Summary

Bayesian vector autoregressions (BVARs) are standard multivariate autoregressive models routinely used in empirical macroeconomics and finance for structural analysis, forecasting, and scenario analysis in an ever-growing number of applications.

A preeminent field of application of BVARs is forecasting. BVARs with informative priors have often proved to be superior tools compared to standard frequentist/flat-prior VARs. In fact, VARs are highly parametrized autoregressive models, whose number of parameters grows with the square of the number of variables times the number of lags included. Prior information, in the form of prior distributions on the model parameters, helps in forming sharper posterior distributions of parameters, conditional on an observed sample. Hence, BVARs can be effective in reducing parameters uncertainty and improving forecast accuracy compared to standard frequentist/flat-prior VARs.

This feature in particular has favored the use of Bayesian techniques to address “big data” problems, in what is arguably one of the most active frontiers in the BVAR literature. Large-information BVARs have in fact proven to be valuable tools to handle empirical analysis in data-rich environments.

BVARs are also routinely employed to produce conditional forecasts and scenario analysis. Of particular interest for policy institutions, these applications permit evaluating “counterfactual” time evolution of the variables of interests conditional on a pre-determined path for some other variables, such as the path of interest rates over a certain horizon.

The “structural interpretation” of estimated VARs as the data generating process of the observed data requires the adoption of strict “identifying restrictions.” From a Bayesian perspective, such restrictions can be seen as dogmatic prior beliefs about some regions of the parameter space that determine the contemporaneous interactions among variables and for which the data are uninformative. More generally, Bayesian techniques offer a framework for structural analysis through priors that incorporate uncertainty about the identifying assumptions themselves.