Inference on Impulse Response Functions in Structural VAR Models

41 Pages Posted: 16 Jun 2011

See all articles by Atsushi Inoue

Atsushi Inoue

Southern Methodist University

Lutz Kilian

University of Michigan at Ann Arbor - Department of Economics; Centre for Economic Policy Research (CEPR)

Date Written: June 2011


Skepticism toward traditional identifying assumptions based on exclusion restrictions has led to a surge in the use of structural VAR models in which structural shocks are identified by restricting the sign of the responses of selected macroeconomic aggregates to these shocks. Researchers commonly report the vector of pointwise posterior medians of the impulse responses as a measure of central tendency of the estimated response functions, along with pointwise 68 percent posterior error bands. It can be shown that this approach cannot be used to characterize the central tendency of the structural impulse response functions. We propose an alternative method of summarizing the evidence from sign-identified VAR models designed to enhance their practical usefulness. Our objective is to characterize the most likely admissible model(s) within the set of structural VAR models that satisfy the sign restrictions. We show how the set of most likely structural response functions can be computed from the posterior mode of the joint distribution of admissible models both in the fully identified and in the partially identified case, and we propose a highest-posterior density credible set that characterizes the joint uncertainty about this set. Our approach can also be used to resolve the long-standing problem of how to conduct joint inference on sets of structural impulse response functions in exactly identified VAR models. We illustrate the differences between our approach and the traditional approach for the analysis of the effects of monetary policy shocks and of the effects of oil demand and oil supply shocks.

Keywords: Credible Set, Impulse responses, Median, Mode, Sign restrictions, Simultaneous inference, Vector autoregression

JEL Classification: C32, C52, E37, Q43

Suggested Citation

Inoue, Atsushi and Kilian, Lutz, Inference on Impulse Response Functions in Structural VAR Models (June 2011). CEPR Discussion Paper No. DP8419. Available at SSRN:

Atsushi Inoue (Contact Author)

Southern Methodist University ( email )

Dallas, TX 75275
United States

Lutz Kilian

University of Michigan at Ann Arbor - Department of Economics ( email )

611 Tappan Street
Ann Arbor, MI 48109-1220
United States
734-764-2320 (Phone)
734-764-2769 (Fax)

Centre for Economic Policy Research (CEPR)

United Kingdom

Here is the Coronavirus
related research on SSRN

Paper statistics

Abstract Views
PlumX Metrics