Improving inference and forecasting in VAR models using cross-sectional information

We propose a prior for VAR models that exploits the panel structure of macroeconomic time series while also providing shrinkage towards zero to address overfitting concerns. The prior is flexible as it detects shared dynamics of individual variables across endogenously determined groups of countries. We demonstrate the usefulness of our approach in three applications. In the first, using a euro area dataset, we demonstrate that combining pairwise pooling with zero shrinkage helps with structural analysis by lowering the estimation uncertainty. In the second application, we use artificial data to study the bias–variance trade-off between pooling, zero shrinkage and no regularization. If the countries are similar, pooling leads only to a small bias but still provides a large reduction in the estimation variance. Finally, we use a real dataset of a large group of heterogeneous countries to demonstrate that combining pairwise pooling with zero shrinkage can improve out-of-sample forecasting relative to only zero shrinkage or only pooling specifications.