Integrability and Identification in Multinomial Choice Models
29 Pages Posted: 16 Oct 2018 Last revised: 19 May 2021
Date Written: May 1, 2021
Abstract
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.
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: Suggested Citation