Random Utility with Unobservable Alternatives

The random utility model (RUM), a cornerstone in economics, is typically studied under the assumption that choice frequencies of all alternatives are observable. In practice, however, some alternatives have unobservable choice frequencies and are commonly aggregated into a single category called an outside option. We study RUM in such environments and derive a finite, nonredundant system of inequality constraints on observed choice frequencies that characterizes RU-rationalizability. We show that the conventional practice of aggregating unobserved alternatives can miss key information leading to incorrect conclusions such as that observed choices are rationalizable, even when no RUM is consistent with them.