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Balanced bootstrap joint confidence bands for structural impulse response functions

Author

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  • Stefan Bruder
  • Michael Wolf

Abstract

Constructing joint confidence bands for structural impulse response functions based on a VAR model is a difficult task because of the non-linear nature of such functions. We propose new joint confidence bands that cover the entire true structural impulse response function up to a chosen maximum horizon with a prespecified probability (1 − α), at least asymptotically. Such bands are based on a certain bootstrap procedure from the multiple testing literature. We compare the finite-sample properties of our method with those of existing methods via extensive Monte Carlo simulations. We also investigate the effect of endogenizing the lag order in our bootstrap procedure on the finite-sample properties. Furthermore, an empirical application to a real data set is provided.

Suggested Citation

  • Stefan Bruder & Michael Wolf, 2017. "Balanced bootstrap joint confidence bands for structural impulse response functions," ECON - Working Papers 246, Department of Economics - University of Zurich, revised Jan 2018.
    • Handle: RePEc:zur:econwp:246
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    References listed on IDEAS

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    1. Jentsch, Carsten & Kreiss, Jens-Peter, 2010. "The multiple hybrid bootstrap -- Resampling multivariate linear processes," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2320-2345, November.
    2. 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.
    3. Staszewska, Anna, 2007. "Representing uncertainty about response paths: The use of heuristic optimisation methods," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 121-132, September.
    4. Andr? Kurmann & Christopher Otrok, 2013. "News Shocks and the Slope of the Term Structure of Interest Rates," American Economic Review, American Economic Association, vol. 103(6), pages 2612-2632, October.
    5. Tom Engsted & Thomas Q. Pedersen, 2014. "Bias-Correction in Vector Autoregressive Models: A Simulation Study," Econometrics, MDPI, vol. 2(1), pages 1-27, March.
    6. Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
    7. 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 1053-1069, June.
    8. Lütkepohl, Helmut & Staszewska-Bystrova, Anna & Winker, Peter, 2015. "Comparison of methods for constructing joint confidence bands for impulse response functions," International Journal of Forecasting, Elsevier, vol. 31(3), pages 782-798.
    9. Bian, Timothy Yang & Gete, Pedro, 2015. "What drives housing dynamics in China? A sign restrictions VAR approach," Journal of Macroeconomics, Elsevier, vol. 46(C), pages 96-112.
    10. James H. Stock & Mark W. Watson, 2001. "Vector Autoregressions," Journal of Economic Perspectives, American Economic Association, vol. 15(4), pages 101-115, Fall.
    11. Kilian, Lutz, 2001. "Impulse Response Analysis in Vector Autoregressions with Unknown Lag Order," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(3), pages 161-179, April.
    12. Òscar Jordà, 2009. "Simultaneous Confidence Regions for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 91(3), pages 629-647, August.
    13. 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.
    14. Barsky, Robert B. & Sims, Eric R., 2011. "News shocks and business cycles," Journal of Monetary Economics, Elsevier, vol. 58(3), pages 273-289.
    15. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    16. 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.
    17. Alexander Benkwitz & Michael Neumann & Helmut Lutekpohl, 2000. "Problems related to confidence intervals for impulse responses of autoregressive processes," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 69-103.
    18. 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.
    19. Cao, Bolong & Sun, Yixiao, 2011. "Asymptotic distributions of impulse response functions in short panel vector autoregressions," Journal of Econometrics, Elsevier, vol. 163(2), pages 127-143, August.
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    Cited by:

    1. 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.
    2. Inoue, Atsushi & Kilian, Lutz, 2022. "Joint Bayesian inference about impulse responses in VAR models," Journal of Econometrics, Elsevier, vol. 231(2), pages 457-476.
    3. 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.
    4. Inoue, Atsushi & Kilian, Lutz, 2020. "The uniform validity of impulse response inference in autoregressions," Journal of Econometrics, Elsevier, vol. 215(2), pages 450-472.
    5. Micheli, Martin, 2019. "Labor market effects of minimum wage shocks," Ruhr Economic Papers 830, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    6. Jonas E. Arias & Juan F. Rubio-Ramirez & Daniel F. Waggoner, 2020. "Uniform Priors for Impulse Responses," Working Papers 22-30, Federal Reserve Bank of Philadelphia.
    7. 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.
    8. Lenard Lieb & Stephan Smeekes, 2017. "Inference for Impulse Responses under Model Uncertainty," Papers 1709.09583, arXiv.org, revised Oct 2019.

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    More about this item

    Keywords

    Bootstrap; impulse response functions; joint confidence bands; vector autoregressive process;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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