Identifying Restrictions on the Random Utility Model

TL;DR

This paper characterizes the ex-ante restrictions on the random utility model that lead to identification, providing a framework to understand when distributions over preferences can be uniquely determined from data.

Contribution

It introduces a class of perturbations that transform preference distributions, offering new criteria for when restrictions on the support of the model ensure identification.

Findings

Characterizes when preference distributions are behaviorally equivalent

Provides conditions for identification based on support restrictions

Offers a local test for model identification in smooth-parameter cases

Abstract

We characterize those ex-ante restrictions on the random utility model which lead to identification. We first identify a simple class of perturbations which transfer mass from a suitable pair of preferences to the pair formed by swapping certain compatible lower contour sets. We show that two distributions over preferences are behaviorally equivalent if and only if they can be obtained from each other by a finite sequence of such transformations. Using this, we obtain specialized characterizations of which restrictions on the support of a random utility model yield identification, as well as of the extreme points of the set of distributions rationalizing a given data set. Finally, when a model depends smoothly on some set of parameters, we show that under mild topological assumptions, identification is characterized by a straightforward, local test.