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Integrability and identification in multinomial choice models

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  • Bhattacharya, Debopam

Abstract

McFadden's random-utility model of multinomial choice has long been the workhorse of applied research. We establish shape-restrictions with respect to price and income which are necessary and sufficient for multinomial choice-probability functions to be rationalized via random-utility models with additive but nonparametric unobserved heterogeneity and general income-effects. Our proof is constructive, and facilitates nonparametric identification of preference-distributions without requiring identification-at-infinity type arguments. A corollary shows that symmetry, a key condition for previous rationalizability results, is equivalent to absence of income-effects. Our results imply theory-consistent nonparametric bounds for choice-probabilities on counterfactual budget-sets. They also apply to widely used random-coefficient models, upon conditioning on observable choice characteristics. The theory of partial differential equations plays a key role in our analysis.

Suggested Citation

  • Bhattacharya, Debopam, 2025. "Integrability and identification in multinomial choice models," Journal of Economic Theory, Elsevier, vol. 223(C).
  • Handle: RePEc:eee:jetheo:v:223:y:2025:i:c:s0022053124001443
    DOI: 10.1016/j.jet.2024.105938
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    References listed on IDEAS

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    1. Arthur Lewbel, 2001. "Demand Systems with and without Errors," American Economic Review, American Economic Association, vol. 91(3), pages 611-618, June.
    2. Armstrong, Mark & Vickers, John, 2015. "Which demand systems can be generated by discrete choice?," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 293-307.
    3. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680, Decembrie.
    4. Matzkin, Rosa L., 1993. "Nonparametric identification and estimation of polychotomous choice models," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 137-168, July.
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    More about this item

    Keywords

    Multinomial choice; Unobserved heterogeneity; Random utility; Integrability; Symmetry; Income effects; Partial differential equations; Nonparametric identification; Random coefficient models; Bounds on counterfactuals;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C25 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Discrete Regression and Qualitative Choice Models; Discrete Regressors; Proportions; Probabilities
    • D11 - Microeconomics - - Household Behavior - - - Consumer Economics: Theory

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