THE MISSING CYCLE IN THE HP FILTER AND THE MEASUREMENT OF CYCLICALLY-ADJUSTED BUDGET BALANCES

The HP filter suffers from a pro-cyclical bias in end-of-sample trend estimates. This paper argues that this feature is related to the ”missing cycle ” in the stochastic model of the filter. The paper suggest an extensions of the HP filter by including a stochastic cycle component in the underlying model of the filter. As a consequence, the derived trend and cyclical components are more consistent with the underlying filter model, and the end-point behavior improves significantly because the pro-cyclical bias in end-of-sample trend estimates is virtually removed. 1