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Estimating and Testing Multiple Structural Changes in Linear Models Using Band Spectral Regressions

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  • Pierre Perron

    ()
    (Department of Economics, Boston University)

  • Yohei Yamamoto

    ()
    (University of Alberta School of Business)

Abstract

This paper considers methods for estimating and testing multiple structural changes occuring at unknown dates in linear models using band spectral regressions. We con- sider changes over time within some frequency bands, permitting the coefficients to be di¤erent across frequency bands. Using standard assumptions, we show that the limit distributions obtained are similar to those in the time domain counterpart. We show that when the coefficients change only within some frequency band we can have increased e¢ ciency of the estimates and power of the tests. We also discuss a very useful application related to contexts in which the data is contaminated by some low frequency process (e.g., level shifts or trends) and that the researcher is interested in whether the original non-contaminated model is stable. We show that all that is needed to obtain estimates of the break dates and tests for structural changes that are not a¤ected by such low frequency contaminations is to truncate a low frequency band that shrinks to zero at rate log(T)=T . Simulations show that the tests have good sizes for a wide range of truncations so that the method is quite robust. We analyze the stability of the relation between hours worked and productivity. When applying the structural change tests in the time domain we document strong evidence of instabil- ities. When excluding a few low frequencies, none of the structural change tests are significant. Hence, the results provide evidence to the e¤ect that the relation between hours worked and productivity is stable over any spectral band that excludes the lowest frequencies, in particular it is stable over the business-cycle band.

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Bibliographic Info

Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2011-049.

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Length: 33 pages
Date of creation: Jan 2011
Date of revision:
Handle: RePEc:bos:wpaper:wp2011-049

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References

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  1. R. F. Engle, 1972. "Band Spectrum Regressions," Working papers 96, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-38, May.
  3. Qu, Zhongjun, 2011. "A Test Against Spurious Long Memory," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 423-438.
  4. Pierre Perron & Zhongjun Qu, 2008. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Boston University - Department of Economics - Working Papers Series wp2008-004, Boston University - Department of Economics.
  5. Susanto Basu & Alan M. Taylor, 1999. "Business Cycles in International Historical Perspective," Journal of Economic Perspectives, American Economic Association, vol. 13(2), pages 45-68, Spring.
  6. Neville Francis & Valerie A. Ramey, 2009. "Measures of per Capita Hours and Their Implications for the Technology-Hours Debate," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 41(6), pages 1071-1097, 09.
  7. Martin Lettau & Stijn Van Nieuwerburgh, 2006. "Reconciling the Return Predictability Evidence," 2006 Meeting Papers 29, Society for Economic Dynamics.
  8. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
  9. GOSPODINOV, Nikolay & MAYNARD, Alex & PESAVENTO, Elena, 2009. "Sensitivity of Impulse Responses to Small Low Frequency Co-Movements : Reconciling the Evidence on the Effects of Technology Shocks," Cahiers de recherche 03-2009, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  10. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  11. Dean Corbae & Sam Ouliaris & Peter C.B. Phillips, 1997. "Band Spectral Regression with Trending Data," Cowles Foundation Discussion Papers 1163, Cowles Foundation for Research in Economics, Yale University.
  12. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Universite de Montreal, Departement de sciences economiques.
  13. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
  14. Pierre Perron & Zhongjun Qu, 2007. "An Analytical Evaluation of the Log-periodogram Estimate in the Presence of Level Shifts," Boston University - Department of Economics - Working Papers Series wp2007-044, Boston University - Department of Economics.
  15. Pierre Perron & Yohei Yamamoto, 2011. "Using OLS to Estimate and Test for Structural Changes in Models with Endogenous Regressors," Boston University - Department of Economics - Working Papers Series WP2011-053, Boston University - Department of Economics.
  16. Pierre Perron & Adam McCloskey, 2010. "Memory Parameter Estimation in the Presence of Level Shifts and Deterministic Trends," Boston University - Department of Economics - Working Papers Series WP2010-048, Boston University - Department of Economics.
  17. Fernald, John G., 2007. "Trend breaks, long-run restrictions, and contractionary technology improvements," Journal of Monetary Economics, Elsevier, vol. 54(8), pages 2467-2485, November.
  18. Fabrizio Iacone, 2010. "Local Whittle estimation of the memory parameter in presence of deterministic components," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(1), pages 37-49, 01.
  19. Lawrence J. Christiano & Martin Eichenbaum & Robert Vigfusson, 2003. "What Happens After a Technology Shock?," NBER Working Papers 9819, National Bureau of Economic Research, Inc.
  20. Harvey, Andrew C, 1978. "Linear Regression in the Frequency Domain," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 19(2), pages 507-12, June.
  21. Katsumi Shimotsu, 2006. "Simple (but effective) tests of long memory versus structural breaks," Working Papers 1101, Queen's University, Department of Economics.
  22. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
  23. Engle, Robert F, 1978. "Testing Price Equations for Stability across Spectral Frequency Bands," Econometrica, Econometric Society, vol. 46(4), pages 869-81, July.
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