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Studies in Nonlinear Dynamics & Econometrics

Ed. by Mizrach, Bruce

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Volume 24 (2020)

Combining sign and parametric restrictions in SVARs by utilising Givens rotations

Lance A. Fisher / Hyeon-seung Huh
  • Corresponding author
  • School of Economics, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea, Phone: +82-2-2123-5499
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Published Online: 2019-10-26 | DOI: https://doi.org/10.1515/snde-2018-0104


This paper shows how to impose parametric restrictions in conjunction with sign restrictions to separate the shocks in SVARs. In sign restrictions, it is common to rotate an initial set of orthogonal shocks by utilising a Givens rotation matrix. In this paper, we show how to construct the Givens rotation matrix when parametric restrictions are part of the identification in sign restricted SVARs. The properties of Givens matrices are such that the parametric restrictions imply a system of equations which can be solved for the unknown parameters (or “angles”) in a rotation matrix, conditional on the values of the parameters which are drawn. The Givens rotation matrix formed in this manner is such that the parametric restrictions on the impulse responses are satisfied on each draw in sign restrictions. The method is demonstrated in an influential SVAR and is shown to generate results similar to those from a recent method which imposes the orthogonality and zero parametric restrictions on the columns of the rotation matrix in sign restrictions.

This article offers supplementary material which is provided at the end of the article.

Keywords: Givens rotations; QR decomposition; sign and parametric restrictions; structural vector autoregressions

JEL Classification: C32; C51; E32


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About the article

Published Online: 2019-10-26

Funding Source: Macquarie University

Award identifier / Grant number: OSP

Funding Source: Ministry of Education of the Republic of Korea and the National Research Foundation of Korea

Award identifier / Grant number: NRF-2019S1A5A2A01038776

The research by the first author was supported by a Macquarie University, Funder Id: http://dx.doi.org/10.13039/501100001230, OSP grant. The research by the second author is supported by the Ministry of Education of the Republic of Korea and the National Research Foundation of Korea (Funder Id: http://dx.doi.org/10.13039/501100003725, NRF-2019S1A5A2A01038776).

Citation Information: Studies in Nonlinear Dynamics & Econometrics, 20180104, ISSN (Online) 1558-3708, DOI: https://doi.org/10.1515/snde-2018-0104.

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