A simple nonparametric approach to estimating the distribution of random coefficients in structural models

We explore least squares and likelihood nonparametric mixtures estimators of the joint distribution of random coefficients in structural models. The estimators fix a grid of heterogeneous parameters and estimate only the weights on the grid points, an approach that 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 most of the consistency conditions for three discrete choice models. We also derive the convergence rates of the least squares nonparametric mixtures estimator under additional restrictions. We perform a Monte Carlo study on a dynamic programming model.