In multinomial choice settings with additive heterogeneity, 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.
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
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In multinomial choice settings with additive heterogeneity, Daly-Zachary (1978) and Armstrong-Vickers (2015) provided closed-form conditions, under which choice probability
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
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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
random-utility models with nonparametric heterogeneity and general
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Next, for general multinomial choice that allows for income-effects, we provide global shape restrictions on choice probability functions, which
When combined with an additional restriction, the above conditions
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sufficient for rationalizability. Finally, we outline
necessary and sufficient for the canonical Additive Random Utility Model (ARUM). The sufficiency-proof is constructive, and facilitates
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preference distributions using these results
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
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linear
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analysis.
analys