Revealed Statistical Consumer Theory

We investigate deterministic stochastic choice in the standard consumer framework. We present a model of statistical consumer theory where the individual maximizes their utility with respect to a distribution of bundles that is constrained by a statistic of the distribution (e.g. mean expenditure). We show that this behavior 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 characterization only matters through a finite-dimensional statistic. Statistical consumer theory neither nests nor is nested in the random utility approach