Nonparametric Analysis of Random Utility Models

TL;DR

This paper introduces a nonparametric testing framework for Random Utility Models to verify if demand data aligns with rational consumer behavior, accommodating unobserved heterogeneity and endogenous expenditure.

Contribution

It develops a necessary and sufficient nonparametric test for RUMs that does not restrict unobserved heterogeneity or the number of goods, and proposes a control function approach for endogenous expenditure.

Findings

Test successfully applied to UK demand data with 5 goods.

Method is computationally feasible for demand analysis.

Provides a new econometric test for linear inequality constraints.

Abstract

This paper develops and implements a nonparametric test of Random Utility Models. The motivating application is to test the null hypothesis that a sample of cross-sectional demand distributions was generated by a population of rational consumers. We test a necessary and sufficient condition for this that does not rely on any restriction on unobserved heterogeneity or the number of goods. We also propose and implement a control function approach to account for endogenous expenditure. An econometric result of independent interest is a test for linear inequality constraints when these are represented as the vertices of a polyhedron rather than its faces. An empirical application to the U.K. Household Expenditure Survey illustrates computational feasibility of the method in demand problems with 5 goods.