Title: Joint Bayesian inference about impulse responses in VAR models
Authors: Atsushi Inoue - Vanderbilt (United States) [presenting]
Abstract: Structural VAR models are routinely estimated by Bayesian methods. Several recent studies have voiced concerns about the common use of posterior median (or mean) response functions in applied VAR analysis. We show that these response functions can be misleading because in empirically relevant settings there need not exist a posterior draw for the impulse response function that matches the posterior median or mean response function, even as the number of posterior draws approaches infinity. As a result, the use of these summary statistics may distort the shape of the impulse response function, which is of foremost interest in applied work. The same concern applies to error bands based on the upper and lower quantiles of the marginal posterior distributions of the impulse responses. In addition, these error bands fail to capture the full uncertainty about the estimates of the structural impulse responses. In response to these concerns, we propose new estimators of impulse response functions that are consistent with Bayesian statistical decision theory, that respect the dynamics of the impulse response functions and that are easy to implement. We also propose joint credible sets for these estimators derived under the same loss function.