IDEAS home Printed from https://ideas.repec.org/p/azt/cemmap/45-14.html
   My bibliography  Save this paper

Inference about Non-Identified SVARs

Author

Listed:
  • Raffaella Giacomini
  • Toru Kitagawa

Abstract

We propose a method for conducting inference on impulse responses in structural vector autoregressions (SVARs) when the impulse response is not point identified because the number of equality restrictions one can credibly impose is not sufficient for point identification and/or one imposes sign restrictions. We proceed in three steps. We first define the object of interest as the identified set for a given impulse response at a given horizon and discuss how inference is simple when the identified set is convex, as one can limit attention to the set’s upper and lower bounds. We then provide easily verifiable conditions on the type of equality and sign restrictions that guarantee convexity. These cover most cases of practical interest, with exceptions including sign restrictions on multiple shocks and equality restrictions that make the impulse response locally, but not globally, identified. Second, we show how to conduct inference on the identified set. We adopt a robust Bayes approach that considers the class of all possible priors for the non-identified aspects of the model and delivers a class of associated posteriors. We summarize the posterior class by reporting the "posterior mean bounds", which can be interpreted as an estimator of the identified set. We also consider a "robustified credible region" which is a measure of the posterior uncertainty about the identified set. The two intervals can be obtained using a computationally convenient numerical procedure. Third, we show that the posterior bounds converge asymptotically to the identified set if the set is convex. If the identified set is not convex, our posterior bounds can be interpreted as an estimator of the convex hull of the identified set. Finally, a useful diagnostic tool delivered by our procedure is the posterior belief about the plausibility of the imposed identifying restrictions.

Suggested Citation

  • Raffaella Giacomini & Toru Kitagawa, 2014. "Inference about Non-Identified SVARs," CeMMAP working papers 45/14, Institute for Fiscal Studies.
  • Handle: RePEc:azt:cemmap:45/14
    DOI: 10.1920/wp.cem.2014.4514
    as

    Download full text from publisher

    File URL: https://www.cemmap.ac.uk/wp-content/uploads/2020/08/CWP4514.pdf
    Download Restriction: no

