How McFadden Met Rockafellar and Learnt to Do More With Less

We study the additive random utility model of discrete choice under minimal assumptions. We place no restrictions on the joint 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 without resorting to differential theory. We characterize demand with a generalized Williams-Daly-Zachary theorem. A similarly generalized version of Hotz-Miller inversion yields constructive partial identication of systematic utilities for any known joint
distribution of stochastic utility components. Estimators based on our partial identication result remain well defined in the presence of zeros in demand. We also provide conditions for point identication, which are not only sufficient, but also necessary.