IDEAS home Printed from
   My bibliography  Save this article

Simultaneous confidence bands: Theory, implementation, and an application to SVARs


  • José Luis Montiel Olea
  • Mikkel Plagborg‐Møller


Simultaneous confidence bands are versatile tools for visualizing estimation uncertainty for parameter vectors, such as impulse response functions. In linear models, it is known that that the sup‐t confidence band is narrower than commonly used alternatives—for example, Bonferroni and projection bands. We show that the same ranking applies asymptotically even in general nonlinear models, such as vector autoregressions (VARs). Moreover, we provide further justification for the sup‐t band by showing that it is the optimal default choice when the researcher does not know the audience's preferences. Complementing existing plug‐in and bootstrap implementations, we propose a computationally convenient Bayesian sup‐t band with exact finite‐sample simultaneous credibility. In an application to structural VAR impulse response function estimation, the sup‐t band—which has been surprisingly overlooked in this setting—is at least 35% narrower than other off‐the‐shelf simultaneous bands.

Suggested Citation

  • José Luis Montiel Olea & Mikkel Plagborg‐Møller, 2019. "Simultaneous confidence bands: Theory, implementation, and an application to SVARs," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(1), pages 1-17, January.
  • Handle: RePEc:wly:japmet:v:34:y:2019:i:1:p:1-17
    DOI: 10.1002/jae.2656

    Download full text from publisher

    File URL:
    Download Restriction: no


    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.

    Cited by:

    1. Giovanni Angelini & Luca Fanelli, 2019. "Exogenous uncertainty and the identification of structural vector autoregressions with external instruments," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(6), pages 951-971, September.
    2. Atsushi Inoue & Lutz Kilian, 2020. "The Role of the Prior in Estimating VAR Models with Sign Restrictions," Working Papers 2030, Federal Reserve Bank of Dallas.
    3. Atsushi Inoue & Lutz Kilian, 2020. "Joint Bayesian Inference about Impulse Responses in VAR Models," Working Papers 2022, Federal Reserve Bank of Dallas.
    4. Lynda Khalaf & Beatriz Peraza López, 2020. "Simultaneous Indirect Inference, Impulse Responses and ARMA Models," Econometrics, MDPI, Open Access Journal, vol. 8(2), pages 1-26, April.
    5. Inoue, Atsushi & Kilian, Lutz, 2020. "The uniform validity of impulse response inference in autoregressions," Journal of Econometrics, Elsevier, vol. 215(2), pages 450-472.
    6. Justine S. Hastings & Ryan E. Kessler & Jesse M. Shapiro, 2019. "The Effect of SNAP on the Composition of Purchased Foods: Evidence and Implications," NBER Working Papers 25953, National Bureau of Economic Research, Inc.
    7. Biewen, Martin & Fitzenberger, Bernd & Seckler, Matthias, 2020. "Counterfactual quantile decompositions with selection correction taking into account Huber/Melly (2015): An application to the German gender wage gap," Labour Economics, Elsevier, vol. 67(C).

    More about this item


    Access and download statistics


    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:wly:japmet:v:34:y:2019:i:1:p:1-17. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Wiley Content Delivery). General contact details of provider: .

    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.

    We have no references for this item. You can help adding them by using 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.