The Uniform Validity of Impulse Response Inference in Autoregressions

52 Pages Posted: 22 Oct 2019

See all articles by Atsushi Inoue

Atsushi Inoue

Vanderbilt University - College of Arts and Science - Department of Economics

Lutz Kilian

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

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Date Written: 2019-08-11

Abstract

Existing proofs of the asymptotic validity of conventional methods of impulse response inference based on higher-order autoregressions are pointwise only. In this paper, we establish the uniform asymptotic validity of conventional asymptotic and bootstrap inference about individual impulse responses and vectors of impulse responses when the horizon is fixed with respect to the sample size. For inference about vectors of impulse responses based on Wald test statistics to be uniformly valid, lag-augmented autoregressions are required, whereas inference about individual impulse responses is uniformly valid under weak conditions even without lag augmentation. We introduce a new rank condition that ensures the uniform validity of inference on impulse responses and show that this condition holds under weak conditions. Simulations show that the highest finite-sample accuracy is achieved when bootstrapping the lag-augmented autoregression using the bias adjustments of Kilian (1999). The conventional bootstrap percentile interval for impulse responses based on this approach remains accurate even at long horizons. We provide a formal asymptotic justification for this result.

Keywords: Impulse response, autoregression, lag augmentation, asymptotic normality, bootstrap, uniform inference

JEL Classification: C22, C52

Suggested Citation

Inoue, Atsushi and Kilian, Lutz, The Uniform Validity of Impulse Response Inference in Autoregressions (2019-08-11). FRB of Dallas Working Paper No. 1908. Available at SSRN: https://ssrn.com/abstract=3473102 or http://dx.doi.org/10.24149/wp1908

Atsushi Inoue (Contact Author)

Vanderbilt University - College of Arts and Science - Department of Economics ( email )

Box 1819 Station B
Nashville, TN 37235
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)

London
United Kingdom

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