Identification of the Distribution of Random Coefficients in Static and Dynamic Discrete Choice Models

We show that the distributions of random coefficients in various discrete choice models are nonparametrically identified. Our identification results apply to static discrete choice models including binary logit, multinomial logit, nested logit, and probit models as well as to dynamic programming discrete choice models. In these models the only key condition we need to verify for identification is that the type specific model choice probability belongs to a class of functions that include analytic functions. Therefore our identification results are general enough to include most of commonly used discrete choice models in the literature. Our identification argument builds on insights from nonparametric specification testing. We find that the role of analytic function in our identification results is to effectively remove the full support requirement often exploited in other identification approaches.