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Demand estimation without outside good shares

Federico A. Bugni, Joel L. Horowitz, Linqi Zhang

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.

Demand estimation without outside good shares

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.
Paper Structure (12 sections, 9 theorems, 118 equations)

This paper contains 12 sections, 9 theorems, 118 equations.

Table of Contents

  1. Introduction
  2. Literature review
  3. The standard BLP model
  4. Identification without outside good shares
  5. Identification of the structural parameters
  6. Can we get the identified set by repeated applications of BLP?
  7. Identification of other equilibrium objects
  8. Numerical illustration
  9. Inference without outside good shares
  10. Empirical illustration
  11. Conclusions
  12. Appendix

Key Result

Theorem 1

Assume that the distribution of $\{(\tilde{s},x,p)|z\}$ is non-atomic a.e. $z\in \mathbb{S}_{z}$, and that, for any $\theta =( \alpha ,\beta ,\lambda ) \in \Theta$, the following random set is integrable: Then, the identified set of $\theta =( \alpha ,\beta ,\lambda )$ is where $\sigma ^{-1}$ is the inverse of the function in eq:sigma_defn with respect to the first argument, and $S_0$ represents

Theorems & Definitions (19)

  • Theorem 1: Identified set of the structural parameters
  • Theorem 2: Alternative characterization of the identified set
  • Theorem 3
  • Theorem 4: Identified set for other equilibrium objects
  • Example 1: Hypercubes in andrews/shi:2013
  • Corollary 1
  • Lemma 1
  • proof
  • proof : Proof of Theorem \ref{['thm:Id_set_expression']}
  • proof : Proof of Theorem \ref{['thm:eq_objects']}
  • ...and 9 more