Joint Bayesian inference about impulse responses in VAR models

We derive the Bayes estimator of vectors structural VAR impulse responses under a range alternative loss functions. also discuss construction joint credible regions for as lowest posterior risk region same show that conventional response estimators such median function or mean are not in general vector obtained by stacking interest. illustrate pointwise may imply shapes incompatible with any possible parameterization underlying model. Moreover, quantile error bands valid measure estimation uncertainty about because they ignore mutual dependence responses. In practice, tend to understate substantially vector.