Global Robust Bayesian Analysis in Large Models

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. The author develops a sequential Monte Carlo algorithm and uses approximations to the likelihood and statistic of interest to implement the calculations. Applying the methodology to the error bands for the impulse response of output to a monetary policy shock in the New Keynesian model of Smets and Wouters (2007), the author shows that the upper bound of the error bands is very sensitive to the prior but the lower bound is not, with the prior on wage rigidity playing a particularly important role.