Identification in the Random Utility Model

TL;DR

This paper investigates conditions under which the random utility model is uniquely identified, providing graphical criteria and tests for uniqueness, and linking support identification to the model's overall identification.

Contribution

It offers two new characterizations for the existence of a unique random utility representation, one graphical and one direct testing method.

Findings

Unique representation characterized by graph inflow-outflow conditions

A direct test for the uniqueness of the random utility representation

Support of the representation is identified if and only if the representation is identified

Abstract

The random utility model is known to be unidentified, but there are times when the model admits a unique representation. We offer two characterizations for the existence of a unique random utility representation. Our first characterization puts conditions on a graphical representation of the data set. Non-uniqueness arises when multiple inflows can be assigned to multiple outflows on this graph. Our second characterization provides a direct test for uniqueness given a random utility representation. We also show that the support of a random utility representation is identified if and only if the representation itself is identified.