Asymmetric Conjugate Priors for Large Bayesian VARs

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 modelling exibility, 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. In a forecasting exercise, we show
that a data-driven asymmetric prior outperforms two useful benchmarks: a data-driven
symmetric prior and a subjective asymmetric prior.