Bayesian Inference for Econometric Models using Empirical Likelihood Functions

Estimators based on moment conditions of the form E[g(X,t)], where t is a finite-dimensional parameter vector of interest, are a popular tool in applied econometrics. Unlike likelihood-based estimators, moment-based estimators do not require the researcher to specify the probability distribution of the random vector X in detail. While the use of inappropriate auxiliary assumptions about the distribution of X potentially leads to misspecification bias, reasonable distributional assumptions may improve the precision of the estimator substantially, in particular in small samples. Most Bayesian inference procedures in econometrics are based on fully specified parametric models. Empirical likelihood functions enable Bayesian inference with semiparametric models. We propose to combine an empirical likelihood function with a prior distribution to conduct Bayesian inference. A prior is constructed by completing the moment-based model with a probability distribution that satisfies the moment constraints. Heuristically, we augment the actual sample with artificial observations from a parametric completion. We examine the large-sample behavior of the posterior and develop Markov-Chain- Monte-Carlo methods to generate draws from the posterior and conduct small-sample inferences