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Small sample confidence intervals for multivariate impulse response functions at long horizons

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  • Barbara Rossi (Duke)
  • Elena Pesavento (Emory)

Abstract

Existing methods for constructing confidence bands for multivariate impulse response functions depend on auxiliary assumptions on the order of integration of the variables. Thus, they may have poor coverage at long lead times when variables are highly persistent. Solutions that have been proposed in the literature may be computationally challenging. The goal of this paper is to propose a simple method for constructing confidence bands for impulse response functions that are robust to the presence of highly persistent processes. We do so by using alternative approximations based on local-to-unity asymptotic theory and by allowing the lead time of the impulse response function to be a fixed fraction of the sample size. Monte Carlo simulations, in which this method is compared with those existing in the literature, show that our method has good coverage properties. We also investigate the properties of the various methods in terms of the length of their confidence bands. Finally, we show, with empirical applications, that our method may provide different economic interpretations of the data. An example to the analysis of nominal versus real sources of fluctuations in real and nominal exchange rates is discussed

Suggested Citation

  • Barbara Rossi (Duke) & Elena Pesavento (Emory), 2004. "Small sample confidence intervals for multivariate impulse response functions at long horizons," Econometric Society 2004 North American Winter Meetings 364, Econometric Society.
  • Handle: RePEc:ecm:nawm04:364
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    References listed on IDEAS

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    11. Ivanov Ventzislav & Kilian Lutz, 2005. "A Practitioner's Guide to Lag Order Selection For VAR Impulse Response Analysis," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(1), pages 1-36, March.
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    Cited by:

    1. Pesavento, Elena & Rossi, Barbara, 2007. "Impulse response confidence intervals for persistent data: What have we learned?," Journal of Economic Dynamics and Control, Elsevier, vol. 31(7), pages 2398-2412, July.
    2. Gorodnichenko, Yuriy & Mikusheva, Anna & Ng, Serena, 2012. "Estimators For Persistent And Possibly Nonstationary Data With Classical Properties," Econometric Theory, Cambridge University Press, vol. 28(05), pages 1003-1036, October.
    3. Helmut Lütkepohl, 2013. "Vector autoregressive models," Chapters,in: Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 6, pages 139-164 Edward Elgar Publishing.
    4. Pesavento, Elena & Rossi, Barbara, 2005. "Do Technology Shocks Drive Hours Up Or Down? A Little Evidence From An Agnostic Procedure," Macroeconomic Dynamics, Cambridge University Press, vol. 9(04), pages 478-488, September.
    5. Alfred A. Haug & Christie Smith, 2012. "Local Linear Impulse Responses for a Small Open Economy," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 74(3), pages 470-492, June.
    6. Kascha, Christian & Mertens, Karel, 2009. "Business cycle analysis and VARMA models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 267-282, February.
    7. Barbara Rossi, 2007. "Expectations hypotheses tests at Long Horizons," Econometrics Journal, Royal Economic Society, vol. 10(3), pages 554-579, November.
    8. Juan F. Rubio-Ramírez & Daniel F. Waggoner & Tao Zha, 2010. "Structural Vector Autoregressions: Theory of Identification and Algorithms for Inference," Review of Economic Studies, Oxford University Press, vol. 77(2), pages 665-696.
    9. Barbara Rossi & Elena Pesavento, 2004. "Do Technology Shocks Drive Hours Up or Down?," Econometric Society 2004 North American Summer Meetings 96, Econometric Society.
    10. repec:eee:macchp:v2-527 is not listed on IDEAS
    11. Ulrich Mueller & Mark W. Watson, 2013. "Measuring Uncertainty about Long-Run Prediction," NBER Working Papers 18870, National Bureau of Economic Research, Inc.
    12. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, Elsevier.
    13. Stefano Puddu, 2013. "Real Sector and Banking System: Real and Feedback Effects. A Non-Linear VAR Approach," IRENE Working Papers 13-01, IRENE Institute of Economic Research.
    14. Elena Pesavento, 2006. "Near-optimal Unit Root Test with Stationary Covariate with Better Finite Sample Size," Emory Economics 0606, Department of Economics, Emory University (Atlanta).
    15. Nikolay Gospodinov & Alex Maynard & Elena Pesavento, 2011. "Sensitivity of Impulse Responses to Small Low-Frequency Comovements: Reconciling the Evidence on the Effects of Technology Shocks," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(4), pages 455-467, October.
    16. Constantin ANGHELACHE & Ion PARTACHI & Madalina-Gabriela ANGHEL & Gyorgy BODO & Radu STOIAN, 2016. "General theoretical notions on univariate regression," Romanian Statistical Review Supplement, Romanian Statistical Review, vol. 64(11), pages 136-144, November.
    17. Lenard Lieb & Stephan Smeekes, 2017. "Inference for Impulse Responses under Model Uncertainty," Papers 1709.09583, arXiv.org, revised May 2018.
    18. Kilian, Lutz & Kim, Yun Jung, 2009. "Do Local Projections Solve the Bias Problem in Impulse Response Inference?," CEPR Discussion Papers 7266, C.E.P.R. Discussion Papers.

    More about this item

    Keywords

    Local to unity asymptotics; persistence; impulse response functions; confidence bands;

    JEL classification:

    • 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
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • F40 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - General

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