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Estimating and testing multiple structural changes in linear models using band spectral regressions

  • Yohei Yamamoto
  • Pierre Perron

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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File URL: http://hdl.handle.net/10.1111/ectj.2013.16.issue-3
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Article provided by Royal Economic Society in its journal Econometrics Journal.

Volume (Year): 16 (2013)
Issue (Month): 3 (October)
Pages: 400-429

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Handle: RePEc:wly:emjrnl:v:16:y:2013:i:3:p:400-429
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  1. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  2. Engle, Robert F, 1974. "Band Spectrum Regression," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 1-11, February.
  3. 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.
  4. 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.
  5. Katsumi Shimotsu, 2006. "Simple (but effective) tests of long memory versus structural breaks," Working Papers 1101, Queen's University, Department of Economics.
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  8. 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.
  9. Nikolay Gospodinov & Alex Maynard & Elena Pesavento, 2011. "Sensitivity of Impulse Responses to Small Low-Frequency Comovements: Reconciling the Evidence on the Effects of Technology Shocks," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(4), pages 455-467, October.
  10. 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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  12. Perron, P. & Bai, J., 1995. "Estimating and Testing Linear Models with Multiple Structural Changes," Cahiers de recherche 9552, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  13. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
  14. 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.
  15. 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.
  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. Pierre Perron & Yohei Yamamoto, 2015. "Using OLS to Estimate and Test for Structural Changes in Models with Endogenous Regressors," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 30(1), pages 119-144, 01.
  18. 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.
  19. Susanto Basu & Alan M. Taylor, 1999. "Business Cycles in International Historical Perspective," NBER Working Papers 7090, National Bureau of Economic Research, Inc.
  20. Corbae, D. & Ouliaris, S. & Phillips, P.C.B., 1997. "Band Spectral Regression with Trending Data," Working Papers 97-09, University of Iowa, Department of Economics.
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  23. 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.
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