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A note on global identi?cation in structural vector autoregressions

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  • Emanuele Bacchiocchi

    (Institute for Fiscal Studies)

  • Toru Kitagawa

    (Institute for Fiscal Studies and University College London)

Abstract

In a landmark contribution to the structural vector autoregression (SVARs) literature, Rubio-Ramirez, Waggoner, and Zha (2010, `Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference,’ Review of Economic Studies) shows a necessary and sufficient condition for equality restrictions to globally identify the structural parameters of a SVAR. The simplest form of the necessary and sufficient condition shown in Theorem 7 of Rubio-Ramirez et al (2010) checks the number of zero restrictions and the ranks of particular matrices without requiring knowledge of the true value of the structural or reduced-form parameters. However, this note shows by counterexample that this condition is not sufficient for global identification. Analytical investigation of the counterexample clarifies why their sufficiency claim breaks down. The problem with the rank condition is that it allows for the possibility that restrictions are redundant, in the sense that one or more restrictions may be implied by other restrictions, in which case the implied restriction contains no identifying information. We derive a modified necessary and sufficient condition for SVAR global identification and clarify how it can be assessed in practice.

Suggested Citation

  • Emanuele Bacchiocchi & Toru Kitagawa, 2021. "A note on global identi?cation in structural vector autoregressions," CeMMAP working papers CWP03/21, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    • Handle: RePEc:ifs:cemmap:03/21
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    References listed on IDEAS

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    1. Raffaella Giacomini & Toru Kitagawa & Matthew Read, 2021. "Identification and Inference Under Narrative Restrictions," Papers 2102.06456, arXiv.org.
    2. Arias, Jonas E. & Rubio-Ramírez, Juan F. & Waggoner, Daniel F., 2021. "Inference in Bayesian Proxy-SVARs," Journal of Econometrics, Elsevier, vol. 225(1), pages 88-106.
    3. Juan F. Rubio-Ramírez & Daniel F. Waggoner & Tao Zha, 2010. "Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(2), pages 665-696.
    4. Juan Antolín-Díaz & Juan F. Rubio-Ramírez, 2018. "Narrative Sign Restrictions for SVARs," American Economic Review, American Economic Association, vol. 108(10), pages 2802-2829, October.
    5. Blanchard, Olivier Jean, 1989. "A Traditional Interpretation of Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 79(5), pages 1146-1164, December.
    6. Raffaella Giacomini & Toru Kitagawa, 2021. "Robust Bayesian Inference for Set‐Identified Models," Econometrica, Econometric Society, vol. 89(4), pages 1519-1556, July.
    7. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    8. Olivier Blanchard & Roberto Perotti, 2002. "An Empirical Characterization of the Dynamic Effects of Changes in Government Spending and Taxes on Output," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 117(4), pages 1329-1368.
    9. Emanuele Bacchiocchi & Toru Kitagawa, 2020. "Locally- but not globally-identified SVARs," CeMMAP working papers CWP40/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    10. Bernanke, Ben S., 1986. "Alternative explanations of the money-income correlation," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 25(1), pages 49-99, January.
    11. Pooyan Amir‐Ahmadi & Thorsten Drautzburg, 2021. "Identification and inference with ranking restrictions," Quantitative Economics, Econometric Society, vol. 12(1), pages 1-39, January.
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    Cited by:

    1. Matthew Read, 2022. "Algorithms for inference in SVARs identified with sign and zero restrictions [Identification and inference with ranking restrictions]," The Econometrics Journal, Royal Economic Society, vol. 25(3), pages 699-718.
    2. Emanuele Bacchiocchi & Toru Kitagawa, 2020. "Locally- but not globally-identified SVARs," CeMMAP working papers CWP40/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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