Demand estimation without outside good shares

TL;DR

This paper addresses the challenge of estimating demand in the BLP model when the outside good share is unobserved, providing identification results and inference methods using moment inequalities.

Contribution

It introduces a framework for partial identification and valid inference in the BLP demand model without observing outside good shares.

Findings

Model is partially identified without outside good shares

Derived sharp identified sets for parameters and equilibrium objects

Developed inference procedures with valid confidence sets

Abstract

The BLP model is the workhorse framework in empirical IO and enables estimation of demand models for differentiated products using aggregate product shares. In practice, however, the share of the outside good is often unobserved. This paper studies identification and inference in the BLP model when the share of the outside good is unobserved. We show that the model is partially identified, and we derive sharp identified sets for structural parameters and equilibrium objects. We also develop inference procedures based on moment inequalities that deliver valid confidence sets for these structural parameters and equilibrium objects.