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Confidence Bands for Impulse Responses: Bonferroni versus Wald

  • Helmut Luetkepohl
  • Anna Staszewska-Bystrova
  • Peter Winker

In impulse response analysis estimation uncertainty is typically displayed by constructing bands around estimated impulse response functions. These bands may be based on frequentist or Bayesian methods. If they are based on the joint distribution in the Bayesian framework or the joint asymptotic distribution possibly constructed with bootstrap methods in the frequentist framework often individual confidence intervals or credibility sets are simply connected to obtain the bands. Such bands are known to be too narrow and have a joint confidence content lower than the desired one. If instead the joint distribution of the impulse response coefficients is taken into account and mapped into the band it is shown that such a band is typically rather conservative. It is argued that a smaller band can often be obtained by using the Bonferroni method. While these considerations are equally important for constructing forecast bands, we focus on the case of impulse responses in this study.

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Paper provided by CESifo Group Munich in its series CESifo Working Paper Series with number 4634.

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Date of creation: 2014
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Handle: RePEc:ces:ceswps:_4634
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  1. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2013. "Comparison of Methods for Constructing Joint Confidence Bands for Impulse Response Functions," Discussion Papers of DIW Berlin 1292, DIW Berlin, German Institute for Economic Research.
  2. Ben S. Bernanke & Ilian Mihov, 1998. "Measuring Monetary Policy," The Quarterly Journal of Economics, MIT Press, vol. 113(3), pages 869-902, August.
  3. Uhlig, Harald, 1999. "What are the Effects of Monetary Policy on Output? Results from an Agnostic Identification Procedure," CEPR Discussion Papers 2137, C.E.P.R. Discussion Papers.
  4. Christopher A. Sims & Tao Zha, 1995. "Error bands for impulse responses," Working Paper 95-6, Federal Reserve Bank of Atlanta.
  5. Jordà, Òscar & Marcellino, Massimiliano, 2008. "Path Forecast Evaluation," CEPR Discussion Papers 7009, C.E.P.R. Discussion Papers.
  6. Staszewska-Bystrova, Anna & Winker, Peter, 2013. "Constructing narrowest pathwise bootstrap prediction bands using threshold accepting," International Journal of Forecasting, Elsevier, vol. 29(2), pages 221-233.
  7. Anna Staszewska, 2006. "Representing Uncertainty about Response Paths: the Use of Heuristic Optimisation Methods," Computing in Economics and Finance 2006 379, Society for Computational Economics.
  8. Kim, Jae H., 1999. "Asymptotic and bootstrap prediction regions for vector autoregression," International Journal of Forecasting, Elsevier, vol. 15(4), pages 393-403, October.
  9. Inoue, Atsushi & Kilian, Lutz, 2013. "Inference on impulse response functions in structural VAR models," Journal of Econometrics, Elsevier, vol. 177(1), pages 1-13.
  10. Anna Staszewska‐Bystrova, 2011. "Bootstrap prediction bands for forecast paths from vector autoregressive models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(8), pages 721-735, December.
  11. Lutz Kilian, 2009. "Not All Oil Price Shocks Are Alike: Disentangling Demand and Supply Shocks in the Crude Oil Market," American Economic Review, American Economic Association, vol. 99(3), pages 1053-69, June.
  12. Jae H. Kim, 2004. "Bias-corrected bootstrap prediction regions for vector autoregression," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(2), pages 141-154.
  13. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, vol. 80(2), pages 218-230, May.
  14. repec:hal:journl:hal-00287137 is not listed on IDEAS
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