Random Utility with Aggregation

We characterize when discrete-choice datasets that involve aggregation, such as category-level items or an outside option, are consistent with a random utility model (RUM). The underlying alternatives that an aggregated category represents may differ across individuals and remain unobserved by the analyst. We characterize the observable implications of RUMs with unknown composition of aggregated categories and show that they are surprisingly weak, implying only limited monotonicity of choice frequencies and standard RUM consistency on unaggregated menus. These restrictions are insufficient to justify the aggregated random utility model (ARUM) commonly assumed in empirical work. We identify two sufficient conditions that restore the implication of ARUM: non-overlapping preferences and menu-independent aggregation. Simulations show that violations of these conditions generate estimation bias, highlighting the practical importance of how data are aggregated.