A Note on Nonparametric Identification of Distributions of Random Coefficients in Multinomial Choice Models

I prove that the joint distribution of random coefficients and additive errors is identified in a mulltinomial choice model. No restrictions are imposed on the support of the random coefficients and additive errors. The proof uses large support variation in choice-specific explanatory variables following Lewbel (2000) but does not rely on an identification at infinity technique where the payoffs of all but two choices are set to minus infinity.