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Vectorautogressions (VARs) are widely applied when it comes to modeling andforecasting macroeconomic variables. In high dimensions, however, they areprone to overfitting. Bayesian methods, more concretely shrinking priors, haveshown to be successful in improving prediction performance. In the presentpaper, we introduce the semi-global framework, in which we replace thetraditional global shrinkage parameter with group-specific shrinkageparameters. We show how this framework can be applied to various shrinkingpriors, such as global-local priors and stochastic search variable selectionpriors. We demonstrate the virtues of the proposed framework in an extensivesimulation study and in an empirical application forecasting data of the USeconomy. Further, we shed more light on the ongoing ``Illusion of Sparsity''debate, finding that forecasting performances under sparse/dense priors varyacross evaluated economic variables and across time frames. Dynamic modelaveraging, however, can combine the merits of both worlds.

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