Estimation of random coefficients logit demand models with interactive fixed effects

Hyungsik Roger Moon,Matthew Shum,Martin Weidner

doi:10.1016/j.jeconom.2018.06.016

Abstract

We extend the Berry, Levinsohn and Pakes (BLP, 1995) random coefficients discrete-choice demand model, which underlies much recent empirical work in IO. We add interactive fixed effects in the form of a factor structure on the unobserved product characteristics. The interactive fixed effects can be arbitrarily correlated with the observed product characteristics (including price), which accommodate endogeneity and, at the same time, capture strong persistence in market shares across products and markets. We propose a two-step least squares-minimum distance (LS-MD) procedure to calculate the estimator. Our estimator is easy to compute, and Monte Carlo simulations show that it performs well. We consider an empirical illustration to US automobile demand.

Highlights

The Berry, Levinsohn and Pakes (1995) demand model, based on the random coefficients logit multinomial choice model, has become the workhorse of demand modelling in empirical industrial organization and antitrust analysis
We focus on the case where these unobserved product characteristics vary across products and markets according to a factor structure: ξj0t = λ0j ft0 + ejt, 2The t subscript can denote different time periods
We report the bias corrected least squares-minimum distance (LS-MD) estimator, which accounts for bias due to heteroscedasticity in the error terms, and due to pre-determined regressors

Summary

Introduction

The Berry, Levinsohn and Pakes (1995) (hereafter BLP) demand model, based on the random coefficients logit multinomial choice model, has become the workhorse of demand modelling in empirical industrial organization and antitrust analysis. The nested simulated GMM procedure proposed by BLP accommodates possible endogeneity of the observed product-specific regressors, notably price. This model and estimation approach has proven very popular Bai and Ng (2006), Bai (2009), and Moon and Weidner (2013a; 2013b)), we extend the standard BLP demand model by adding interactive fixed effects to the unobserved product characteristic, which is the main “structural error” in the BLP model This interactive fixed effect specification combines market (or time) specific fixed effects with product specific fixed effects in a multiplicative form, which is often referred to as a factor structure

Results

Discussion

Conclusion