Posterior Consistency of Nonparametric Conditional Moment Restricted Models

• Activity Number: 303
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Yuan Liao*+ and Wenxin Jiang
• Companies: Northwestern University and Northwestern University
• Keywords: Limited information likelihood ; frequentist properties ; identified region ; nonparametric instrumental variable ; sieve approximation ; ill-posedness

Abstract

This paper addresses the estimation of the conditional moment restricted model that involves a nonparametric structural function g0. One of the most important examples of such a model is the nonparametric regression when the covariates are dependent on the error term, in which case g0 is no longer a conditional mean function. The dependence on the error term often arises in applied economics. I will start with the identification of g0, followed by consistent estimations. The estimation suffers from a so-called 'ill-posed inverse problem', meaning that the relation that identifies g0 is a Fredholm equation of the first kind, which requires a regularization scheme to consistently estimate g0. I will propose a Bayesian procedure with two regularization approaches, and show that in either way, the posterior density converges to a probability mass around g0.