MCMC Approach to Classical Estimation with Overidentifying Restrictions

We extend the Laplace estimators approach proposed by Chernozhukov and Hong (2003) by incorporating information in the space of overidentifying re- strictions (OR) in GMM, information previously ignored during parameter es- timation in Bayesian methods. Parameters and test statistics are estimated simultaneously using the entire equation domain, not only the global mini- mum. Markov Chain Monte Carlo avoids the curse of dimensionality while kernel density estimation allows estimators that condition on OR being satis- fied. This method uses economic theory as criteria for estimate selection when facing multiplicity. Our estimators outperform counterparts in simulation of an asset pricing model in Hall and Horowitz (1996).