Measuring Hidden Consumer Heterogeneity with Revealed Preferences

Abstract

Consumer heterogeneity in revealed-preference data is larger than bilateral rationality tests can reveal. We construct a continuous nonparametric metric of this hidden heterogeneity by repeatedly subsampling choices, partitioning agents into groups whose pooled data are jointly rationalisable under a chosen consistency criterion and recording how often each pair is co-classified. The resulting kernel is positive semi-definite, embeds the population in a Hilbert space, and induces a metric with the triangle inequality. Under a necessary-and-sufficient contrast-rank condition, its spectral structure recovers latent preference types. Inference on demographic correlates proceeds via a Monte-Carlo-conditional test and a finite-sample-valid permutation test. Applied to US grocery scanner data, the construction reveals a joint-rationality gap of 0.62 between near-saturated pairwise compatibility and population-level co-typing; binary lottery data yield a comparable gap of 0.38. Standard demographics organise only a modest part of the scanner kernel structure.