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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. In this paper, we document an apparently common source of bias in the estimation of the VAR error covariance matrix. The bias is easily corrected with a straightforward scale adjustment. This bias is often 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 even if the original IRF estimate relies on unbiased parameter estimates.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 23503.

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Date of creation: Feb 2010
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Handle: RePEc:pra:mprapa:23503

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Keywords: impulse response function; structural VAR; bias; bootstrap;

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  1. GalĂ­, Jordi, 1996. "Technology, Employment, and the Business Cycle: Do Technology Shocks Explain Aggregate Fluctuations?," CEPR Discussion Papers, C.E.P.R. Discussion Papers 1499, C.E.P.R. Discussion Papers.
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  3. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, Taylor & Francis Journals, vol. 19(1), pages 1-48.
  4. Christopher A. Sims & Tao Zha, 1999. "Error Bands for Impulse Responses," Econometrica, Econometric Society, Econometric Society, vol. 67(5), pages 1113-1156, September.
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  6. Peters, S C & Freedman, D A, 1984. "Some Notes on the Bootstrap in Regression Problems," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 2(4), pages 406-09, October.
  7. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 1998. "Monetary Policy Shocks: What Have We Learned and to What End?," NBER Working Papers, National Bureau of Economic Research, Inc 6400, National Bureau of Economic Research, Inc.
  8. Lawrence J. Christiano & Martin Eichenbaum & Robert Vigfusson, 2006. "Assessing Structural VARs," NBER Working Papers, National Bureau of Economic Research, Inc 12353, National Bureau of Economic Research, Inc.
  9. Lutz Kilian, 1998. "Small-Sample Confidence Intervals For Impulse Response Functions," The Review of Economics and Statistics, MIT Press, MIT Press, vol. 80(2), pages 218-230, May.
  10. David E. Runkle, 1987. "Vector autoregressions and reality," Staff Report, Federal Reserve Bank of Minneapolis 107, Federal Reserve Bank of Minneapolis.
  11. Runkle, David E, 1987. "Vector Autoregressions and Reality," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 5(4), pages 437-42, October.
  12. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, National Bureau of Economic Research, Inc, number tayl99-1.
  13. Kilian, Lutz & Chang, Pao-Li, 2000. "How accurate are confidence intervals for impulse responses in large VAR models?," Economics Letters, Elsevier, Elsevier, vol. 69(3), pages 299-307, December.
  14. Runkle, David E, 1987. "Vector Autoregressions and Reality: Reply," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 5(4), pages 454, October.
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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, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich 12/168, CER-ETH - Center of Economic Research (CER-ETH) at ETH Zurich.

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