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Simultaneous Confidence Regions for Impulse Responses

Author

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  • Òscar Jordà

    (Department of Economics, University of California, Davis)

Abstract

Inference about an impulse response is a multiple testing problem with serially correlated coefficient estimates. This paper provides a method to construct simultaneous confidence regions for impulse responses and conditional bands to examine significance levels of individual impulse response coefficients given propagation trajectories. The paper also shows how to constrain a subset of impulse response paths to anchor structural identification and how to formally test the validity of such identifying constraints. Simulation and empirical evidence illustrate the new techniques. A broad summary of asymptotic analytic formulas is provided to make the methods easy to implement with commonly available statistical software. Copyright by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.

Suggested Citation

  • Òscar Jordà, 2009. "Simultaneous Confidence Regions for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 91(3), pages 629-647, August.
    • Handle: RePEc:tpr:restat:v:91:y:2009:i:3:p:629-647
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    Cited by:

    1. Taylor, Alan M. & Schularick, Moritz & Jordà , Òscar, 2011. "When Credit Bites Back: Leverage, Business Cycles, and Crises," CEPR Discussion Papers 8678, C.E.P.R. Discussion Papers.
    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. 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.
    4. Atsushi Inoue & `Oscar Jord`a & Guido M. Kuersteiner, 2023. "Inference for Local Projections," Papers 2306.03073, arXiv.org, revised Aug 2024.
    5. Wojciech Charemza & Svetlana Makarova & Imran Shah, 2015. "Making the most of high inflation," Applied Economics, Taylor & Francis Journals, vol. 47(34-35), pages 3723-3739, July.
    6. 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.
    7. Òscar Jordà & Massimiliano Marcellino, 2010. "Path forecast evaluation," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 635-662.
    8. Òscar Jordà & Alan M. Taylor, 2024. "Local Projections," NBER Working Papers 32822, National Bureau of Economic Research, Inc.
    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. Staszewska-Bystrova Anna, 2013. "Modified Scheffé’s Prediction Bands," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 233(5-6), pages 680-690, October.
    11. Chiappini, Raphaël & Lahet, Delphine, 2020. "Exchange rate movements in emerging economies - Global vs regional factors in Asia," China Economic Review, Elsevier, vol. 60(C).
    12. Ryan R. Brady & Derek Stimel & Steven Sumner, 2012. "A Time Series Test of the Direct Wealth Effect," Departmental Working Papers 40, United States Naval Academy Department of Economics.
    13. Kole, Erik & van Dijk, Dick, 2023. "Moments, shocks and spillovers in Markov-switching VAR models," Journal of Econometrics, Elsevier, vol. 236(2).
    14. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2014. "Confidence Bands for Impulse Responses: Bonferroni versus Wald," Discussion Papers of DIW Berlin 1354, DIW Berlin, German Institute for Economic Research.
    15. Makram El-Shagi & Yishuo Ma, 2021. "Nine blind men and the PBoC," CFDS Discussion Paper Series 2021/2, Center for Financial Development and Stability at Henan University, Kaifeng, Henan, China.
    16. Michael Donadelli & Marcus Jüppner & Antonio Paradiso & Christian Schlag, 2019. "Temperature Volatility Risk," Working Papers 2019:05, Department of Economics, University of Venice "Ca' Foscari".
    17. 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.
    18. Inoue, Atsushi & Kilian, Lutz, 2016. "Joint confidence sets for structural impulse responses," Journal of Econometrics, Elsevier, vol. 192(2), pages 421-432.
    19. Inoue, Atsushi & Jordà , Òscar & Kuersteiner, Guido, 2023. "Significance Bands for Local Projections," CEPR Discussion Papers 18271, C.E.P.R. Discussion Papers.
    20. Theodoridis, Konstantinos, 2011. "An efficient minimum distance estimator for DSGE models," Bank of England working papers 439, Bank of England.
    21. Chiappini, Raphaël & Groslambert, Bertrand & Bruno, Olivier, 2024. "A method to measure bank output while excluding credit risk and retaining liquidity effects," The Quarterly Review of Economics and Finance, Elsevier, vol. 94(C), pages 167-179.
    22. Brady, Ryan R., 2014. "The spatial diffusion of regional housing prices across U.S. states," Regional Science and Urban Economics, Elsevier, vol. 46(C), pages 150-166.
    23. Wu, Jyh-Lin & Lee, Chingnun & Wang, Tzu-Wei, 2011. "A re-examination on dissecting the purchasing power parity puzzle," Journal of International Money and Finance, Elsevier, vol. 30(3), pages 572-586, April.
    24. Inoue, Atsushi & Jordà , Òscar & Kuersteiner, Guido, 2023. "Significance Bands for Local Projections," CEPR Discussion Papers 18271, C.E.P.R. Discussion Papers.

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