Bayesian Vector Autoregressions

This article provides an introduction to the burgeoning academic literature on Bayesian vector autoregressions, benchmark models for applied macroeconomic research. I first explain Bayes' theorem and the derivation of the closed-form solution for the posterior distribution of the parameters of the model's given data. I further consider parameter shrinkage, a distinguishing feature of the prior distributions commonly employed in the analysis of large data. Finally, I describe the mechanisms that enable feasible computations for these linear models that efficiently extract the information content of many variables for economic forecasting and other applications.