Joint Bayesian inference about impulse responses in VAR models

  • 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.

Download full text files

Export metadata

Author:Atsushi Inoue, Lutz KilianGND
Parent Title (English):Center for Financial Studies (Frankfurt am Main): CFS working paper series ; No. 650
Series (Serial Number):CFS working paper series (650)
Publisher:Center for Financial Studies
Place of publication:Frankfurt, M.
Document Type:Working Paper
Year of Completion:2020
Year of first Publication:2020
Publishing Institution:Universit├Ątsbibliothek Johann Christian Senckenberg
Release Date:2021/01/05
Tag:joint inference; loss function; mean response function; median response function; modal model; posterior risk
Issue:First draft: January 21, 2020. This version: November 2, 2020
Page Number:55
Institutes:Wirtschaftswissenschaften / Wirtschaftswissenschaften
Wissenschaftliche Zentren und koordinierte Programme / Center for Financial Studies (CFS)
Dewey Decimal Classification:3 Sozialwissenschaften / 33 Wirtschaft / 330 Wirtschaft
JEL-Classification:C Mathematical and Quantitative Methods / C2 Single Equation Models; Single Variables / C22 Time-Series Models; Dynamic Quantile Regressions (Updated!)
C Mathematical and Quantitative Methods / C3 Multiple or Simultaneous Equation Models / C32 Time-Series Models; Dynamic Quantile Regressions (Updated!)
C Mathematical and Quantitative Methods / C5 Econometric Modeling / C52 Model Evaluation and Selection
Licence (German):License LogoDeutsches Urheberrecht