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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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References

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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.
  2. 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.
  3. Olivier Jean Blanchard & Danny Quah, 1988. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," NBER Working Papers 2737, National Bureau of Economic Research, Inc.
  4. 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.
  5. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1, June.
  6. Runkle, David E, 1987. "Vector Autoregressions and Reality," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 437-42, October.
  7. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 1997. "Monetary policy shocks: what have we learned and to what end?," Working Paper Series, Macroeconomic Issues WP-97-18, Federal Reserve Bank of Chicago.
  8. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119, September.
  9. David E. Runkle, 1987. "Vector autoregressions and reality," Staff Report 107, Federal Reserve Bank of Minneapolis.
  10. Jordi Gali, 1999. "Technology, Employment, and the Business Cycle: Do Technology Shocks Explain Aggregate Fluctuations?," American Economic Review, American Economic Association, vol. 89(1), pages 249-271, March.
  11. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 1-48.
  12. 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.
  13. Runkle, David E, 1987. "Vector Autoregressions and Reality: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 454, October.
  14. Christopher A. Sims & Tao Zha, 1995. "Error bands for impulse responses," Working Paper 95-6, Federal Reserve Bank of Atlanta.
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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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