Bayesian Vector Autoregressions

This article provides an introduction to the burgeoning academic literature on Bayesian Vector Autoregressions, benchmark models for applied macroeconomic research. We first explain Bayes’ theorem and the derivation of the closed-form solution for the posterior distribution of the parameters of the model given data. We further consider parameter shrinkage, a distinguishing feature of the prior distributions commonly employed in the analysis of large datasets, as well as an alternative way of specifying the prior distribution using dummy observations. Finally, we 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.