Do Mechanical Filters Provide a Good Approximation of Business Cycles?
In this paper, the authors examine how well the Hodrick-Prescott filter (HP) and the band-pass filter recently proposed by Baxter and King (BK) extract the business-cycle component of macroeconomic time series. The authors assess these filters using two different definitions of the business-cycle component. First, they define that component to be fluctuations lasting no fewer than six and no more than thirty-two quarters; this is the definition of business-cycle frequencies used by Baxter and King. Second, they define the business-cycle component on the basis of a decomposition of the series into permanent and transitory components. In both cases the conclusions are the same. The filters perform adequately when the spectrum of the original series has a peak at business-cycle frequencies. When the spectrum is dominated by low frequencies, the filters provide a distorted business cycle. Since most macroeconomic series have the typical Granger shape, the HP and BK filters perform poorly in terms of identifying the business cycles of these series.