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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

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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Bibliographic Info

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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  7. 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.
  8. 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.
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  10. Mccloskey, Adam & Perron, Pierre, 2013. "Memory Parameter Estimation In The Presence Of Level Shifts And Deterministic Trends," Econometric Theory, Cambridge University Press, vol. 29(06), pages 1196-1237, December.
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  15. 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.
  16. Katsumi Shimotsu, 2006. "Simple (but effective) tests of long memory versus structural breaks," Working Papers 1101, Queen's University, Department of Economics.
  17. Engle, Robert F, 1978. "Testing Price Equations for Stability across Spectral Frequency Bands," Econometrica, Econometric Society, vol. 46(4), pages 869-81, July.
  18. 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.
  19. Perron, Pierre & Qu, Zhongjun, 2006. "Estimating restricted structural change models," Journal of Econometrics, Elsevier, vol. 134(2), pages 373-399, October.
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