MCMC Approach to Classical Estimation with Overidentifying Restrictions

This paper extends the Laplace estimators proposed by Chernozhukov and Hong (2003) to incorporate the statistic that tests the overidentifying restrictions in the GMM. This information was previously ignored during parameter estimation in econometrics with Bayesian methods. The parameters and the test statistic are estimated simultaneously using information in the entire domain of the estimation equations, not at the global minimum only. We avoid the curse of dimensionality by using MCMC, following Chernozhukov and Hong (2003). Multivariate kernel density estimation gives a smooth distribution of the parameter values that are a solution to the optimization in Laplace estimation. The transformed estimators perform better in a simulation exercise than those version that do not use the information in the OR during parameter estimation. Furthermore, the kernel density also allows for the calculation of alternative estimators that condition the estimation on the OR being satisfied. In the presence of multiple solutions of the GMM objective function, conditioning on the OR brings economic theory as a criteria for estimate selection. As a consequence, our estimators perform better than their unconditional counterparts in a simulation exercise. We simulate a model in Hall and Horowitz (1996) that frequently presents multiple local solutions.