Measuring Hidden Consumer Heterogeneity with Revealed Preferences

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 consumers into groups whose pooled choices are jointly rationalisable, and recording how often each pair is co-classified. The resulting co-classification matrix is a revealed-preference kernel: it is positive semi-definite, embeds the population in a Hilbert space, and induces a distance with the triangle inequality. In US grocery scanner data, we find that 97% of household pairs are pairwise rationalisable but the mean co-typing probability falls to 0.37: a joint-rationality gap of 0.62. The same construction yields a gap of 0.38 in binary lottery data, directly comparable across consumption and risk domains. We show that under a necessary-and-sufficient contrast-rank condition, the kernel's spectral structure recovers latent preference types. We develop mean-difference and finite-sample-exact permutation tests of demographic correlates of the kernel. The evidence points to a large revealed-preference component of heterogeneity that is missed by bilateral tests, only weakly organized by standard demographics, and robust to relaxing exact rationality.