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How McFadden met Rockafellar and learned to do more with less

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

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.

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  • Sørensen, Jesper R.-V. & Fosgerau, Mogens, 2022. "How McFadden met Rockafellar and learned to do more with less," Journal of Mathematical Economics, Elsevier, vol. 100(C).
    • Handle: RePEc:eee:mateco:v:100:y:2022:i:c:s0304406821001737
    DOI: 10.1016/j.jmateco.2021.102629
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    1. Sam Cosaert & Adrián Nieto & Konstantinos Tatsiramos, 2023. "Temperature and Joint Time Use," CESifo Working Paper Series 10464, CESifo.
    2. Ejrnæs, Mette & García-Miralles, Esteban & Gørtz, Mette & Lundborg, Petter, 2023. "When Death Was Postponed: The Effect of HIV Medication on Work, Savings, and Marriage," IZA Discussion Papers 16228, Institute of Labor Economics (IZA).
    3. Fosgerau, Mogens & Melo, Emerson & Shum, Matthew & Sørensen, Jesper R.-V., 2021. "Some remarks on CCP-based estimators of dynamic models," Economics Letters, Elsevier, vol. 204(C).
    4. Richard T. Carson & Derrick H. Sun & Yixiao Sun, 2024. "Random Utility Models with Skewed Random Components: the Smallest versus Largest Extreme Value Distribution," Papers 2405.08222, arXiv.org, revised May 2024.
    5. Francesca Arduini, 2023. "Estimating intra-household sharing from time-use data," IFS Working Papers W23/23, Institute for Fiscal Studies.
    6. Mogens Fosgerau & Nikolaj Nielsen & Mads Paulsen & Thomas Kj{ae}r Rasmussen & Rui Yao, 2024. "Substitution in the perturbed utility route choice model," Papers 2409.08347, arXiv.org.
    7. Emerson Melo, 2021. "Learning in Random Utility Models Via Online Decision Problems," Papers 2112.10993, arXiv.org, revised Aug 2022.
    8. Paul S. Koh, 2024. "Merger Analysis with Latent Price," Papers 2404.07684, arXiv.org, revised Jul 2024.
    9. Yang, Erya & Kopylov, Igor, 2023. "Random quasi-linear utility," Journal of Economic Theory, Elsevier, vol. 209(C).
    10. Roy Allen, 2024. "Exogenous Consideration and Extended Random Utility," Papers 2405.13945, arXiv.org.
    11. Fedor Sandomirskiy & Philip Ushchev, 2024. "The geometry of consumer preference aggregation," Papers 2405.06108, arXiv.org.
    12. Dieter Saelens, 2022. "Unitary or collective households? A nonparametric rationality and separability test using detailed data on consumption expenditures and time use," Empirical Economics, Springer, vol. 62(2), pages 637-677, February.
    13. Mogens Fosgerau & John Rehbeck, 2023. "Nontransitive Preferences and Stochastic Rationalizability: A Behavioral Equivalence," Papers 2304.14631, arXiv.org.

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    More about this item

    Keywords

    Additive random utility model; Discrete choice; Convex duality; Demand inversion; Partial identification;
    All these keywords.

    JEL classification:

    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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