Bias Reduction for Bayesian and Frequentist Estimators

Abstract

We show that in parametric likelihood models the first order bias in the posterior mode and the posterior mean can be removed using objective Bayesian priors. These bias-reducing priors are defined as the solution to a set of differential equations which may not be available in closed form. We provide a simple and tractable data dependent prior that solves the differential equations asymptotically and removes the first order bias. When we consider the posterior mode, this approach can be interpreted as penalized maximum likelihood in a frequentist setting. We illustrate the construction and use of the bias-reducing priors in simple examples and a simulation study.

Keywords: Bias, Objective Bayes, Penalized likelihood

JEL Classification: C11, C13