In this paper we propose a hierarchical shrinkage approach for multi-country VAR models. In implementation, we consider three different scale mixtures of Normals priors — specifically, Horseshoe, Normal- Gamma, and Normal-Gamma-Gamma priors. We provide new theoretical results for the Normal-Gamma prior. Empirically, we use a quarterly data set for the G7 economies to examine how model specifications and prior choices affect the forecasting performance for GDP growth, inflation, and a short-term interest rate. We find that hierarchical shrinkage, particularly as implemented with the Horseshoe prior, is very useful in forecasting inflation. It also has the best density forecast performance for output growth and the interest rate. Adding foreign information yields benefits, as multi-country models generally improve on the forecast accuracy of single-country models.
