An MCMC approach to classical estimation

This paper studies computationally and theoretically attractive estimators referred here as to the Laplace type estimators (LTE). The LTE include means and quantiles of Quasi-posterior distributions defined as transformations of general(non-likelihood-based) statistical criterion functions, such as those in GMM, nonlinear IV, empirical likelihood, and minimum distance methods. The approach generates an alternative to classical extremum estimation and also falls outside the parametric Bayesian approach. For example, it offers a new attractive estimation method for such important semi-parametric problems as censored and instrumental quantile regression, nonlinear IV, GMM, and value-at-risk, models. The LTE's are computed using Markov Chain Monte Carlo methods, which help circumvent the computational curse of dimensionality. A large sample theory is obtained and illustrated for regular cases. Keywords: Laplace, Bayes, Markov Chain Monte Carlo, GMM, Instrumental Regression, Censored Quantile Regression, Instrumental Quantile Regression, Empirical Likelihood, Value-at-Risk. JEL Classification: C10, C11, C13, C15.