Random Utility with Aggregation

TL;DR

This paper examines the relationship between random utility rationality and aggregation in choice models, revealing weaker testable implications for RU and identifying conditions for equivalence with ARUM.

Contribution

It characterizes RU rationality under aggregation, compares it with ARUM, and identifies conditions for their equivalence, highlighting potential biases in empirical estimation.

Findings

RU rationality has weaker testable implications than ARUM.

Two conditions ensure equivalence between RU and ARUM.

Violating these conditions causes estimation bias.

Abstract

We study random utility (RU) rationality with aggregation when the underlying alternatives in each aggregate vary across consumers and are unobserved, as is typical for an outside option. RUM over the underlying alternatives is the natural assumption on the data generating process, while an aggregated random utility model (ARUM) is the standard empirical tool. We characterize RU rationality in three frameworks and show its testable implications are substantially weaker than those of an ARUM. We provide two independent conditions for their equivalence: non-overlapping preferences within aggregates and menu-independent aggregation. Simulations show that violating either condition produces meaningful estimation bias when imposing an ARUM.