Integrability and Identification in Multinomial Choice Models
- Authors
- Publication Date
- Dec 03, 2024
- Source
- Apollo - University of Cambridge Repository
- Keywords
- Language
- English
- License
- Green
- External links
Abstract
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.
