Global Robust Bayesian Analysis in Large Models

Abstract

This paper develops a tool for global prior sensitivity analysis in large Bayesian models. Without imposing parametric restrictions, the methodology provides bounds for posterior means or quantiles given any prior close to the original in relative entropy, and reveals features of the prior that are important for the posterior statistics of interest. We develop a sequential Monte Carlo algorithm and use approximations to the likelihood and statistic of interest to implement the calculations. Applying the methodology to study the error bands for the impulse response of output to a monetary policy shock in the New Keynesian model of Smets and Wouters (2007), we find a high degree of prior sensitivity. The error bands depend asymmetrically on the prior through features of the likelihood such as correlations or modes in the tail of the posterior, which are hard to account for without the systematic and global analysis here.