IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Joint Confidence Sets for Structural Impulse Responses

  • Atsushi Inoue

    ()

    (Southern Methodist University)

  • Lutz Kilian

    ()

    (University of Michigan)

Many users of structural VAR models are primarily interested in learning about the shape of structural impulse response functions. This requires joint inference about sets of structural impulse responses, allowing for dependencies across time as well as across response functions. Such joint inference is complicated by the fact that the joint distribution of structural impulse response becomes degenerate when the number of structural impulse responses of interest exceeds the number of model parameters, as is often the case in applied work. This degeneracy may be overcome by transforming the estimator appropriately. We show that the joint Wald test is invariant to this transformation and converges to a nonstandard distribution, which can be approximated by the bootstrap, allowing the construction of asymptotically valid joint confidence sets for any subset of structural impulse responses, regardless of whether the joint distribution of the structural impulse responses is degenerate or not. We demonstrate by simulation the coverage accuracy of these sets in finite samples under realistic conditions. We make the case for representing these joint confidence sets in the form of "shotgun plots" rather than joint confidence bands for impulse response functions. Several empirical examples demonstrate that this approach not only conveys the same information as confidence bands about the statistical significance of response functions, but provides economically relevant additional information about the shape of response functions that is lost when reducing the joint confidence set to two-dimensional bands Classification-JEL: C32, C52, C53.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: ftp://ftp1.economics.smu.edu/WorkingPapers/2014/INOUE/INOUE-2014-01.pdf
Download Restriction: no

Paper provided by Southern Methodist University, Department of Economics in its series Departmental Working Papers with number 1401.

as
in new window

Length:
Date of creation: Feb 2014
Date of revision:
Handle: RePEc:smu:ecowpa:1401
Contact details of provider: Postal: Department of Economics, P.O. Box 750496, Southern Methodist University, Dallas, TX 75275-0496
Phone: 214-768-2715
Fax: 214-768-1821
Web page: http://www.smu.edu/economics

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. �scar Jordà, 2009. "Simultaneous Confidence Regions for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 91(3), pages 629-647, August.
  2. Lutz Kilian, 1999. "Finite-Sample Properties of Percentile and Percentile-t Bootstrap Confidence Intervals for Impulse Responses," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 652-660, November.
  3. Lutz Kilian, 2008. "A Comparison of the Effects of Exogenous Oil Supply Shocks on Output and Inflation in the G7 Countries," Journal of the European Economic Association, MIT Press, vol. 6(1), pages 78-121, 03.
  4. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2014. "Confidence Bands for Impulse Responses: Bonferroni versus Wald," SFB 649 Discussion Papers SFB649DP2014-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  5. 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.
  6. Inoue, Atsushi & Kilian, Lutz, 2011. "Inference on Impulse Response Functions in Structural VAR Models," CEPR Discussion Papers 8419, C.E.P.R. Discussion Papers.
  7. Christopher A. Sims & Tao Zha, 1994. "Error Bands for Impulse Responses," Cowles Foundation Discussion Papers 1085, Cowles Foundation for Research in Economics, Yale University.
  8. Bao, Yong & Ullah, Aman, 2007. "The second-order bias and mean squared error of estimators in time-series models," Journal of Econometrics, Elsevier, vol. 140(2), pages 650-669, October.
  9. Andrews, Donald W. K., 1987. "Asymptotic Results for Generalized Wald Tests," Econometric Theory, Cambridge University Press, vol. 3(03), pages 348-358, June.
  10. Helmut Lütkepohl & Anna Staszewska-Bystrova & Peter Winker, 2013. "Comparison of Methods for Constructing Joint Confidence Bands for Impulse Response Functions," MAGKS Papers on Economics 201325, Philipps-Universität Marburg, Faculty of Business Administration and Economics, Department of Economics (Volkswirtschaftliche Abteilung).
  11. Barsky, Robert & Kilian, Lutz, 2004. "Oil and the Macroeconomy Since the 1970s," CEPR Discussion Papers 4496, C.E.P.R. Discussion Papers.
  12. Bertille Antoine & Eric Renault, 2012. "Efficient Minimum Distance Estimation with Multiple Rates of Convergence," Discussion Papers dp12-03, Department of Economics, Simon Fraser University.
  13. Nigar Hashimzade & Michael A. Thornton (ed.), 2013. "Handbook of Research Methods and Applications in Empirical Macroeconomics," Books, Edward Elgar, number 14327.
  14. Blanchard, Olivier Jean, 1989. "A Traditional Interpretation of Macroeconomic Fluctuations," American Economic Review, American Economic Association, vol. 79(5), pages 1146-64, December.
  15. Lutz Kilian & Yun Jung Kim, 2011. "How Reliable Are Local Projection Estimators of Impulse Responses?," The Review of Economics and Statistics, MIT Press, vol. 93(4), pages 1460-1466, November.
  16. Kilian, Lutz & Chang, Pao-Li, 2000. "How accurate are confidence intervals for impulse responses in large VAR models?," Economics Letters, Elsevier, vol. 69(3), pages 299-307, December.
  17. Guerron-Quintana, Pablo A. & Inoue, Atsushi & Kilian, Lutz, 2014. "Impulse Response Matching Estimators for DSGE Models," CEPR Discussion Papers 10298, C.E.P.R. Discussion Papers.
  18. Kilian, Lutz, 2001. "Impulse Response Analysis in Vector Autoregressions with Unknown Lag Order," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(3), pages 161-79, April.
  19. Lutkepohl, Helmut, 1990. "Asymptotic Distributions of Impulse Response Functions and Forecast Error Variance Decompositions of Vector Autoregressive Models," The Review of Economics and Statistics, MIT Press, vol. 72(1), pages 116-25, February.
  20. Lütkepohl, Helmut & Poskitt, D.S., 1991. "Estimating Orthogonal Impulse Responses via Vector Autoregressive Models," Econometric Theory, Cambridge University Press, vol. 7(04), pages 487-496, December.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:smu:ecowpa:1401. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Bo Chen)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.