# Heterogeneous Choice Sets and Preferences

## TL;DR

This paper introduces a robust method for analyzing discrete choices with unobserved choice sets, allowing for heterogeneity and minimal assumptions, and applies it to auto insurance data to uncover household preferences.

## Contribution

It develops a new identification approach using moment inequalities for models with unobserved choice sets, and demonstrates its application to real-world insurance data.

## Key findings

- Most households have limited choice sets in deductible choices.
- Expected utility theory with low risk aversion explains the data well.
- The method is computationally feasible for larger and more complex models.

## Abstract

We propose a robust method of discrete choice analysis when agents' choice sets are unobserved. Our core model assumes nothing about agents' choice sets apart from their minimum size. Importantly, it leaves unrestricted the dependence, conditional on observables, between choice sets and preferences. We first characterize the sharp identification region of the model's parameters by a finite set of conditional moment inequalities. We then apply our theoretical findings to learn about households' risk preferences and choice sets from data on their deductible choices in auto collision insurance. We find that the data can be explained by expected utility theory with low levels of risk aversion and heterogeneous non-singleton choice sets, and that more than three in four households require limited choice sets to explain their deductible choices. We also provide simulation evidence on the computational tractability of our method in applications with larger feasible sets or higher-dimensional unobserved heterogeneity.

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Source: https://tomesphere.com/paper/1907.02337