taisuke
  • Pesendorfer, Martin
  • Takahashi, Yuya

Abstract

This paper proposes several statistical tests for finite state Markov games to examine the null hypothesis that the data are generated from a single equilibrium. We formulate tests of (i) the conditional choice probabilities, (ii) the steady-state distribution of states and (iii) the conditional distribution of states conditional on an initial state. In a Monte Carlo study we find that the chi-squared test of the steady-state distribution performs well and has high power even with a small number of markets and time periods. We apply the chi-squared test to the empirical application of Ryan (2012) that analyzes dynamics of the U.S. Portland Cement industry and test if his assumption of single equilibrium is supported by the data.

Suggested Citation

  • Otsu, Taisuke & Pesendorfer, Martin & Takahashi, Yuya, 2013. "Testing for equilibrium multiplicity in dynamic Markov games," LSE Research Online Documents on Economics 101968, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:101968
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/101968/
    File Function: Open access version.
    Download Restriction: no

    References listed on IDEAS

    as
    1. Srisuma, Sorawoot & Linton, Oliver, 2012. "Semiparametric estimation of Markov decision processes with continuous state space," Journal of Econometrics, Elsevier, vol. 166(2), pages 320-341.
    2. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    3. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov‐perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243, June.
    4. Mireia Jofre-Bonet & Martin Pesendorfer, 2003. "Estimation of a Dynamic Auction Game," Econometrica, Econometric Society, vol. 71(5), pages 1443-1489, September.
    5. 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.
    6. Junichi Suzuki, 2013. "Land Use Regulation As A Barrier To Entry: Evidence From The Texas Lodging Industry," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(2), pages 495-523, May.
    7. Naoaki Minamihashi, 2012. "Natural Monopoly and Distorted Competition: Evidence from Unbundling Fiber-Optic Networks," Staff Working Papers 12-26, Bank of Canada.
    8. Peter Arcidiacono & Patrick Bayer & Jason R. Blevins & Paul B. Ellickson, 2016. "Estimation of Dynamic Discrete Choice Models in Continuous Time with an Application to Retail Competition," Review of Economic Studies, Oxford University Press, vol. 83(3), pages 889-931.
    9. Hiroyuki Kasahara & Katsumi Shimotsu, 2012. "Sequential Estimation of Structural Models With a Fixed Point Constraint," Econometrica, Econometric Society, vol. 80(5), pages 2303-2319, September.
    10. 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.
    11. Aureo de Paula & Xun Tang, 2010. "Inference of Signs of Interaction Effects in Simultaneous Games with Incomplete Information, Second Version," PIER Working Paper Archive 11-003, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania, revised 12 Feb 2011.
    12. Przemysław Jeziorski, 2014. "Estimation of cost efficiencies from mergers: application to US radio," RAND Journal of Economics, RAND Corporation, vol. 45(4), pages 816-846, December.
    13. 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.
    14. Peter Arcidiacono & Robert A. Miller, 2011. "Conditional Choice Probability Estimation of Dynamic Discrete Choice Models With Unobserved Heterogeneity," Econometrica, Econometric Society, vol. 79(6), pages 1823-1867, November.
    15. Pierre-Andre Chiappori & Bernard Salanie, 2000. "Testing for Asymmetric Information in Insurance Markets," Journal of Political Economy, University of Chicago Press, vol. 108(1), pages 56-78, February.
    16. Navarro, Salvador & Takahashi, Yuya, 2012. "A Semiparametric Test of Agent's Information Sets for Games of Incomplete Information," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 432, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    17. Andrews, Donald W. K., 1988. "Chi-square diagnostic tests for econometric models : Introduction and applications," Journal of Econometrics, Elsevier, vol. 37(1), pages 135-156, January.
    18. Stephen P. Ryan, 2012. "The Costs of Environmental Regulation in a Concentrated Industry," Econometrica, Econometric Society, vol. 80(3), pages 1019-1061, May.
    19. Orazio P. Attanasio, 2000. "Consumer Durables and Inertial Behaviour: Estimation and Aggregation of (S, s) Rules for Automobile Purchases," Review of Economic Studies, Oxford University Press, vol. 67(4), pages 667-696.
    20. Hiroyuki Kasahara & Katsumi Shimotsu, 2009. "Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices," Econometrica, Econometric Society, vol. 77(1), pages 135-175, January.
    21. Martin Pesendorfer & Philipp Schmidt-Dengler, 2008. "Asymptotic Least Squares Estimators for Dynamic Games -super-1," Review of Economic Studies, Oxford University Press, vol. 75(3), pages 901-928.
    22. Andrews, Donald W K, 1988. "Chi-Square Diagnostic Tests for Econometric Models: Theory," Econometrica, Econometric Society, vol. 56(6), pages 1419-1453, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hansen, Stephen & McMahon, Michael & Velasco Rivera, Carlos, 2014. "Preferences or private assessments on a monetary policy committee?," Journal of Monetary Economics, Elsevier, vol. 67(C), pages 16-32.

