A Simple Nonparametric Estimator for the Distribution of Random Coefficients in Discrete Choice Models

We propose an estimator for discrete choice models, such as the logit, with a nonparametric distribution of random coefficients. The estimator is linear regression subject to linear inequality constraints and is robust, simple to program and quick to compute compared to alternative estimators for mixture models. We discuss three methods for proving identi?fication of the distribution of heterogeneity for any given economic model. We prove the identi?fication of the logit mixtures model, which, surprisingly given the wide use of this model over the last 30 years, is a new result. We also derive our estimator?s non-standard asymptotic distribution and demonstrate its excellent small sample properties in a Monte Carlo. The estimator we propose can be extended to allow for endogenous prices. The estimator can also be used to reduce the computational burden of nested ?fixed point methods for complex models like dynamic programming discrete choice.