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Set Inference for Semiparametric Discrete Games

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  • Kyoo il Kim

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    (School of Economics and Social Sciences, Singapore Management University)

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    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 confidence 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.

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    Bibliographic Info

    Paper provided by Singapore Management University, School of Economics in its series Working Papers with number 16-2006.

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    Length: 27 pages
    Date of creation: Sep 2006
    Date of revision:
    Publication status: Published in SMU Economics and Statistics Working Paper Series
    Handle: RePEc:siu:wpaper:16-2006

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    Related research

    Keywords: Semiparametric Estimation; Set Inference; Infinite Dimensional Parameters; Inequality Moment Conditions; Signaling Game with Discrete Types;

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    References

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    1. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
    2. Pesendorfer, Martin & Schmidt-Dengler, Philipp, 2003. "Identification and Estimation of Dynamic Games," CEPR Discussion Papers 3965, C.E.P.R. Discussion Papers.
    3. Patrick Bajari & C. Lanier Benkard & Jonathan Levin, 2004. "Estimating Dynamic Models of Imperfect Competition," NBER Working Papers 10450, National Bureau of Economic Research, Inc.
    4. Kyoo il Kim, 2006. "Semiparametric Estimation of Signaling Games," Working Papers 19-2006, Singapore Management University, School of Economics.
    5. Elie Tamer, 2003. "Incomplete Simultaneous Discrete Response Model with Multiple Equilibria," Review of Economic Studies, Wiley Blackwell, vol. 70(1), pages 147-165, January.
    6. Kyoo il Kim, 2006. "Semiparametric Estimation of Signaling Games," Labor Economics Working Papers 22452, East Asian Bureau of Economic Research.
    7. Kooreman, P., 1994. "Estimation of econometric models of some discrete games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-377584, Tilburg University.
    8. 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.
    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. Aradillas-Lopez, Andres, 2010. "Semiparametric estimation of a simultaneous game with incomplete information," Journal of Econometrics, Elsevier, vol. 157(2), pages 409-431, August.
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