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.