Alternative definitions of the business cycle and their implications for business cycle models: A reply to Torben Mark Pederson

In our 1995 JEDC paper, James Nason and I argued that the Hodrick-Prescott (HP) filter can produce 'spurious' business cycles, in the sense that HP fi ltered data may exhibit business cycle dynamics even if none were present i n the original data. Pederson (1998) criticizes our analysis on the grounds that we fail to define 'business cycles' or what we mean by the term 'spur ious', He argues that if one defines business cycles in terms of an ideal h igh-pass filter, then the HP filter cannot produce 'spurious cycles', becau se it well approximates an ideal high-pass filter. Indeed, based on this de finition of the business cycle, our analysis would imply that even an ideal high-pass filter generates a spurious cycle, a conclusion which is nonsens ical. Pederson's arguments are correct, provided that one accepts his definition of the business cycle. But Nason and I had a different definition in mind. I plead guilty of the charge of failing to provide adequate definitions, an d in this note I try to clarify what we meant.