How McFadden Met Rockafellar and Learned 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 identi cation of systematic utilities for any known jointdistribution of stochastic utility components. Estimators based on our partial identi cation result remain well de fined in the presence of zeros in demand. We also provide conditions for point identi cation, which are not only sufficient, but also necessary