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

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  • Yohei Yamamoto
  • Pierre Perron

Abstract

We provide methods for estimating and testing multiple structural changes occurring at unknown dates in linear models using band spectral regressions. We consider changes over time within some frequency bands, permitting the coefficients to be different 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 have increased efficiency 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. All that is needed to obtain estimates of the break dates and tests for structural changes that are not affected 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 structural change tests in the time domain we document strong evidence of instabilities. When excluding a few low frequencies, none of the structural change tests are significant. Hence, the results provide evidence to the effect 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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File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd12-250.pdf
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Bibliographic Info

Paper provided by Institute of Economic Research, Hitotsubashi University in its series Global COE Hi-Stat Discussion Paper Series with number gd12-250.

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Date of creation: Oct 2012
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Handle: RePEc:hst:ghsdps:gd12-250

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Keywords: multiple structural changes; band spectral regression; low frequency contaminations; hours-productivity; business-cycle;

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  1. 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.
  2. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
  3. Adam McCloskey & Pierre Perron, 2012. "Memory Parameter Estimation in the Presence of Level Shifts and Deterministic Trends," Working Papers 2012-15, Brown University, Department of Economics.
  4. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  5. Gospodinov, Nikolay & Maynard, Alex & Pesavento, Elena, 2011. "Sensitivity of Impulse Responses to Small Low-Frequency Comovements: Reconciling the Evidence on the Effects of Technology Shocks," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 455-467.
  6. Perron, Pierre & Qu, Zhongjun, 2010. "Long-Memory and Level Shifts in the Volatility of Stock Market Return Indices," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 275-290.
  7. Zhongjun Qu, 2010. "A Test Against Spurious Long Memory," Boston University - Department of Economics - Working Papers Series WP2010-051, Boston University - Department of Economics.
  8. Donald W.K. Andrews, 1990. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Cowles Foundation Discussion Papers 943, Cowles Foundation for Research in Economics, Yale University.
  9. Martin Lettau & Stijn Van Nieuwerburgh, 2008. "Reconciling the Return Predictability Evidence," Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1607-1652, July.
  10. 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.
  11. 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.
  12. 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.
  13. Lawrence J. Christiano & Martin Eichenbaum & Robert Vigfusson, 2003. "What Happens After a Technology Shock?," NBER Working Papers 9819, National Bureau of Economic Research, Inc.
  14. Valerie A. Ramey & Neville Francis, 2007. "Measures of Per Capita Hours and their Implications for the Technology-Hours Debate," 2007 Meeting Papers 314, Society for Economic Dynamics.
  15. 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.
  16. 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.
  17. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
  18. 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.
  19. R. F. Engle, 1972. "Band Spectrum Regressions," Working papers 96, Massachusetts Institute of Technology (MIT), Department of Economics.
  20. Engle, Robert F, 1978. "Testing Price Equations for Stability across Spectral Frequency Bands," Econometrica, Econometric Society, vol. 46(4), pages 869-81, July.
  21. 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.
  22. Katsumi Shimotsu, 2006. "Simple (but effective) tests of long memory versus structural breaks," Working Papers 1101, Queen's University, Department of Economics.
  23. 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.
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