Integrability and identification in multinomial choice models

• 成果类型: Article
• 署名作者: Bhattacharya, Debopam
• 署名单位: University of Cambridge
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2024.105938
• 发表日期: 2025
• 关键词: Multinomial choice; unobserved heterogeneity; random utility; Integrability; symmetry; income effects; Partial differential equations; nonparametric identification; Random coefficient models; Bounds on counterfactuals

摘要

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.