Nonparametric Estimation in Random Coefficients Binary Choice Models
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.