Gaussian processes and Bayesian moment estimation

Abstract

When a large number of moment restrictions is available there may be restrictions that are more important or credible than others. In these situations it might be desirable to weight each restriction based on our beliefs. This is automatically implemented by a Bayesian procedure. We study, in this paper, how to impose moment restrictions on the data distribution through a semiparametric prior distribution for the data generating process F and the structural parameter theta. We show that a Gaussian process prior for the density function associated with F is particularly convenient in order to impose over-identifying restrictions and allows to have a posterior distribution in closed-form. The posterior distribution resulting from our prior specification is shown to be consistent and asymptotically normal. Key words: Moment conditions, Gaussian processes, overidentification, posterior consistency.