A Gibbs sampler for mixed logit analysis of differentiated product markets using aggregate data

Abstract

In this paper, we offer the Gibbs sampler as an alternative to the GMM estimator developed by Berry, Levinsohn, and Pakes (Econometrica 63(4), 841---890, 1995) in their equilibrium differentiated product market analysis of the automobile industry. We use the GMM objective as the basis for forming a posterior distribution, thereby making use of certain attributes of the GMM approach that reduce the computational cost of conducting posterior inference. The advantages provided by the our Bayesian GMM approach are that it enables us to conduct inference under the exact posterior distribution for the parameters, to estimate moments of functions of interest that are not readily available using GMM, and to capture non-normalities in the parameter distributions. The cost of posterior inference takes the form of additional distributional assumptions and longer computational time. In an illustration within, we find the random coefficients to be only weakly identified by the data. This results in highly non-normal distributions. The GMM estimates hint at this problem, but it can only be fully characterized by the Gibbs sampler.