A Gibbs Sampler for Mixed Logit Analysis of Differentiated Product Markets Using Aggregate Data

Berry, Levinsohn, and Pakes (1995) developed an estimator for an equilibium model of differentiated products markets using aggregate data, without assuming the existence of a representative agent, or imposing prior restrictions on elasticities. Their estimator though, was computationally burdensome as it required an estimate of aggregate demand in each iteration in search of the mode of their GMM objective function. By imposing additional distributional assumptions for the errors in the demand and supply relations, we show how to define a Gibbs sampler that solves the same problem while avoiding problem of estimating aggregate demand. A comparison of the estimators indicates that this should substantially reduce the computational burden, thereby making study of this important class of problems accessible to a wider group of researchers.