A Frequentist Approach to Revealed Preference Analysis

TL;DR

This paper introduces a statistical framework for revealed preference tests, linking sample size and data richness to the ability to detect meaningful deviations from economic models, with practical implications for demand analysis.

Contribution

It develops a new frequentist approach to revealed preference testing that accounts for data richness and provides practical tests and confidence intervals for demand functions.

Findings

Power of tests increases with sample size and data richness.

Standard sample sizes may have limited power to reject certain models.

Simulations demonstrate variability in test power across different models.

Abstract

This paper develops a framework to study the statistical power of revealed-preference tests. With randomly sampled budgets and mild smoothness of demand, statistical learning implies that any model consistent with the data must approximate true choice behaviour. We interpret this result as follows: passing a revealed-preference test is informative only to the extent that the data are sufficiently rich to rule out economically meaningful departures from the maintained model. We make this precise by linking sample size and confidence to the magnitude of detectable departures, and by characterising how power rises with additional observations. Extending our approach beyond revealed-preference inequalities to smooth functional restrictions yields practical tests, even when exact revealed-preference tests are computationally infeasible. We also provide confidence intervals for smooth functionals of demand, including welfare effects. Simulations show that standard sample sizes can generate widely different power across models, contextualizing why some conditions ``rarely reject'' in practice.