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Do Local Projections Solve the Bias Problem in Impulse Response Inference?

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Author Info
Kilian, Lutz
Kim, Yun Jung

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Abstract

It is well documented that the small-sample accuracy of asymptotic and bootstrap approximations to the pointwise distribution of VAR impulse response estimators is undermined by the estimator’s bias. A natural conjecture is that impulse response estimators based on the local projection (LP) method of Jordà (2005, 2007) are less susceptible to this problem and hence potentially more reliable in small samples than VAR-based estimators. We show that - contrary to this conjecture - LP estimators tend to have both higher bias and higher variance, resulting in pointwise impulse response confidence intervals that are typically less accurate and wider on average than suitably constructed VAR-based intervals. Bootstrapping the LP estimator only worsens its finite-sample accuracy. We also evaluate recently proposed joint asymptotic intervals for VAR and LP impulse response functions. Our analysis suggests that the accuracy of joint intervals can be erratic in practice, and neither joint interval is uniformly preferred over the other.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 7266.

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Date of creation: Apr 2009
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Handle: RePEc:cpr:ceprdp:7266

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Related research
Keywords: Bias; Confidence interval; Impulse response function; Joint interval; Local projection; Vector autoregression;

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Find related papers by JEL classification:
C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications

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  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. 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)
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    Other versions:
  5. 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.
  6. Òscar Jordà, 2005. "Estimation and Inference of Impulse Responses by Local Projections," American Economic Review, American Economic Association, vol. 95(1), pages 161-182, March. [Downloadable!]
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    Other versions:
  8. David E. Runkle, 1987. "Vector autoregressions and reality," Staff Report 107, Federal Reserve Bank of Minneapolis. [Downloadable!]
  9. Goncalves, Silvia & Kilian, Lutz, 2004. "Bootstrapping autoregressions with conditional heteroskedasticity of unknown form," Journal of Econometrics, Elsevier, vol. 123(1), pages 89-120, November. [Downloadable!] (restricted)
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  10. Berkowitz, J. & Birgean, I. & Kilian, L., 1999. "On the Finite-Sample Accuracy of Nonparametric Resampling Algorithms for Economic Time Series," Papers 99-01, Michigan - Center for Research on Economic & Social Theory.
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  13. Alexander Benkwitz & Michael Neumann & Helmut Lütekpohl, 2000. "Problems related to confidence intervals for impulse responses of autoregressive processes," Econometric Reviews, Taylor and Francis Journals, vol. 19(1), pages 69-103. [Downloadable!] (restricted)
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  15. 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)
  16. Christiano, Lawrence J. & Eichenbaum, Martin & Evans, Charles L., 1999. "Monetary policy shocks: What have we learned and to what end?," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 2, pages 65-148 Elsevier. [Downloadable!] (restricted)
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  17. Braun, Phillip A. & Mittnik, Stefan, 1993. "Misspecifications in vector autoregressions and their effects on impulse responses and variance decompositions," Journal of Econometrics, Elsevier, vol. 59(3), pages 319-341, October. [Downloadable!] (restricted)
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