Nonparametric identification and estimation of random coefficients in multinomial choice models

Multinomial choice and other nonlinear models are often used to estimate demand. We show how to nonparametrically identify the distribution of unobservables, such as random coefficients, that characterizes the heterogeneity among consumers in multinomial models. In particular, we provide general identification conditions for a class of nonlinear models and then verify these conditions using the primitives of the multinomial choice model. We require that the distribution of unobservables lie in the class of all distributions with finite support, which under our most general assumptions resembles a product space where some of the product members are function spaces. We allow prices to be endogenous and also study the case where consumers purchase multiple products at once, with bundle-specific prices. We show how identification leads to the consistency of a nonparametric estimator. ∗Thanks to Stephane Bonhomme, Steven Durlauf, James Heckman, Salvador Navarro, Philip Reny, Susanne Schennach, Azeem Shaikh, Christopher Taber, Harald Uhlig and Edward Vytlacil for helpful comments. Also thanks to seminar participants at many workshops. Fox thanks the National Science Foundation, the Olin Foundation, and the Stigler Center for financial support. Thanks to Chenchuan Li for research assistance. Our email addresses are [email protected] and [email protected].