Maximum Likelihood Estimation of Differentiated Products Demand Systems

TL;DR

This paper develops a maximum likelihood estimator for differentiated products demand systems, specifically the BLP model, demonstrating its superior performance over GMM in simulations and applying it to car data for more precise estimates.

Contribution

It introduces a maximum likelihood estimation method for the BLP demand system with endogenous prices, improving estimation accuracy and standard errors.

Findings

MLE outperforms GMM in bias and mean squared error

MLE provides coverage close to nominal levels, unlike GMM

Application to car data yields similar estimates with tighter standard errors

Abstract

We discuss estimation of the differentiated products demand system of Berry et al (1995) (BLP) by maximum likelihood estimation (MLE). We derive the maximum likelihood estimator in the case where prices are endogenously generated by firms that set prices in Bertrand-Nash equilibrium. In Monte Carlo simulations the MLE estimator outperforms the best-practice GMM estimator on both bias and mean squared error when the model is correctly specified. This remains true under some forms of misspecification. In our simulations, the coverage of the ML estimator is close to its nominal level, whereas the GMM estimator tends to under-cover. We conclude the paper by estimating BLP on the car data used in the original Berry et al (1995) paper, obtaining similar estimates with considerably tighter standard errors.