How McFadden Met Rockafellar and Learnt to Do More With Less

Abstract

We study the additive random utility model of discrete choice under minimal assumptions. We make no assumptions regarding the distribution of random utility components or the functional form of systematic utility components. Exploiting the power of convex analysis, we are nevertheless able to generalize a range of important results. We characterize demand with a generalized Williams-Daly-Zachary theorem. A similarly generalized version of Hotz-Miller inversion yields constructive partial identification of systematic utilities. Estimators based on our partial identification result remain well defined in the presence of zeros in demand. We also provide necessary and sufficient conditions for point identification.