McFadden's Random-Utility Model of multinomial choice has long been the workhorse of applied research. We establish shape-restrictions under which multinomial choice-probability functions can be rationalized via random-utility models with nonparametric  heterogeneity and general income-effects. When combined with an additional restriction, the above conditions are shown to be necessary and sufficient for the canonical Additive Random Utility Model (ARUM) . The sufficiency-proof is constructive, and facilitates nonparametric identification of preference-distributions  . A corollary establishes that Slutsky-symmetry, a key condition for previous rationalizability results (Daly-Zachary 1978, Armstrong-Vickers 2015), is equivalent to absence of income-effects.  The theory of partial differential equations plays a key role in our analys
McFadden's random-utility model of multinomial choice has long been the workhorse of applied research. We establish shape-restrictions under which multinomial choice-probability functions can be rationalized via random-utility models with nonparametric unobserved heterogeneity and general income-effects. When combined with an additional restriction, the above conditions are equivalent to the canonical Additive Random Utility Model . The sufficiency-proof is constructive, and facilitates nonparametric identification of preference-distributions without requiring identification-at-infinity type arguments . A corollary shows that Slutsky-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.
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Random-Utility Model
random-utility model
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unobserved
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shown to be necessary and sufficient for
equivalent to
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(ARUM)
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without requiring identification-at-infinity type arguments
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establishes
shows
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(Daly-Zachary 1978, Armstrong-Vickers 2015),
,
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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.
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analys
analysis.