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Impulse Response Confidence Intervals for Persistent Data: What Have We Learned?

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  • Elena Pesavento, Barbara Rossi

Abstract

This paper is a comprehensive comparison of existing methods for constructing confidence bands for univariate impulse response functions in the presence of high persistence. Monte Carlo results show that Kilian (1998a), Wright (2000), Gospodinov (2004) and Pesavento and Rossi (2005) have favorable coverage properties, although they differ in terms of robustness at various horizons, median unbiasedness, and reliability in the possible presence of a unit or mildly explosive root. On the other hand, methods like Runkle’s (1987) bootstrap, Andrews and Chen (1994), and regressions in levels or first differences (even when based on pre-tests) may not have accurate coverage properties. The paper makes recommendations as to the appropriateness of each method in empirical work.

Suggested Citation

  • Elena Pesavento, Barbara Rossi, 2006. "Impulse Response Confidence Intervals for Persistent Data: What Have We Learned?," Economics Working Papers ECO2006/19, European University Institute.
    • Handle: RePEc:eui:euiwps:eco2006/19
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    References listed on IDEAS

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    1. Runkle, David E, 1987. "Vector Autoregressions and Reality," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 437-442, October.
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    12. Rossi, Barbara, 2005. "Confidence Intervals for Half-Life Deviations From Purchasing Power Parity," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 432-442, October.
    13. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Smooth Functions of Slope Parameters and Innovation Variances in VAR (∞) Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 43(2), pages 309-332, May.
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    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.
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    19. Lopez, Claude & Murray, Christian J & Papell, David H, 2005. "State of the Art Unit Root Tests and Purchasing Power Parity," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 37(2), pages 361-369, April.
    20. 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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    23. Murray, Christian J. & Papell, David H., 2002. "The purchasing power parity persistence paradigm," Journal of International Economics, Elsevier, vol. 56(1), pages 1-19, January.
    24. Cavanagh, Christopher L. & Elliott, Graham & Stock, James H., 1995. "Inference in Models with Nearly Integrated Regressors," Econometric Theory, Cambridge University Press, vol. 11(5), pages 1131-1147, October.
    25. Graham Elliott, 1998. "On the Robustness of Cointegration Methods when Regressors Almost Have Unit Roots," Econometrica, Econometric Society, vol. 66(1), pages 149-158, January.
    26. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-165, January.
    27. Lutz Kilian & Tao Zha, 2002. "Quantifying the uncertainty about the half-life of deviations from PPP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(2), pages 107-125.
    28. Lutz Kilian, 1998. "Confidence intervals for impulse responses under departures from normality," Econometric Reviews, Taylor & Francis Journals, vol. 17(1), pages 1-29.
    29. Sims, Christopher A & Stock, James H & Watson, Mark W, 1990. "Inference in Linear Time Series Models with Some Unit Roots," Econometrica, Econometric Society, vol. 58(1), pages 113-144, January.
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    Citations

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    Cited by:

    1. Neil Kellard & Denise Osborn & Jerry Coakley & Simone D. Grose & Gael M. Martin & Donald S. Poskitt, 2015. "Bias Correction of Persistence Measures in Fractionally Integrated Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 36(5), pages 721-740, September.
    2. Fernández-Villaverde, J. & Rubio-Ramírez, J.F. & Schorfheide, F., 2016. "Solution and Estimation Methods for DSGE Models," Handbook of Macroeconomics, in: J. B. Taylor & Harald Uhlig (ed.), Handbook of Macroeconomics, edition 1, volume 2, chapter 0, pages 527-724, Elsevier.
    3. 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.
    4. José Luis Montiel Olea & Mikkel Plagborg‐Møller, 2021. "Local Projection Inference Is Simpler and More Robust Than You Think," Econometrica, Econometric Society, vol. 89(4), pages 1789-1823, July.
    5. Inoue, Atsushi & Kilian, Lutz, 2020. "The uniform validity of impulse response inference in autoregressions," Journal of Econometrics, Elsevier, vol. 215(2), pages 450-472.
    6. Richard T. Baillie & George Kapetanios & Fotis Papailias, 2017. "Inference for impulse response coefficients from multivariate fractionally integrated processes," Econometric Reviews, Taylor & Francis Journals, vol. 36(1-3), pages 60-84, March.
    7. K. Azim Ozdemir, 2015. "Interest Rate Surprises and Transmission Mechanism in Turkey: Evidence from Impulse Response Analysis," Working Papers 1504, Research and Monetary Policy Department, Central Bank of the Republic of Turkey.
    8. Andres Elberg, 2014. "Temporal Aggregation and Convergence to the Law of One Price: Evidence from Micro Data," Working Papers 53, Facultad de Economía y Empresa, Universidad Diego Portales.
    9. 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

    Local to unity asymptotics; persistence; impulse response functions;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables

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