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Income Effects and Rationalizability in Multinomial Choice Models

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  • Bhattacharya, D.

Abstract

In multinomial choice settings, Daly-Zachary (1978) and Armstrong-Vickers (2015) provided closedform conditions, under which choice probability functions can be rationalized via random utility models. A key condition is Slutsky symmetry. We first show that in the multinomial context, Daly-Zachary’s Slutsky symmetry is equivalent to absence of income-effects. Next, for general multinomial choice that allows for income-effects, we provide global shape restrictions on choice probability functions, which are shown to be sufficient for rationalizability. Finally, we outline nonparametric identification of preference distributions using these results. The theory of linear partial differential equations plays a key role in our analysis.

Suggested Citation

  • Bhattacharya, D., 2018. "Income Effects and Rationalizability in Multinomial Choice Models," Cambridge Working Papers in Economics 1884, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:1884
    Note: db692
    as

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    References listed on IDEAS

    as
    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.
    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.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Multinomial Choice; Unobserved Heterogeneity; random Utility; Rationalizability/Integrability; Slutsky-Symmetry; Income Effects; Partial Differential Equations; Nonparametric Identification.;
    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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