Integrability and identification in multinomial choice models

Journal article

McFadden's random-utility model of multinomial choice has long been the workhorse of applied research. We establish shape-restrictions with respect to price and income which are necessary and sufficient for multinomial choice-probability functions to be rationalized via random-utility models with additive but nonparametric unobserved heterogeneity and general income-effects. Our proof is constructive, and facilitates nonparametric identification of preference-distributions without requiring identification-at-infinity type arguments. A corollary shows that 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.

Authors: Bhattacharya, D

• Publication status: Published
• Peer review status: Peer reviewed
• Publisher: Elsevier
• Journal: Journal of Economic Theory
• Volume: 223
• Article number: 105938
• Publication date: 2024-11-29
• Acceptance date: 2024-11-23
• DOI: 10.1016/j.jet.2024.105938
• EISSN: 1095-7235
• ISSN: 0022-0531
• Language: English
• Keywords: multinomial choice; unobserved heterogeneity; random utility; integrability; symmetry; income effects; partial differential equations; nonparametric identification; random coefficient models; bounds on counterfactuals