Marginal stochastic choice

TL;DR

This paper investigates the identification and testable implications of stochastic choice models using only marginal choice and availability data, rather than conditional choice probabilities, and characterizes feasible marginal distributions under two-stage menu selection models.

Contribution

It introduces a framework for analyzing stochastic choice models with limited data, focusing on marginal distributions, and characterizes the set of distributions compatible with two-stage menu choice models.

Findings

Identifies conditions under which model parameters are identifiable.

Derives testable implications for models using marginal choice data.

Characterizes feasible marginal distributions in two-stage choice models.

Abstract

Models of stochastic choice typically use conditional choice probabilities given menus as the primitive for analysis, but in the field these are often hard to observe. Moreover, studying preferences over menus is not possible with this data. We assume that an analyst can observe marginal frequencies of choice and availability, but not conditional choice frequencies, and study the testable implications of some prominent models of stochastic choice for this dataset. We also analyze whether parameters of these models can be identified. Finally, we characterize the marginal distributions that can arise under two-stage models in the spirit of Gul and Pesendorfer [2001] and of kreps [1979] where agents select the menu before choosing an alternative.