Revealed statistical consumer theory

We investigate a model of deterministic stochastic choice for the standard con- sumer problem. We introduce the framework of statistical consumer theory where the individual maximizes their utility with respect to a distribution of bundles that is constrained by a statistic (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. Statistical consumer theory neither nests nor is nested in the random utility approach. We provide a formal statistical test of the model accounting for sampling variability and demonstrate it in an illustrative example using data on capuchin monkeys.