Bayesian generalized method of moments

Abstract

We propose the Bayesian generalized method of moments (GMM), which is particularly useful when likelihood-based methods are difficult. By deriving 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 exponentiate it to substitute for the usual likelihood. After specifying the prior distributions, 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.