A Simple Nonparametric Approach to Estimating the Distribution of Random Coefficients in Structural Models

We explore a nonparametric mixtures estimator for recovering the joint distribution of random coefficients in structural models. The estimator is based on linear regression subject to linear inequality constraints and is computationally attractive compared to alternative, nonparametric estimators. We provide conditions under which the estimated distribution function converges to the true distribution in the weak topology on the space of distributions. We verify the consistency conditions for discrete choice, continuous outcome and selection models. We also derive the convergence rates of the nonparametric mixtures estimator for a more restricted class of models. A Monte Carlo study on a dynamic programming example shows our estimator is faster than alternatives. ∗Corresponding authors: Jeremy Fox at [email protected] and Kyoo il Kim at [email protected].