    File URL: https://libkey.io/10.1920/wp.cem.2014.4514?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Uhlig, Harald, 2005. "What are the effects of monetary policy on output? Results from an agnostic identification procedure," Journal of Monetary Economics, Elsevier, vol. 52(2), pages 381-419, March.
    2. S. Boragan Aruoba & Frank Schorfheide, 2011. "Sticky Prices versus Monetary Frictions: An Estimation of Policy Trade-Offs," American Economic Journal: Macroeconomics, American Economic Association, vol. 3(1), pages 60-90, January.
    3. Inoue, Atsushi & Kilian, Lutz, 2013. "Inference on impulse response functions in structural VAR models," Journal of Econometrics, Elsevier, vol. 177(1), pages 1-13.
    4. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148, Elsevier.
    5. Jonas E. Arias & Juan Rubio-Ramirez & Daniel F. Waggoner, 2013. "Inference Based on SVARs Identied with Sign and Zero Restrictions: Theory and Applications," Working Papers 2013-24, FEDEA.
    6. 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.
    7. Yuan Liao & Anna Simoni, 2012. "Semi-parametric Bayesian Partially Identified Models based on Support Function," Papers 1212.3267, arXiv.org, revised Nov 2013.
    8. Canova, Fabio & Nicolo, Gianni De, 2002. "Monetary disturbances matter for business fluctuations in the G-7," Journal of Monetary Economics, Elsevier, vol. 49(6), pages 1131-1159, September.
    9. Faust, Jon, 1998. "The robustness of identified VAR conclusions about money," Carnegie-Rochester Conference Series on Public Policy, Elsevier, vol. 49(1), pages 207-244, December.
    10. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497190, October.
    11. Poirier, Dale J., 1998. "Revising Beliefs In Nonidentified Models," Econometric Theory, Cambridge University Press, vol. 14(4), pages 483-509, August.
    12. Leamer, Edward E, 1982. "Sets of Posterior Means with Bounded Variance Priors," Econometrica, Econometric Society, vol. 50(3), pages 725-736, May.
    13. Sundaram,Rangarajan K., 1996. "A First Course in Optimization Theory," Cambridge Books, Cambridge University Press, number 9780521497701, October.
    14. Efe A. Ok, 2007. "Preliminaries of Real Analysis, from Real Analysis with Economic Applications," Introductory Chapters, in: Real Analysis with Economic Applications, Princeton University Press.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Giacomini, Raffaella & Kitagawa, Toru, 2014. "Inference about Non-Identified SVARs," CEPR Discussion Papers 10287, C.E.P.R. Discussion Papers.
    2. Raffaella Giacomini & Toru Kitagawa, 2021. "Robust Bayesian Inference for Set‐Identified Models," Econometrica, Econometric Society, vol. 89(4), pages 1519-1556, July.
    3. Raffaella Giacomini & Toru Kitagawa & Alessio Volpicella, 2022. "Uncertain identification," Quantitative Economics, Econometric Society, vol. 13(1), pages 95-123, January.
    4. Robin Braun & Ralf Brüggemann, 2017. "Identification of SVAR Models by Combining Sign Restrictions With External Instruments," Working Paper Series of the Department of Economics, University of Konstanz 2017-07, Department of Economics, University of Konstanz.
    5. Stock, J.H. & Watson, M.W., 2016. "Dynamic Factor Models, Factor-Augmented Vector Autoregressions, and Structural Vector Autoregressions in Macroeconomics," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 415-525, Elsevier.
    6. Harrison, Andre & Reed, Robert R., 2023. "Gross capital inflows, the U.S. economy, and the response of the Federal Reserve," Journal of International Money and Finance, Elsevier, vol. 139(C).
    7. Castelnuovo, Efrem, 2016. "Modest macroeconomic effects of monetary policy shocks during the great moderation: An alternative interpretation," Journal of Macroeconomics, Elsevier, vol. 47(PB), pages 300-314.
    8. Uhrin, Gábor B. & Herwartz, Helmut, 2016. "Monetary policy shocks, set-identifying restrictions, and asset prices: A benchmarking approach for analyzing set-identified models," University of Göttingen Working Papers in Economics 295, University of Goettingen, Department of Economics.
    9. Sandra Eickmeier & Norbert Metiu & Esteban Prieto, 2016. "Time-varying volatility, financial intermediation and monetary policy," CAMA Working Papers 2016-32, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    10. Francesco Furlanetto & Francesco Ravazzolo & Samad Sarferaz, 2019. "Identification of Financial Factors in Economic Fluctuations," The Economic Journal, Royal Economic Society, vol. 129(617), pages 311-337.
    11. David S. Jacks & Martin Stuermer, 2021. "Dry bulk shipping and the evolution of maritime transport costs, 1850–2020," Australian Economic History Review, Economic History Society of Australia and New Zealand, vol. 61(2), pages 204-227, July.
    12. 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.
    13. Baumeister, Christiane & Hamilton, James D., 2018. "Inference in structural vector autoregressions when the identifying assumptions are not fully believed: Re-evaluating the role of monetary policy in economic fluctuations," Journal of Monetary Economics, Elsevier, vol. 100(C), pages 48-65.
    14. Klug, Thorsten & Mayer, Eric & Schuler, Tobias, 2022. "The corporate saving glut and the current account in Germany," Journal of International Money and Finance, Elsevier, vol. 121(C).
    15. Herwartz, Helmut & Wang, Shu, 2023. "Point estimation in sign-restricted SVARs based on independence criteria with an application to rational bubbles," Journal of Economic Dynamics and Control, Elsevier, vol. 151(C).
    16. Hairault, Jean-Olivier & Zhutova, Anastasia, 2018. "The cyclicality of labor-market flows: A multiple-shock approach," European Economic Review, Elsevier, vol. 103(C), pages 150-172.
    17. Dominik Bertsche, 2019. "The effects of oil supply shocks on the macroeconomy: a Proxy-FAVAR approachThe effects of oil supply shocks on the macroeconomy: a Proxy-FAVAR approach," Working Paper Series of the Department of Economics, University of Konstanz 2019-06, Department of Economics, University of Konstanz.
    18. Ramey, V.A., 2016. "Macroeconomic Shocks and Their Propagation," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 71-162, Elsevier.
    19. Herwartz, Helmut & Rohloff, Hannes & Wang, Shu, 2022. "Proxy SVAR identification of monetary policy shocks - Monte Carlo evidence and insights for the US," Journal of Economic Dynamics and Control, Elsevier, vol. 139(C).
    20. Pooyan Amir-Ahmadi & Thorsten Drautzburg, 2017. "Identification through Heterogeneity," CESifo Working Paper Series 6359, CESifo.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:azt:cemmap:45/14. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Dermot Watson (email available below). General contact details of provider: https://edirc.repec.org/data/ifsssuk.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.