Forecasting macroeconomic data with Bayesian VARs: Sparse or dense? It depends!

Vectorautogressions (VARs) are widely applied when it comes to modeling and forecasting macroeconomic variables. In high dimensions, however, they are prone to overfitting. Bayesian methods, more concretely shrinking priors, have shown to be successful in improving prediction performance. In the present paper, we introduce the recently developed $R^2$-induced Dirichlet-decomposition prior to the VAR framework and compare it to refinements of well-known priors in the VAR literature. In addition, we develop a semi-global framework, in which we replace the traditional global shrinkage parameter with group specific shrinkage parameters. We demonstrate the virtues of the proposed framework in an extensive simulation study and in an empirical application forecasting data of the US economy. Further, we shed more light on the ongoing "Illusion of Sparsity" debate. We find that forecasting performances under sparse/dense priors vary across evaluated economic variables and across time frames; dynamic model averaging, however, can combine the merits of both worlds.