# Identification and Estimation of Discrete Choice Models with Unobserved Choice Sets

## TL;DR

This paper develops a nonparametric framework to identify and estimate discrete choice models accounting for unobserved choice sets, using panel data to recover preferences and choice set distributions, with applications showing bias reduction.

## Contribution

It introduces a computationally efficient method using mixed-integer optimization to recover sparse choice set distributions in discrete choice models.

## Key findings

- Ignoring unobserved choice sets biases preference estimates
- Choice sets are often nested or partitioned, enabling sparsity assumptions
- Application to cereal industry reveals significant latent heterogeneity

## Abstract

We propose a framework for nonparametric identification and estimation of discrete choice models with unobserved choice sets. We recover the joint distribution of choice sets and preferences from a panel dataset on choices. We assume that either the latent choice sets are sparse or that the panel is sufficiently long. Sparsity requires the number of possible choice sets to be relatively small. It is satisfied, for instance, when the choice sets are nested, or when they form a partition. Our estimation procedure is computationally fast and uses mixed-integer optimization to recover the sparse support of choice sets. Analyzing the ready-to-eat cereal industry using a household scanner dataset, we find that ignoring the unobservability of choice sets can lead to biased estimates of preferences due to significant latent heterogeneity in choice sets.