How Sensitive Are VAR Forecasts to Prior Hyperparameters? An Automated Sensitivity Analysis

Vector autoregressions combined with Minnesota-type priors are widely used for
macroeconomic forecasting. The fact that strong but sensible priors can substantially
improve forecast performance implies VAR forecasts are sensitive to prior
hyperparameters. But the nature of this sensitivity is seldom investigated. We develop a
general method based on Automatic Differentiation to systematically compute the
sensitivities of forecasts—both points and intervals—with respect to any prior
hyperparameters. In a forecasting exercise using US data, we find that forecasts are
relatively sensitive to the strength of shrinkage for the VAR coefficients, but they are not
much affected by the prior mean of the error covariance matrix or the strength of
shrinkage for the intercepts.