Bayesian generalized method of moments

Abstract

We propose the Bayesian generalized method of moments (GMM), which is particularly useful when likelihood-based methods are di±cult. By de-riving the moments and concatenating them together, we build up a weighted quadratic objective function in the GMM framework. As in a normal density function, we take the negative GMM quadratic function divided by two and ex-ponentiate it to substitute for the usual likelihood. After specifying the prior dis-tributions, we apply the Markov chain Monte Carlo procedure to sample from the posterior distribution. We carry out simulation studies to examine the proposed Bayesian GMM procedure, and illustrate it with a real data example.