Gautier, Eric and Kitamura, Yuichi (2013) Nonparametric estimation in random coefficients binary choice models. Econometrica, vol. 81. pp. 581-607.

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Abstract

This paper considers random coefficients binary choice models. The main goal is to estimate the density of the random coefficients nonparametrically. This is an ill-posed inverse prob- lem characterized by an integral transform. A new density estimator for the random coefficients is developed, utilizing Fourier-Laplace series on spheres. This approach offers a clear insight on the identification problem. More importantly, it leads to a closed form estimator formula that yields a simple plug-in procedure requiring no numerical optimization. The new estimator, therefore, is easy to implement in empirical applications, while being flexible about the treatment of unobserved hetero- geneity. Extensions including treatments of non-random coefficients and models with endogeneity are discussed.