Semiparametric Bayesian Estimation and Comparison of Moment Condition Models

Mardi | 2016-03-29
Sully05 de 16h à 17h20

Anna SIMONI – Siddhartha CHIB – Minchul SHIN

In this paper we consider the problem of inference in statistical models characterized via moment restrictions and develop a semiparametric Bayes procedure for selecting valid and relevant moments. We cast the moment estimation problem in the Exponentially Tilted Empirical Likelihood (ETEL) framework introduced by Schennach (2007). Because the ETEL has a well-defined probabilistic interpretation and plays the role of a likelihood, a fully Bayesian framework can be developed. We show how the moment selection problem can be tackled on the basis of marginal likelihoods. These are computed exactly (up to simulation error) by Chib (1995)’s method. We show that our proposed marginal likelihood-based moment selection procedure is consistent in the sense that it discards misspecified as well as irrelevant moment restrictions. As a byproduct, we prove that a posterior distribution obtained from the ETEL satisfies the Bernstein-von Mises theorem in misspecified moment models. The finite sample properties of our procedure are illustrated in simulation exercises in the settings of linear instrumental regression and quantile instrumental regression.