On the cyclical properties of Hamilton's regression filter - Yves S. Schüler (Deutsche Bundesbank, 2018)
Hamilton (2017) criticises the Hodrick and Prescott (1981, 1997) filter (HP filter) because of three drawbacks (i. spurious cycles, ii. end-of-sample bias, iii. ad hoc assumptions regarding the smoothing parameter) and proposes a regression filter as an alternative. I demonstrate that Hamilton's regression filter shares some of these drawbacks. For instance, Hamilton's ad hoc formulation of a 2-year regression filter implies a cancellation of two-year cycles and an amplification of cycles longer than typical business cycles. This is at odds with stylised business cycle facts, such as the one-year duration of a typical recession, leading to inconsistencies, for example, with the NBER business cycle chronology. Nonetheless, I show that Hamilton's regression filter should be preferred to the HP filter for constructing a credit-to-GDP gap. The filter extracts the various medium-term frequencies more equally. Due to this property, a regression-filtered credit-to-GDP ratio indicates that imbalances prior to the global financial crisis started earlier than shown by the Basel III creditto-GDP gap.
Keywords: C10; E32; E58; G01; 330; detrending; spurious cycles; business cycles; financial cycles; Basel III