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Set Inference for Semiparametric Discrete Games

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  • Kyoo il Kim

    (SMU)

Abstract

We consider estimation and inference of parameters in discrete games allowing for multiple equilibria, without using an equilibrium selection rule. We do a set inference while a game model can contain infinite dimensional parameters. Examples can include signaling games with discrete types where the type distribution is nonparametrically specified and entry-exit games with partially linear payoffs functions. A consistent set estimator and a con.dence interval of a function of parameters are provided in this paper. We note that achieving a consistent point estimation often requires an information reduction. Due to this less use of information, we may end up a point estimator with a larger variance and have a wider confidence interval than those of the set estimator using the full information in the model. This finding justifies the use of the set inference even though we can achieve a consistent point estimation. It is an interesting future research to compare these two alternatives : CI from the point estimation with the usage of less information vs. CI from the set estimation with the usage of the full information.

Suggested Citation

  • Kyoo il Kim, 2006. "Set Inference for Semiparametric Discrete Games," Labor Economics Working Papers 22454, East Asian Bureau of Economic Research.
  • Handle: RePEc:eab:laborw:22454
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    References listed on IDEAS

    as
    1. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2007. "Estimating Dynamic Models of Imperfect Competition," Econometrica, Econometric Society, pages 1331-1370.
    2. Martin Pesendorfer & Philipp Schmidt-Dengler, 2003. "Identification and Estimation of Dynamic Games," NBER Working Papers 9726, National Bureau of Economic Research, Inc.
    3. Kyoo il Kim, 2006. "Semiparametric Estimation of Signaling Games," Labor Economics Working Papers 22452, East Asian Bureau of Economic Research.
    4. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    5. 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.
    6. Federico Ciliberto & Elie Tamer, 2009. "Market Structure and Multiple Equilibria in Airline Markets," Econometrica, Econometric Society, vol. 77(6), pages 1791-1828, November.
    7. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, pages 409-431.
    8. Andrew Sweeting, 2005. "Coordination Games, Multiple Equilibria and the Timing of Radio Commercials," 2005 Meeting Papers 490, Society for Economic Dynamics.
    9. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 147-165.
    10. Bresnahan, Timothy F. & Reiss, Peter C., 1991. "Empirical models of discrete games," Journal of Econometrics, Elsevier, pages 57-81.
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    More about this item

    Keywords

    Semiparametric Estimation; Set Inference; Inequality Moment Conditions; Signaling Game with Discrete Types;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C35 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
    • C73 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Stochastic and Dynamic Games; Evolutionary Games

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