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Bootstrapping structural VARs: Avoiding a potential bias in confidence intervals for impulse response functions

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  • Phillips, Kerk L.
  • Spencer, David E.

Abstract

Constructing bootstrap confidence intervals for impulse response functions (IRFs) from structural vector autoregression (SVAR) models has become standard practice in empirical macroeconomic research. The accuracy of such confidence intervals can deteriorate severely, however, if the bootstrap IRFs are biased. We document an apparently common source of bias in the estimation of the VAR error covariance matrix which can be easily reduced by a scale adjustment. This bias is generally unrecognized because it only affects the bootstrap estimates of the error variance, not the original OLS estimates. Nevertheless, as we illustrate here, analytically, with sampling experiments, and in an example from the literature, the bootstrap error variance bias can have significant distorting effects on bootstrap IRF confidence intervals. We also show that scale-adjusted bootstrap confidence intervals can be expected to exhibit improved coverage accuracy.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Macroeconomics.

Volume (Year): 33 (2011)
Issue (Month): 4 ()
Pages: 582-594

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Handle: RePEc:eee:jmacro:v:33:y:2011:i:4:p:582-594

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Web page: http://www.elsevier.com/locate/inca/622617

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Keywords: Impulse response function; Structural VAR; Bias; Bootstrap;

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  1. Peters, S C & Freedman, D A, 1984. "Some Notes on the Bootstrap in Regression Problems," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 406-09, October.
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  4. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1, October.
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  8. Christopher A. Sims & Tao Zha, 1995. "Error bands for impulse responses," Working Paper 95-6, Federal Reserve Bank of Atlanta.
  9. Runkle, David E, 1987. "Vector Autoregressions and Reality," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 437-42, October.
  10. Lawrence J. Christiano & Martin Eichenbaum & Robert Vigfusson, 2006. "Assessing Structural VARs," NBER Working Papers 12353, National Bureau of Economic Research, Inc.
    • Lawrence J. Christiano & Martin Eichenbaum & Robert Vigfusson, 2007. "Assessing Structural VARs," NBER Chapters, in: NBER Macroeconomics Annual 2006, Volume 21, pages 1-106 National Bureau of Economic Research, Inc.
  11. 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.
  12. Jeremy Berkowitz & Lutz Kilian, 1996. "Recent developments in bootstrapping time series," Finance and Economics Discussion Series 96-45, Board of Governors of the Federal Reserve System (U.S.).
  13. 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.
  14. 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.
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Cited by:
  1. Filippo Lechthaler & Lisa Leinert, 2012. "Moody Oil - What is Driving the Crude Oil Price?," CER-ETH Economics working paper series 12/168, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.

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