Nonparametric Analysis of Random Utility Models Robust to Nontransitive Preferences

TL;DR

This paper introduces the Random Preference Model (RPM), a new framework that allows for nontransitive consumer preferences, challenging the traditional transitive assumption of the Random Utility Model (RUM) and better capturing real-world consumer behavior.

Contribution

It develops RPM, a novel nonparametric framework accommodating nontransitive preferences, and extends stochastic revealed preference methods to analyze such behaviors.

Findings

Data supports RPM over RUM in UK consumer choices.

RPM captures nontransitive preferences ignored by RUM.

Method generalizes revealed preference tests to nontransitive cases.

Abstract

The Random Utility Model (RUM) is the gold standard in describing the behavior of a population of consumers. The RUM operates under the assumption of transitivity in consumers' preference relationships, but the empirical literature has regularly documented its violation. In this paper, I introduce the Random Preference Model (RPM), a novel framework for understanding the choice behavior in a population akin to RUMs, which preserves monotonicity and accommodates nontransitive behaviors. The primary objective is to test the null hypothesis that a population of rational consumers generates cross-sectional demand distributions without imposing constraints on the unobserved heterogeneity or the number of goods. I analyze data from the UK Family Expenditure Survey and find evidence that contradicts RUMs and supports RPMs. These findings underscore RPMs' flexibility and capacity to explain a wider spectrum of consumer behaviors compared to RUMs. This paper generalizes the stochastic revealed preference methodology of McFadden & Richter (1990) for finite choice sets to settings with nontransitive and possibly nonconvex preference relations.