How McFadden Met Rockafellar and Learned to Do More With Less

Sørensen, Jesper R.-V.; Fosgerau, Mogens

doi:10.2139/ssrn.3581570

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How McFadden Met Rockafellar and Learned to Do More With Less

31 Pages Posted: 29 Apr 2020 Last revised: 5 Nov 2021

See all articles by Jesper R.-V. Sørensen

Mogens Fosgerau

University of Copenhagen

Date Written: November 4, 2021

Abstract

We exploit the power of convex analysis to synthesize and extend a range of important results concerning the additive random utility model of discrete choice. With no restrictions on the joint distribution of random utility components or the functional form of systematic utility components, we formulate general versions of the Williams-Daly-Zachary theorem for demand and the Hotz-Miller demand inversion theorem. Based on these theorems, we provide necessary and sufficient conditions for demand and its inverse to reduce to functions. These conditions jointly imply that demand is a continuous function with a continuous inverse.

Keywords: Additive random utility model; Discrete choice; Convex duality; Demand inversion; Partial identification

JEL Classification: C25, C6, D11

Suggested Citation: Suggested Citation

Sørensen, Jesper Riis-Vestergaard and Fosgerau, Mogens, How McFadden Met Rockafellar and Learned to Do More With Less (November 4, 2021). Available at SSRN: https://ssrn.com/abstract=3581570 or http://dx.doi.org/10.2139/ssrn.3581570