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

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  • José Luis Montiel Olea
  • Mikkel Plagborg‐Møller

Abstract

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
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    File URL: https://doi.org/10.1002/jae.2656
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    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).

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