  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 semi-global framework, in which we replace the
traditional global shrinkage parameter with group-specific shrinkage
parameters. We show how this framework can be applied to various shrinking
priors, such as global-local priors and stochastic search variable selection
priors. 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, finding 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.
