TY  - UNPD
A1  - Inoue, Atsushi
A1  - Kilian, Lutz
T1  - Joint Bayesian inference about impulse responses in VAR models
T2  - Center for Financial Studies (Frankfurt am Main): CFS working paper series ; No. 650
N2  - We derive the Bayes estimator of vectors of structural VAR impulse responses under a range of alternative loss functions. We also derive joint credible regions for vectors of impulse responses as the lowest posterior risk region under the same loss functions. We show that conventional impulse response estimators such as the posterior median response function or the posterior mean response function are not in general the Bayes estimator of the impulse response vector obtained by stacking the impulse responses of interest. We show that such pointwise estimators may imply response function shapes that are incompatible with any possible parameterization of the underlying model. Moreover, conventional pointwise quantile error bands are not a valid measure of the estimation uncertainty about the impulse response vector because they ignore the mutual dependence of the responses. In practice, they tend to understate substantially the estimation uncertainty about the impulse response vector.
T3  - CFS working paper series - 650 
KW  - loss function
KW  - joint inference
KW  - median response function
KW  - mean response function
KW  - modal model
KW  - posterior risk
Y1  - 2020
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/57388
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30:3-573886
UR  - https://ssrn.com/abstract=3759335
IS  - First draft: January 21, 2020. This version: November 2, 2020
PB  - Center for Financial Studies
CY  - Frankfurt, M.
ER  -