Large Bayesian Vector Autoregressions

Bayesian vector autoregressions are widely used for macroeconomic forecasting and
structural analysis. Until recently, however, most empirical work had considered only
small systems with a few variables due to parameter proliferation concern and
computational limitations. We first review a variety of shrinkage priors that are useful for
tackling the parameter proliferation problem in large Bayesian VARs, followed by a
detailed discussion of efficient sampling methods for overcoming the computational
problem. We then give an overview of some recent models that incorporate various
important model features into conventional large Bayesian VARs, including stochastic
volatility, non-Gaussian and serially correlated errors. Efficient estimation methods for
fitting these more flexible models are also discussed. These models and methods are
illustrated using a forecasting exercise that involves a real-time macroeconomic dataset.
The corresponding MATLAB code is also provided.