Revealed statistical consumer theory

We provide a microfoundation to use aggregates (e.g. mean purchases) to evaluate consumer choice data. We study statistical consumer theory where an individual maximizes a preference over distributions of bundles when constrained by a statistic of the distribution (e.g. mean expenditure). We show statistical consumer theory is observationally equivalent to an individual whose preferences depend only on the statistic of the distribution. This means that despite working with distributions, the empirical content of the model only depends on a finite-dimensional statistic. This approach generalizes random quasilinear utility with random income and mean-variance preferences.