Random Utility with Unobservable Alternatives

TL;DR

This paper extends the random utility model to situations where some choice frequencies are unobservable, deriving new inequality constraints and highlighting limitations of common aggregation practices.

Contribution

It provides the first axiomatic characterization of the random utility model with unobservable alternatives, revealing new testable implications.

Findings

Derived nonredundant inequality constraints for unobservable choices.

Showed that aggregating unobserved alternatives into an outside option misses key implications.

Provided a framework for testing random utility models with incomplete choice data.

Abstract

The random utility model, a cornerstone in economics, is axiomatized by Falmagne (1978) and McFadden and Richter (1990) with the assumption that if a menu is observable, the choice frequencies of all alternatives are also observable. However, in practice, it is common for choice frequencies of some alternatives to remain unobserved. To address this discrepancy, we obtain the testable implications of the random utility model when the choice frequencies of some alternatives are unobservable, which consist of nonredundant inequality constraints on observed choice frequencies. Our findings indicate that the widespread empirical practice of aggregating unobserved alternatives into a single "outside option" fails to capture significant implications of random utility models.