Comparison of SML and GMM estimators for the random coefficient logit model using aggregate data

Abstract

A simulated maximum likelihood (SML) estimator for the random coefficient logit model using aggregate data is found to be more efficient than the widely used generalized method of moments estimator (GMM) of Berry et al. (Econometrica 63:841–890, 1995). In particular, the SML estimator is better than the GMM estimator in recovery of heterogeneity parameters which are often of central interest in marketing research. With the GMM estimator, the analyst must determine what moment conditions to use for parameter identification, especially the heterogeneity parameters. With the SML estimator, the moment conditions are automatically determined as the gradients of the log-likelihood function, and these are the most efficient ones if the model is correctly specified. Another limitation of the GMM estimator is that the product market shares must be strictly positive while the SML estimator can handle zero market share observations. Properties of the SML and GMM estimators are demonstrated in simulated data and in data from the US photographic film market.