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A NOTE ON SEMIPARAMETRIC ESTIMATION OF FINITE MIXTURES OF DISCRETE CHOICE MODELS WITH APPLICATION TO GAME THEORETIC MODELS

Authors

  • Patrick Bajari,

    1. University of Minnesota and NBER, U.S.A.; University of California, Los Angeles, U.S.A.; Stanford University, U.S.A.; University of Southern California, U.S.A.
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  • Jinyong Hahn,

    1. University of Minnesota and NBER, U.S.A.; University of California, Los Angeles, U.S.A.; Stanford University, U.S.A.; University of Southern California, U.S.A.
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  • Han Hong,

    1. University of Minnesota and NBER, U.S.A.; University of California, Los Angeles, U.S.A.; Stanford University, U.S.A.; University of Southern California, U.S.A.
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  • Geert Ridder

    1. University of Minnesota and NBER, U.S.A.; University of California, Los Angeles, U.S.A.; Stanford University, U.S.A.; University of Southern California, U.S.A.
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    • Helpful comments by Bryan Graham and Stephane Bonhomme are greatly acknowledged. Financial support for this research was generously provided through NSF Grant Nos. SES 0921187, 0819638, and 0721015. Please address correspondence to: Jinyong Hahn, Department of Economics, UCLA, 8283 Bunche Hall, Mail Stop: 147703, Los Angeles, CA 90095, USA. E-mail: hahn@econ.ucla.edu.


  • Manuscript received September 2009; revised May 2010.

Abstract

We view a game abstractly as a semiparametric mixture distribution and study the semiparametric efficiency bound of this model. Our results suggest that a key issue for inference is the number of equilibria compared to the number of outcomes. If the number of equilibria is sufficiently large compared to the number of outcomes, root-n consistent estimation of the model will not be possible. We also provide a simple estimator in the case when the efficiency bound is strictly above zero.

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