Nonparametric Analysis of Random Preference Models That Allow for Nontransitivity (New Version!)
This paper develops and tests a Random Preference Model (RPM) that rationalizes stochastic choice without imposing transitivity. Unlike the Random Utility Model (RUM), the RPM allows heterogeneous agents to maximize preference functions consistent with the Weak Axiom of Revealed Preference. I provide a nonparametric characterization of RPM rationalizability and show that stochastic WARP is necessary and sufficient for rationalization under the RPM. I propose a projection-based test and characterize its local power using convex-analytic arguments. An application to U.K. household expenditure data shows that the RPM rationalizes behavior in higher-dimensional commodity spaces where the RUM is rejected. These findings indicate that violations of transitivity are empirically important and that weak-axiom-based models offer a robust alternative for aggregate demand analysis.
Presentations: Canadian Economics Association (June, 2024); EconNect Africa (August & October, 2024); Economic Graduate Students' Conference at Washington University in St. Louis (October, 2024); Applied/Metrics lunch talk (May, 2024), the AMM reading group (April, 2024), and Microeconomic Theory seminar (Novermber, 2024) at the University of Western Ontario, Canadian Econometrics Study Group (October, 2024), 2025 World Congress of the Econometric Society.