    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. Otsu, Taisuke & Pesendorfer, Martin & Takahashi, Yuya, 2014. "Testing Equilibrium Multiplicity in Dynamic Games," CEPR Discussion Papers 10111, C.E.P.R. Discussion Papers.
    2. Taisuke Otsu & Martin Pesendorfer & Yuya Takahashi, 2016. "Pooling data across markets in dynamic Markov games," Quantitative Economics, Econometric Society, vol. 7(2), pages 523-559, July.
    3. Aguirregabiria, Victor & Mira, Pedro, 2010. "Dynamic discrete choice structural models: A survey," Journal of Econometrics, Elsevier, vol. 156(1), pages 38-67, May.
    4. Otsu, Taisuke & Pesendorfer, Martin & Takahashi, Yuya, 2013. "Testing for Equilibrium Multiplicity in Dynamic Markov Games," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 423, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    5. Steven T. Berry & Giovanni Compiani, 2020. "An Instrumental Variable Approach to Dynamic Models," NBER Working Papers 27756, National Bureau of Economic Research, Inc.
    6. Komarova, Tatiana & Sanches, Fábio Adriano & Silva Junior, Daniel & Srisuma, Sorawoot, 2018. "Joint analysis of the discount factor and payoff parameters in dynamic discrete choice games," LSE Research Online Documents on Economics 86858, London School of Economics and Political Science, LSE Library.
    7. Victor Aguirregabiria & Victor Aguirregabiria & Aviv Nevo & Aviv Nevo, 2010. "Recent Developments in Empirical IO: Dynamic Demand and Dynamic Games," Working Papers tecipa-419, University of Toronto, Department of Economics.
    8. Victor Aguirregabiria & Margaret Slade, 2017. "Empirical models of firms and industries," Canadian Journal of Economics, Canadian Economics Association, vol. 50(5), pages 1445-1488, December.
    9. Adam Dearing & Jason R. Blevins, 2019. "Efficient and Convergent Sequential Pseudo-Likelihood Estimation of Dynamic Discrete Games," Papers 1912.10488, arXiv.org, revised Feb 2021.
    10. Fabio A. Miessi Sanches & Daniel Silva Junior, Sorawoot Srisuma, 2014. "Ordinary Least Squares Estimation for a Dynamic Game," Working Papers, Department of Economics 2014_19, University of São Paulo (FEA-USP), revised 23 Feb 2015.
    11. Otero, Karina V., 2016. "Nonparametric identification of dynamic multinomial choice games: unknown payoffs and shocks without interchangeability," MPRA Paper 86784, University Library of Munich, Germany.
    12. Otsu, Taisuke & Pesendorfer, Martin & Sasaki, Yuya & Takahashi, Yuya, 2020. "Estimation of (static or dynamic) games under equilibrium multiplicity," CEPR Discussion Papers 14342, C.E.P.R. Discussion Papers.
    13. C. Lanier Benkard & Przemyslaw Jeziorski & Gabriel Y. Weintraub, 2013. "Oblivious Equilibrium for Concentrated Industries," NBER Working Papers 19307, National Bureau of Economic Research, Inc.
    14. Hu Yingyao & Shum Matthew & Tan Wei & Xiao Ruli, 2017. "A Simple Estimator for Dynamic Models with Serially Correlated Unobservables," Journal of Econometric Methods, De Gruyter, vol. 6(1), pages 1-16, January.
    15. Aamir Rafique Hashmi & Johannes Van Biesebroeck, 2016. "The Relationship between Market Structure and Innovation in Industry Equilibrium: A Case Study of the Global Automobile Industry," The Review of Economics and Statistics, MIT Press, vol. 98(1), pages 192-208, March.
    16. Arcidiacono, Peter & Miller, Robert A., 2020. "Identifying dynamic discrete choice models off short panels," Journal of Econometrics, Elsevier, vol. 215(2), pages 473-485.
    17. Myrto Kalouptsidi, 2014. "Detection and Impact of Industrial Subsidies: The Case of World Shipbuilding," NBER Working Papers 20119, National Bureau of Economic Research, Inc.
    18. Sears, Louis S. & Lin Lawell, C.-Y. Cynthia & Walter, M. Todd, 2020. "Groundwater Under Open Access: A Structural Model of the Dynamic Common Pool Extraction Game," 2020 Annual Meeting, July 26-28, Kansas City, Missouri 304276, Agricultural and Applied Economics Association.
    19. Ulrich Doraszelski & Mark Satterthwaite, 2010. "Computable Markov‐perfect industry dynamics," RAND Journal of Economics, RAND Corporation, vol. 41(2), pages 215-243, June.
    20. Hu, Yingyao & Shum, Matthew, 2012. "Nonparametric identification of dynamic models with unobserved state variables," Journal of Econometrics, Elsevier, vol. 171(1), pages 32-44.

    More about this item

    Keywords

    Dynamic Markov Game; Multiplicity of Equilibria; Testing;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions

    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:ehl:lserod:101968. 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: (LSERO Manager). General contact details of provider: http://edirc.repec.org/data/lsepsuk.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.