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

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Author Info
Elena Pesavento, Barbara Rossi

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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.

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Paper provided by European University Institute in its series Economics Working Papers with number ECO2006/19.

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Date of creation: 2006
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Handle: RePEc:eui:euiwps:eco2006/19

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Related research
Keywords: Local to unity asymptotics persistence impulse response functions

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Find related papers by JEL classification:
C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General
C2 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables

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  1. 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. [Downloadable!] (restricted)
  2. Runkle, David E, 1987. "Vector Autoregressions and Reality," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 437-42, October.
  3. Diebold, Francis X. & Rudebusch, Glenn D., 1989. "Long memory and persistence in aggregate output," Journal of Monetary Economics, Elsevier, vol. 24(2), pages 189-209, September. [Downloadable!] (restricted)
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  4. 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. [Downloadable!] (restricted)
  5. Phillips, Peter C. B., 1998. "Impulse response and forecast error variance asymptotics in nonstationary VARs," Journal of Econometrics, Elsevier, vol. 83(1-2), pages 21-56. [Downloadable!] (restricted)
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  6. Campbell, John Y & Mankiw, N Gregory, 1987. "Are Output Fluctuations Transitory?," The Quarterly Journal of Economics, MIT Press, vol. 102(4), pages 857-80, November. [Downloadable!] (restricted)
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  7. David E. Runkle, 1987. "Vector autoregressions and reality," Staff Report 107, Federal Reserve Bank of Minneapolis. [Downloadable!]
  8. 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 361-69, April.
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  9. Atsushi Inoue & Lutz Kilian, 2002. "Bootstrapping Autoregressive Processes with Possible Unit Roots," Econometrica, Econometric Society, vol. 70(1), pages 377-391, January. [Downloadable!] (restricted)
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  10. Fabio Busetti & Silvia Fabiani & Andrew Harvey, 2006. "Convergence of Prices and Rates of Inflation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 68(s1), pages 863-877, December. [Downloadable!] (restricted)
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  11. 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.
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  12. 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. [Downloadable!] (restricted)
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  13. Andrews, Donald W K, 1993. "Exactly Median-Unbiased Estimation of First Order Autoregressive/Unit Root Models," Econometrica, Econometric Society, vol. 61(1), pages 139-65, January. [Downloadable!] (restricted)
  14. Nikolay Gospodinov, 2004. "Asymptotic confidence intervals for impulse responses of near-integrated processes," Econometrics Journal, Royal Economic Society, vol. 7(2), pages 505-527, December. [Downloadable!] (restricted)
  15. Wright, Jonathan H, 2000. "Confidence Intervals for Univariate Impulse Responses with a Near Unit Root," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 368-73, July.
  16. Andrews, Donald W K & Chen, Hong-Yuan, 1994. "Approximately Median-Unbiased Estimation of Autoregressive Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 187-204, April.
  17. 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. [Downloadable!]
  18. Lutz Kilian, 1998. "Confidence intervals for impulse responses under departures from normality," Econometric Reviews, Taylor and Francis Journals, vol. 17(1), pages 1-29. [Downloadable!] (restricted)
  19. 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 113-44, January. [Downloadable!] (restricted)
  20. Ventzislav Ivanov & Lutz Kilian, 2005. "A Practitioner's Guide to Lag Order Selection For VAR Impulse Response Analysis," Studies in Nonlinear Dynamics & Econometrics, Berkeley Electronic Press, vol. 9(1), pages 1219-1219. [Downloadable!] (restricted)
  21. 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. [Downloadable!] (restricted)
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