Identification in Stochastic Choice

TL;DR

This paper characterizes the identified sets in various stochastic choice models, providing a comprehensive framework for understanding observational equivalence and offering new tools for testing identification in dynamic settings.

Contribution

It introduces a unifying characterization of observational equivalence in stochastic choice models using swapping transforms and derives complete descriptions of their identified sets.

Findings

Two distributions are observationally equivalent if related by swapping transforms.

Complete inequalities and extreme points of identified sets are characterized.

A novel global-inverse test for identification in models with smoothly varying choice frequencies.

Abstract

We characterize the identified sets of a wide range of stochastic choice models, including random utility, various models of boundedly-rational behavior, and dynamic discrete choice. In each of these settings, we show two distributions over choice rules are observationally equivalent if and only if they can be obtained from one another via a finite sequence of simple swapping transforms. We leverage this to obtain complete descriptions of both the defining inequalities and extreme points of these identified sets. In cases where choice frequencies vary smoothly with some parameters, we provide a novel global-inverse result for practically testing identification.