Asymmetric Conjugate Priors for Large Bayesian VARs

TL;DR

This paper introduces a new asymmetric conjugate prior for large Bayesian VARs that allows cross-variable shrinkage while preserving analytical tractability and computational efficiency, enhancing macroeconomic modeling.

Contribution

The authors develop a novel prior that combines the benefits of conjugate priors with flexible cross-variable shrinkage, enabling faster posterior simulation and analytical results.

Findings

Fast posterior sampling for large VARs (e.g., 100 variables, 4 lags) in under half a minute.

Closed-form marginal likelihood expression for the new prior.

Effective structural analysis with sign restrictions in a 15-variable VAR.

Abstract

Large Bayesian VARs are now widely used in empirical macroeconomics. One popular shrinkage prior in this setting is the natural conjugate prior as it facilitates posterior simulation and leads to a range of useful analytical results. This is, however, at the expense of modeling flexibility, as it rules out cross-variable shrinkage -- i.e., shrinking coefficients on lags of other variables more aggressively than those on own lags. We develop a prior that has the best of both worlds: it can accommodate cross-variable shrinkage, while maintaining many useful analytical results, such as a closed-form expression of the marginal likelihood. This new prior also leads to fast posterior simulation -- for a BVAR with 100 variables and 4 lags, obtaining 10,000 posterior draws takes less than half a minute on a standard desktop. We demonstrate the usefulness of the new prior via a structural analysis using a 15-variable VAR with sign restrictions to identify 5 structural shocks.