An MCMC Approach to Classical Estimation

TL;DR

This paper introduces Laplace type estimators (LTE) that use MCMC methods to efficiently estimate complex semi-parametric models, providing an alternative to classical and Bayesian approaches.

Contribution

It develops a new class of estimators called LTE that apply MCMC to non-likelihood-based criteria, expanding estimation tools for semi-parametric models.

Findings

LTE includes means and quantiles of Quasi-posterior distributions.

LTE offers computational advantages over traditional extremum estimation.

Large sample theory supports LTE's validity in regular cases.

Abstract

This paper studies computationally and theoretically attractive estimators called the Laplace type estimators (LTE), which 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, nonlinear 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 for regular cases.