Approximate Bayesian inference and forecasting in huge dimensional multi-country VARs

Panel vector autoregressions (PVARs) are a popular tool for analyzing multicountry data sets. However, the number of estimated parameters can be enormous, leading to computational and statistical issues. In this article, we develop fast Bayesian methods for estimating PVARs using integrated rotated Gaussian approximations. We exploit the fact that domestic information is often more important than international information and group the coefficients accordingly. Fast approximations are used to estimate the latter whereas the former are estimated with precision using Markov chain Monte Carlo techniques. We illustrate, using a huge model of the world economy, that it produces competitive forecasts quickly.