To Boost or Not to Boost? That is the Question

Abstract

Phillips and Shi (2021) have argued that there may be some leakage from the estimate of the permanent component to what is meant to be the transitory component when one uses the Hodrick-Prescott filter. They argue that this can be eliminated by boosting the filter. We show that there is no leakage from the filter per se, so boosting is not needed for that. They also argue that there are DGP's for the components for which the boosted filter tracks these more accurately. We show that there are other plausible DGP's where the boosted filter tracks less accurately, and what is crucial to tracking performance is how important permanent shocks are to growth in the series being filtered. In particular, the DGP's used in Phillips and Shi (2021) have a very high contribution from permanent shocks.