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How McFadden met Rockafellar and learnt to do more with less

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  • Jesper R.-V. Soerensen

    (Department of Economics, University of Copenhagen, Denmark)

  • Mogens Fosgerau

    (Department of Economics, University of Copenhagen, Denmark)

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.

Suggested Citation

  • Jesper R.-V. Soerensen & Mogens Fosgerau, 2020. "How McFadden met Rockafellar and learnt to do more with less," Discussion Papers 20-01, University of Copenhagen. Department of Economics.
    • Handle: RePEc:kud:kuiedp:2001
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    1. Francesca Arduini, 2023. "Estimating intra-household sharing from time-use data," IFS Working Papers W23/23, Institute for Fiscal Studies.
    2. Sam Cosaert & Adrián Nieto & Konstantinos Tatsiramos, 2023. "Temperature and Joint Time Use," CESifo Working Paper Series 10464, CESifo.
    3. 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).
    4. 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).
    5. 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.
    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. Fedor Sandomirskiy & Philip Ushchev, 2024. "The geometry of consumer preference aggregation," Papers 2405.06108, arXiv.org.
    11. Roy Allen, 2024. "Exogenous Consideration and Extended Random Utility," Papers 2405.13945, 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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