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 pos-terior 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. The methodology finds that the prior tightness hyperparameters in the hierarchical vector autoregression model from Giannone et al. (2015) are relatively insensitive to their hyperpriors. However, in the New Keynesian model of Smets and Wouters (2007), the error bands for the impulse response of output to a monetary policy shock depend heavily on the prior. The upper bound is especially sensitive, and the prior on wage rigidity plays a particularly important role.& COPY; 2022 Elsevier B.V. All rights reserved.

Automated summary

This paper develops a tool for global prior sensitivity analysis in large Bayesian models. 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. It finds that the prior tightness hyperparameters in the hierarchical vector autoregression model from Giannone et al. (2015) are relatively insensitive to their hyperpriors, but the error bands for the impulse response of output to a monetary policy shock in the New Keynesian model of Smets and Wouters (2007) depend heavily on the prior.