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Income Effects and Rationalizability in Multinomial Choice Models

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Document pages: 22 pages

Abstract: McFadden s Random-Utility Model of multinomial choice has long been theworkhorse of applied research. We establish shape-restrictions under whichmultinomial choice-probability functions can be rationalized via random-utilitymodels with nonparametric heterogeneity and general income-effects. Whencombined with an additional restriction, the above conditions are shown to benecessary and sufficient for the canonical Additive Random Utility Model(ARUM). The sufficiency-proof is constructive, and facilitates nonparametricidentification of preference-distributions. A corollary establishes thatSlutsky-symmetry, a key condition for previous rationalizability results(Daly-Zachary 1978, Armstrong-Vickers 2015), is equivalent to absence ofincome-effects. The theory of partial differential equations plays a key rolein our analys

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