The Hodrick-Prescott Filter, the Slutzky Effect, and the Distortionary Effect of Filters

The main contribution of this paper is the construction of a metric based on optimal filtering for measuring the distortionary effect of filters. The Hodrick-Prescott filter (HP-filter) has been critizised for inducing spurious cycles when filtering macroeconomic time series with the "typical spectral shape", the so-called Slutzky-effect. It is shown that the HP-filter is not subject to that critique and that the Slutzky-effect is a special case of a more general pattern of distortions of filters. Based on the theory of optimal filtering, we derive a frequency domain measure of the size of distortions when defining business cycles as cycles with a period less than a prespecified number of years. The metric is used for two purposes. First, to determine the optimal value of the smoothing parameter in the HP-filter. Secondly, to measure the size of distortions of ten filters including a new Hodrick-Prescott based band pass filter. The main conclusions are that the standard value of the smoothing parameter of the HP-filter, = 1600, is close to being the optimal value when filtering near-integrated time series and that the HP-filter is less distorting than any of the other filters studied.