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Combining sign and parametric restrictions in SVARs by utilising Givens rotations

Author

Listed:
  • Fisher Lance A.

    (Department of Economics, Macquarie University, Sydney 2109, Australia)

  • Huh Hyeon-seung

    (School of Economics, Yonsei University, 50 Yonsei-ro, Seodaemun-gu, Seoul 03722, Republic of Korea, Phone: +82-2-2123-5499)

Abstract

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.

Suggested Citation

  • Fisher Lance A. & Huh Hyeon-seung, 2020. "Combining sign and parametric restrictions in SVARs by utilising Givens rotations," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 24(3), pages 1-19, June.
    • Handle: RePEc:bpj:sndecm:v:24:y:2020:i:3:p:19:n:4
    DOI: 10.1515/snde-2018-0104
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    More about this item

    Keywords

    Givens rotations; QR decomposition; sign and parametric restrictions; structural vector autoregressions;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles

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