Adaptive Hierarchical Priors for High-Dimensional Vector Autoregessions

This paper proposes a scalable and simulation-free estimation algorithm for vector autoregressions (VARs) that allows fast approximate calculation of marginal posterior distributions. We apply the algorithm to derive analytical expressions for popular Bayesian shrinkage priors that admit a hierarchical representation and which would typically require computationally intensive posterior simulation methods. The proposed algorithm is modular, parallelizable, and scales linearly with the number of predictors, allowing fast and efficient estimation of large Bayesian VARs. The benefits of our approach are explored and computational gains of the proposed estimation algorithm and priors. Second, a forecasting exercise involving VARs estimated on macroeconomic data demonstrates the ability of hierarchical shrinkage priors to find useful parsimonious representations. Finally, we show that our approach can be used successfully for structural analysis and can replicate important features of structural shocks predicted by economic theory.