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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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    Cited by:

    1. 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.
    2. repec:eee:asieco:v:50:y:2017:i:c:p:46-61 is not listed on IDEAS
    3. Seong Yeon Chang & Pierre Perron, 2013. "A Comparison of Alternative Methods to Construct Confidence Intervals for the Estimate of a Break Date in Linear Regression Models," Boston University - Department of Economics - Working Papers Series wp2015-010, Boston University - Department of Economics, revised 11 Oct 2015.
    4. Kaido, Hiroaki, 2017. "Asymptotically Efficient Estimation Of Weighted Average Derivatives With An Interval Censored Variable," Econometric Theory, Cambridge University Press, pages 1218-1241.

    More about this item

    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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