  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.
