  We study a dynamic generalization of stochastic rationality in consumer
behavior, the Dynamic Random Utility Model (DRUM). Under DRUM, a consumer draws
a utility function from a stochastic utility process and maximizes this utility
subject to her budget constraint in each time period. Utility is random, with
unrestricted correlation across time periods and unrestricted heterogeneity in
a cross-section. We provide a revealed preference characterization of DRUM when
we observe a panel of choices from budgets. This characterization is amenable
to statistical testing. Our result unifies Afriat's (1967) theorem that works
with time-series data and the static random utility framework of
McFadden-Richter (1990) that works with cross-sections of choice.
