Macroeconomic forecasting with large Bayesian VARs: global-local priors and the illusion of sparsity

A class of global-local hierarchical shrinkage priors for estimating large Bayesian vector autoregressions (BVARs) has recently been proposed. We question whether three such priors: Dirichlet-Laplace, Horseshoe, and Normal-Gamma, can systematically improve the forecast accuracy of two commonly used benchmarks (the hierarchical Minnesota prior and the stochastic search variable selection (SSVS) prior), when predicting key macroeconomic variables. Using small and large data sets, both point and density forecasts suggest that the answer is no. Instead, our results indicate that a hierarchical Minnesota prior remains a solid practical choice when forecasting macroeconomic variables. In light of existing optimality results, a possible explanation for our finding is that macroeconomic data is not sparse, but instead dense.