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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.

Suggested Citation

  • Phillips, Kerk L. & Spencer, David E., 2010. "Bootstrapping Structural VARs: Avoiding a Potential Bias in Confidence Intervals for Impulse Response Functions," MPRA Paper 23503, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:23503
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    References listed on IDEAS

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    1. Runkle, David E, 1987. "Vector Autoregressions and Reality," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 437-442, October.
    2. Blanchard, Olivier Jean & Quah, Danny, 1989. "The Dynamic Effects of Aggregate Demand and Supply Disturbances," American Economic Review, American Economic Association, vol. 79(4), pages 655-673, September.
    3. 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.
    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 406-409, October.
    5. 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.
    6. Christopher A. Sims & Tao Zha, 1999. "Error Bands for Impulse Responses," Econometrica, Econometric Society, vol. 67(5), pages 1113-1156, September.
    7. 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.
    8. Runkle, David E, 1987. "Vector Autoregressions and Reality: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 454-454, October.
    9. Jeremy Berkowitz & Lutz Kilian, 2000. "Recent developments in bootstrapping time series," Econometric Reviews, Taylor & Francis Journals, vol. 19(1), pages 1-48.
    10. David E. Runkle, 1987. "Vector autoregressions and reality," Staff Report 107, Federal Reserve Bank of Minneapolis.
    11. Davidson, Russell & MacKinnon, James G., 1993. "Estimation and Inference in Econometrics," OUP Catalogue, Oxford University Press, number 9780195060119.
    12. 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.
    13. John B. Taylor, 1999. "Monetary Policy Rules," NBER Books, National Bureau of Economic Research, Inc, number tayl99-1, June.
    14. 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.
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    Cited by:

    1. Bryan Perry & Kerk L Phillips & David E. Spencer, 2015. "State-Level Variation in the Real Wage Response to Monetary Policy," Annals of Economics and Finance, Society for AEF, vol. 16(1), pages 1-17, May.
    2. Adugna Olani, 2016. "Dynamic Capital inflow transmission of monetary policy to emerging markets," Working Papers 1358, Queen's University, Department of Economics.
    3. 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.

    More about this item

    Keywords

    impulse response function; structural VAR; bias; bootstrap;

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • E32 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Business Fluctuations; Cycles
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

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