Income Effects and Rationalizability in Multinomial Choice Models

17 Pages Posted: 16 Oct 2018

Date Written: August 1, 2018


In multinomial choice settings, Daly-Zachary (1978) and Armstrong-Vickers (2015) provided closed-form 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.

Keywords: Multinomial Choice, Unobserved Heterogeneity, random Utility, Rationalizability/Integrability, Slutsky-Symmetry, Income Effects, Partial Differential Equations, Nonparametric Identification

JEL Classification: C14, C25, D11

Suggested Citation

Bhattacharya, Debopam, Income Effects and Rationalizability in Multinomial Choice Models (August 1, 2018). Available at SSRN: or

Debopam Bhattacharya (Contact Author)

University of Cambridge ( email )

Sidgwick Site
Austin Robinson Building
Cambridge, CB3 9DD
United Kingdom

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