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 problem 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 heterogeneity. Extensions including treatments of non-random coeﬀicients and models with endogeneity are discussed.
Gautier, Eric and Kitamura, Yuichi, "Nonparametric Estimation in Random Coefficients Binary Choice Models" (2009). Cowles Foundation Discussion Papers. 2040.