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

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 are 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 analyse 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.