Nonparametric Estimation in Random Coefficients Binary Choice Models

Eric Gautier and Yuichi Kitamura
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Yuichi Kitamura: Crest

No 2008-15, Working Papers from Center for Research in Economics and Statistics

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.

Pages: 51
Date: 2008
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Citations: View citations in EconPapers (5)

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Related works:
Journal Article: Nonparametric Estimation in Random Coefficients Binary Choice Models (2013)
Working Paper: Nonparametric estimation in random coefficients binary choice models (2011)
Working Paper: Nonparametric Estimation in Random Coefficients Binary Choice Models (2009)
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