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Nonparametric Estimation in Random Coefficients Binary Choice Models

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  • Eric Gautier

    (Crest)

  • Yuichi Kitamura

    (Crest)

Abstract

This paper considers nonparametric estimation of the joint density of the random coe±-cients in binary choice models. Nonparametric inference allows to be °exible about the treatment ofunobserved heterogeneity. This is an ill-posed inverse problem characterized by an integral transform,namely the hemispherical transform. The kernel is boxcar and the operator is a convolution operatoron the sphere. Utilizing Fourier-Laplace expansions o®ers a clear insight on the identi¯cation problem.We present a new class of density estimators for the random coe±cients relying on estimates for thechoice probability. Characterizing the degree of ill-posedness we are able to relate the rate of conver-gence of the estimation of the density of the random coe±cient with the rate of convergence of theestimation of the choice probability. We present a particular estimate for the choice probability and itsasymptotic properties. The corresponding estimate of the density of the random coe±cient takes a sim-ple closed form. It is easy to implement in empirical applications. We obtain rates of consistency in allLp spaces and prove asymptotic normality. Extensions including estimation of marginals, treatmentsof non-random coe±cients, models with endogeneity and multiple alternatives are discussed.

Suggested Citation

  • Eric Gautier & Yuichi Kitamura, 2008. "Nonparametric Estimation in Random Coefficients Binary Choice Models," Working Papers 2008-15, Center for Research in Economics and Statistics.
    • Handle: RePEc:crs:wpaper:2008-15
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    References listed on IDEAS

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities

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