In impulse response analysis estimation uncertainty is typically displayed by constructing bands around estimated impulse response functions. If they are based on the joint asymptotic distribution possibly constructed with bootstrap methods in a frequentist framework, often individual confidence intervals are simply connected to obtain the bands. Such bands are known to be too narrow and have a joint coverage probability lower than the desired one. If instead the Wald statistic is used and the joint bootstrap distribution of the impulse response coefficient estimators is taken into account and mapped into the band, it is shown that such a band is typically rather conservative. It is argued that, by using the Bonferroni method, a band can often be obtained which is smaller than the Wald band."> In impulse response analysis estimation uncertainty is typically displayed by constructing bands around estimated impulse response functions. If they are based on the joint asymptotic distribution possibly constructed with bootstrap methods in a frequentist framework, often individual confidence intervals are simply connected to obtain the bands. Such bands are known to be too narrow and have a joint coverage probability lower than the desired one. If instead the Wald statistic is used and the joint bootstrap distribution of the impulse response coefficient estimators is taken into account and mapped into the band, it is shown that such a band is typically rather conservative. It is argued that, by using the Bonferroni method, a band can often be obtained which is smaller than the Wald band."> In impulse response analysis estimation uncertainty is typically displayed by constructing bands around estimated impulse response functio">
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Confidence Bands for Impulse Responses: Bonferroni vs. Wald

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  • Helmut Lütkepohl
  • Anna Staszewska-Bystrova
  • Peter Winker
Abstract
type="main" xml:id="obes12114-abs-0001"> In impulse response analysis estimation uncertainty is typically displayed by constructing bands around estimated impulse response functions. If they are based on the joint asymptotic distribution possibly constructed with bootstrap methods in a frequentist framework, often individual confidence intervals are simply connected to obtain the bands. Such bands are known to be too narrow and have a joint coverage probability lower than the desired one. If instead the Wald statistic is used and the joint bootstrap distribution of the impulse response coefficient estimators is taken into account and mapped into the band, it is shown that such a band is typically rather conservative. It is argued that, by using the Bonferroni method, a band can often be obtained which is smaller than the Wald band.

Suggested Citation

  • Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2015. "Confidence Bands for Impulse Responses: Bonferroni vs. Wald," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 77(6), pages 800-821, December.
    • Handle: RePEc:bla:obuest:v:77:y:2015:i:6:p:800-821
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    Cited by:

    1. Boer, Lukas & Lütkepohl, Helmut, 2021. "Qualitative versus quantitative external information for proxy vector autoregressive analysis," Journal of Economic Dynamics and Control, Elsevier, vol. 127(C).
    2. Stefan Bruder & Michael Wolf, 2018. "Balanced Bootstrap Joint Confidence Bands for Structural Impulse Response Functions," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(5), pages 641-664, September.
    3. 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.
    4. Lütkepohl, Helmut & Schlaak, Thore, 2019. "Bootstrapping impulse responses of structural vector autoregressive models identified through GARCH," Journal of Economic Dynamics and Control, Elsevier, vol. 101(C), pages 41-61.
    5. Fengler, Matthias & Polivka, Jeannine, 2022. "Structural Volatility Impulse Response Analysis," Economics Working Paper Series 2211, University of St. Gallen, School of Economics and Political Science, revised Nov 2022.
    6. Michael Funke & Julius Loermann & Andrew Tsang, 2022. "Volatility transmission and volatility impulse response functions in the main and the satellite Renminbi exchange rate markets," Review of International Economics, Wiley Blackwell, vol. 30(2), pages 606-628, May.
    7. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2018. "Calculating joint confidence bands for impulse response functions using highest density regions," Empirical Economics, Springer, vol. 55(4), pages 1389-1411, December.
    8. Joscha Beckmann & Robert L. Czudaj, 2018. "Monetary Policy Shocks, Expectations, And Information Rigidities," Economic Inquiry, Western Economic Association International, vol. 56(4), pages 2158-2176, October.
    9. Daniel Grabowski & Anna Staszewska-Bystrova & Peter Winker, 2020. "Skewness-adjusted bootstrap confidence intervals and confidence bands for impulse response functions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 104(1), pages 5-32, March.
    10. Bruns, Martin & Lütkepohl, Helmut, 2022. "Comparison of local projection estimators for proxy vector autoregressions," Journal of Economic Dynamics and Control, Elsevier, vol. 134(C).
    11. Mardi Dungey & Denise R. Osborn, 2020. "The Gains from Catch‐up for China and the USA: An Empirical Framework," The Economic Record, The Economic Society of Australia, vol. 96(314), pages 350-365, September.
    12. Inoue, Atsushi & Kilian, Lutz, 2022. "Joint Bayesian inference about impulse responses in VAR models," Journal of Econometrics, Elsevier, vol. 231(2), pages 457-476.
    13. Lütkepohl, Helmut & Staszewska-Bystrova, Anna & Winker, Peter, 2020. "Constructing joint confidence bands for impulse response functions of VAR models – A review," Econometrics and Statistics, Elsevier, vol. 13(C), pages 69-83.
    14. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2018. "Estimation of structural impulse responses: short-run versus long-run identifying restrictions," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 229-244, April.
    15. Povilas Lastauskas & Julius Stakenas, 2019. "Does It Matter When Labor Market Reforms Are Implemented? The Role of the Monetary Policy Environment," Bank of Lithuania Working Paper Series 66, Bank of Lithuania.
    16. Diego Fresoli, 2022. "Bootstrap VAR forecasts: The effect of model uncertainties," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(2), pages 279-293, March.
    17. Hafner, Christian M. & Herwartz, Helmut & Wang, Shu, 2023. "Causal inference with (partially) independent shocks and structural signals on the global crude oil market," LIDAM Discussion Papers ISBA 2023004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. Inoue, Atsushi & Kilian, Lutz, 2020. "The uniform validity of impulse response inference in autoregressions," Journal of Econometrics, Elsevier, vol. 215(2), pages 450-472.
    19. Martin Bruns & Helmut Lütkepohl, 2023. "An Alternative Bootstrap for Proxy Vector Autoregressions," Computational Economics, Springer;Society for Computational Economics, vol. 62(4), pages 1857-1882, December.
    20. Fernando J. Pérez Forero & Marco Vega, 2016. "Asymmetric Exchange Rate Pass-through: Evidence from Nonlinear SVARs," Working Papers 63, Peruvian Economic Association.
    21. Marinko Škare & Małgorzata Porada-Rochoń, 2021. "Measuring the impact of financial cycles on family firms: how to prepare for crisis?," International Entrepreneurship and Management Journal, Springer, vol. 17(3), pages 1111-1130, September.
    22. Grabowski Daniel & Staszewska-Bystrova Anna & Winker Peter, 2017. "Generating prediction bands for path forecasts from SETAR models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 21(5), pages 1-18, December.
    23. Freyberger, Joachim & Rai, Yoshiyasu, 2018. "Uniform confidence bands: Characterization and optimality," Journal of Econometrics, Elsevier, vol. 204(1), pages 119-130.

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