COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1721 Nonparametric Estimation in Random Coefficients Binary Choice Models Eric Gautier and Yuichi Kitamura August 2009 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. |
