A Simple Nonparametric Estimator for the Distribution of Random Coe¢ cients in Discrete Choice Models

We propose an estimator for discrete choice models, such as the logit, with a nonparametric distribution of random coe¢ cients. 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…cation of the distribution of heterogeneity for any given economic model. We prove the identi…cation 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 …xed point methods for complex models like dynamic programming discrete choice. Thanks to helpful comments from seminar participants at the AEA meetings, Paris I, Toronto and UCL, as well as Andrew Chesher, Philippe Fevrier, David Margolis and Jean-Marc Robin.