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Identification of Games of Incomplete Information with Multiple Equilibria and Common Unobserved Heterogeneity

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  • Victor Aguirregabiria
  • Pedro Mira

Abstract

This paper deals with the identification and estimation of discrete games of incomplete information with multiple equilibria when we allow for three types of unobservables for the researcher: (a) payoff-relevant variables that are players' private information; (b) payoff-relevant variables that are common knowledge to all the players; and (c) non-payoff-relevant or "sunspot" variables which are common knowledge to the players. The specification of the payoff function is nonparametric, and the probability distributions of the unobservables is also nonparametric but with finite support (i.e., finite mixture model). We show that if the number of players in the game is greater than two and the number of discrete choice alternatives is greater than the number of mixtures in the distribution of the unobservables, then the model is nonparametrically identified under the same type of exclusion restrictions that we need for identification without unobserved heterogeneity. In particular, it is possible to separately identify the relative contributions of payoff-relevant and "sunspot" type of unobserved heterogeneity to observed players' behavior. We also present results on the identification of counterfactual experiments using the estimated model.

Suggested Citation

  • Victor Aguirregabiria & Pedro Mira, 2013. "Identification of Games of Incomplete Information with Multiple Equilibria and Common Unobserved Heterogeneity," Working Papers tecipa-474, University of Toronto, Department of Economics.
  • Handle: RePEc:tor:tecipa:tecipa-474
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    1. Cragg, John G. & Donald, Stephen G., 1997. "Inferring the rank of a matrix," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 223-250.
    2. Patrick Bayer & Christopher Timmins, 2007. "Estimating Equilibrium Models Of Sorting Across Locations," Economic Journal, Royal Economic Society, vol. 117(518), pages 353-374, March.
    3. 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.
    4. Bajari, Patrick & Hong, Han & Krainer, John & Nekipelov, Denis, 2010. "Estimating Static Models of Strategic Interactions," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(4), pages 469-482.
    5. Robin, Jean-Marc & Smith, Richard J., 2000. "Tests Of Rank," Econometric Theory, Cambridge University Press, vol. 16(2), pages 151-175, April.
    6. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, vol. 75(5), pages 1331-1370, September.
    7. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    8. Donald R. Davis & David E. Weinstein, 2008. "A Search For Multiple Equilibria In Urban Industrial Structure," Journal of Regional Science, Wiley Blackwell, vol. 48(1), pages 29-65, February.
    9. Doraszelski, Ulrich & Escobar, Juan, 2010. "A theory of regular Markov perfect equilibria in dynamic stochastic games: genericity, stability, and purification," Theoretical Economics, Econometric Society, vol. 5(3), September.
    10. Krugman, Paul, 1991. "Increasing Returns and Economic Geography," Journal of Political Economy, University of Chicago Press, vol. 99(3), pages 483-499, June.
    11. Hahn, Jinyong & Moon, Hyungsik Roger, 2010. "Panel Data Models With Finite Number Of Multiple Equilibria," Econometric Theory, Cambridge University Press, vol. 26(3), pages 863-881, June.
    12. Áureo de Paula & Xun Tang, 2012. "Inference of Signs of Interaction Effects in Simultaneous Games With Incomplete Information," Econometrica, Econometric Society, vol. 80(1), pages 143-172, January.
    13. Beenstock, Michael & Szpiro, George, 2002. "Specification search in nonlinear time-series models using the genetic algorithm," Journal of Economic Dynamics and Control, Elsevier, vol. 26(5), pages 811-835, May.
    14. Martin Pesendorfer & Philipp Schmidt-Dengler, 2003. "Identification and Estimation of Dynamic Games," NBER Working Papers 9726, National Bureau of Economic Research, Inc.
    15. Bayer, Patrick & Timmins, Christopher, 2005. "On the equilibrium properties of locational sorting models," Journal of Urban Economics, Elsevier, vol. 57(3), pages 462-477, May.
    16. Victor Aguirregabiria & Pedro Mira, 2007. "Sequential Estimation of Dynamic Discrete Games," Econometrica, Econometric Society, vol. 75(1), pages 1-53, January.
    17. Paul B. Ellickson & Sanjog Misra, 2008. "Supermarket Pricing Strategies," Marketing Science, INFORMS, vol. 27(5), pages 811-828, 09-10.
    18. Delgado, Miguel A. & Hidalgo, Javier, 2000. "Nonparametric inference on structural breaks," Journal of Econometrics, Elsevier, vol. 96(1), pages 113-144, May.
    19. Peter Hall & Amnon Neeman & Reza Pakyari & Ryan Elmore, 2005. "Nonparametric inference in multivariate mixtures," Biometrika, Biometrika Trust, vol. 92(3), pages 667-678, September.
    20. 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.
    21. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 147-165.
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    2. Fabio A. Miessi Sanches & Daniel Junior Silva & Sorawoot Srisuma, 2016. "Ordinary Least Squares Estimation Of A Dynamic Game Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 57(2), pages 623-634, May.
    3. John Rust, 2014. "The Limits of Inference with Theory: A Review of Wolpin (2013)," Journal of Economic Literature, American Economic Association, vol. 52(3), pages 820-850, September.
    4. Jacob Schwartz, 2018. "Schooling Choice, Labour Market Matching, and Wages," Papers 1803.09020, arXiv.org, revised Aug 2019.
    5. Yao Luo, 2018. "Unobserved Heterogeneity in Auctions under Restricted Stochastic Dominance," Working Papers tecipa-606, University of Toronto, Department of Economics.
    6. Erhao Xie, 2018. "Inference in Games Without Nash Equilibrium: An Application to Restaurants, Competition in Opening Hours," Staff Working Papers 18-60, Bank of Canada.
    7. Victor Aguirregabiria & Junichi Suzuki, 2015. "Empirical Games of Market Entry and Spatial Competition in Retail Industries," Working Papers tecipa-534, University of Toronto, Department of Economics.

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    More about this item

    Keywords

    Discrete games of incomplete information; Multiple equilibria in the data; Unobserved heterogeneity; Sunspots; Finite mixture models.;
    All these keywords.

    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

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