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

Author

Listed:
  • 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.

Suggested Citation

  • Pierre Perron & Yohei Yamamoto, 2011. "Estimating and Testing Multiple Structural Changes in Linear Models Using Band Spectral Regressions," Boston University - Department of Economics - Working Papers Series WP2011-049, Boston University - Department of Economics.
    • Handle: RePEc:bos:wpaper:wp2011-049
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    References listed on IDEAS

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    1. Martin Lettau & Stijn Van Nieuwerburgh, 2008. "Reconciling the Return Predictability Evidence," The Review of Financial Studies, Society for Financial Studies, vol. 21(4), pages 1607-1652, July.
    2. Dean Corbae & Sam Ouliaris & Peter C. B. Phillips, 2002. "Band Spectral Regression with Trending Data," Econometrica, Econometric Society, vol. 70(3), pages 1067-1109, May.
    3. 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.
    4. 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, January.
    5. Katsumi Shimotsu, 2006. "Simple (but Effective) Tests Of Long Memory Versus Structural Breaks," Working Paper 1101, Economics Department, Queen's University.
    6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    7. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    8. 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.
    9. 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.
    10. Qu, Zhongjun, 2011. "A Test Against Spurious Long Memory," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 423-438.
    11. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    12. Lawrence J. Christiano & Martin Eichenbaum & Robert Vigfusson, 2003. "What Happens After a Technology Shock?," NBER Working Papers 9819, National Bureau of Economic Research, Inc.
    13. 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, September.
    14. 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.
    15. 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.
    16. Mccloskey, Adam & Perron, Pierre, 2013. "Memory Parameter Estimation In The Presence Of Level Shifts And Deterministic Trends," Econometric Theory, Cambridge University Press, vol. 29(6), pages 1196-1237, December.
    17. 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 507-512, June.
    18. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
    19. Engle, Robert F, 1978. "Testing Price Equations for Stability across Spectral Frequency Bands," Econometrica, Econometric Society, vol. 46(4), pages 869-881, July.
    20. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
    21. 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, January.
    22. 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.
    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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    Cited by:

    1. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    2. Seong Yeon Chang & Pierre Perron, 2018. "A comparison of alternative methods to construct confidence intervals for the estimate of a break date in linear regression models," Econometric Reviews, Taylor & Francis Journals, vol. 37(6), pages 577-601, July.
    3. Marie Busch & Philipp Sibbertsen, 2018. "An Overview of Modified Semiparametric Memory Estimation Methods," Econometrics, MDPI, vol. 6(1), pages 1-21, March.
    4. Aristeidis Samitas & Elias Kampouris & Zaghum Umar, 2022. "Financial contagion in real economy: The key role of policy uncertainty," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 27(2), pages 1633-1682, April.
    5. Christensen, Bent Jesper & Varneskov, Rasmus Tangsgaard, 2017. "Medium band least squares estimation of fractional cointegration in the presence of low-frequency contamination," Journal of Econometrics, Elsevier, vol. 197(2), pages 218-244.
    6. Wada, Tatsuma, 2022. "Out-of-sample forecasting of foreign exchange rates: The band spectral regression and LASSO," Journal of International Money and Finance, Elsevier, vol. 128(C).
    7. Balakrishnan, Pulapre & Das, Mausumi & Parameswaran, M., 2017. "The internal dynamic of Indian economic growth," Journal of Asian Economics, Elsevier, vol. 50(C), pages 46-61.

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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