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A Simple Nonparametric Estimator for the Distribution of Random Coefficients in Discrete Choice Models


  • Patrick Bajari

    (University of Minnesota and NBER)

  • Jeremy T. Fox

    (University of Chicago)

  • Kyoo il Kim

    (University of Minnesota)

  • Stephen Ryan

    (MIT and NBER)


We propose an estimator for discrete choice models, such as the logit, with a nonparametric distribution of random coefficients. The estimator is linear regression subject to linear inequality constraints and is robust, simple to program and quick to compute compared to alternative estimators for mixture models. We discuss three methods for proving identi?fication of the distribution of heterogeneity for any given economic model. We prove the identi?fication of the logit mixtures model, which, surprisingly given the wide use of this model over the last 30 years, is a new result. We also derive our estimator?s non-standard asymptotic distribution and demonstrate its excellent small sample properties in a Monte Carlo. The estimator we propose can be extended to allow for endogenous prices. The estimator can also be used to reduce the computational burden of nested ?fixed point methods for complex models like dynamic programming discrete choice.

Suggested Citation

  • Patrick Bajari & Jeremy T. Fox & Kyoo il Kim & Stephen Ryan, 2007. "A Simple Nonparametric Estimator for the Distribution of Random Coefficients in Discrete Choice Models," Working Papers 36, Portuguese Competition Authority.
  • Handle: RePEc:pca:wpaper:36

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    References listed on IDEAS

    1. João Vareda, 2007. "Unbundling and Incumbent Investment in Quality Upgrades and Cost Reduction," Working Papers 31, Portuguese Competition Authority.
    2. Vareda, João & Hoernig, Steffen, 2007. "The race for telecoms infrastructure investment with bypass: Can access regulation achieve the first best?," FEUNL Working Paper Series wp524, Universidade Nova de Lisboa, Faculdade de Economia.
    3. Biglaiser, Gary & DeGraba, Patrick, 2001. "Downstream Integration by a Bottleneck Input Supplier Whose Regulated Wholesale Prices Are Above Costs," RAND Journal of Economics, The RAND Corporation, vol. 32(2), pages 302-315, Summer.
    4. Brito, Duarte & Pereira, Pedro & Vareda, João, 2010. "Can two-part tariffs promote efficient investment on next generation networks?," International Journal of Industrial Organization, Elsevier, vol. 28(3), pages 323-333, May.
    5. Foros, Oystein, 2004. "Strategic investments with spillovers, vertical integration and foreclosure in the broadband access market," International Journal of Industrial Organization, Elsevier, vol. 22(1), pages 1-24, January.
    6. Gans, Joshua S, 2001. "Regulating Private Infrastructure Investment: Optimal Pricing for Access to Essential Facilities," Journal of Regulatory Economics, Springer, vol. 20(2), pages 167-189, September.
    7. Kotakorpi, Kaisa, 2006. "Access price regulation, investment and entry in telecommunications," International Journal of Industrial Organization, Elsevier, vol. 24(5), pages 1013-1020, September.
    8. Guthrie, Graeme, 2006. "Regulating Infrastructure: The Impact on Risk and Investment," Working Paper Series 3851, Victoria University of Wellington, The New Zealand Institute for the Study of Competition and Regulation.
    9. Graeme Guthrie, 2006. "Regulating Infrastructure: The Impact on Risk and Investment," Journal of Economic Literature, American Economic Association, vol. 44(4), pages 925-972, December.
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    Cited by:

    1. Browning, Martin & Carro, Jesus M., 2014. "Dynamic binary outcome models with maximal heterogeneity," Journal of Econometrics, Elsevier, vol. 178(2), pages 805-823.

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