This note demonstrates that the Baxter-King (1999) filter, and in general any bandpass filter, does not isolate the cycle in an unobserved-components model with a stochastic trend. The first difference of the trend passes through the filter, and as a result, the spectral properties of the filtered series depend on the trend in the unfiltered series. It is demonstrated that for postwar U.S. real GDP, the spectral properties of the BK-filtered series are primarily to due to the stochastic trend in output.

We test for a unit root in postwar unemployment rates for sixteen OECD countries. When a one-time structural break is incorporated, the unit root hypothesis can be rejected for most of the countries and the measured persistence of unemployment falls dramatically. We then test for multiple structural changes and find evidence of one or two breaks for those countries for which the unit root hypothesis could be rejected. Almost all of the breaks are positive, reflecting the sustained rise in European unemployment. The major exception is the United States, where long-term unemployment rose in the 1970s and fell in the 1980s.