What do deviation cycles measure? An analysis of the informational content of filter-based business cycles

Abstract

Background: Empirical business cycle research typically commences with the extraction of a so-called deviation cycle using a time-series smoothing filter. This methodology is appealing for its pragmatism; it is easy to implement, and the output it produces is conveniently interpreted as percentage deviations from the natural level of output. However, recent literature offers staunch criticism of deviation cycle analysis, especially with regards to the assumption implicitly underlying it – that business cycle fluctuations are restricted to distinct intervals on the frequency domain.

Aim: Despite its lack of a basis in theory, the analysis of deviation cycles over particular frequency ranges may still yield useful stylised business cycle facts. This, however, hinges on whether the information that a frequency filter captures consistently aligns with relevant theory-based business cycle concepts. Whether this is the case is an empirical matter, and herein lies the rationale for our research.

Setting: We investigate the informational content of South Africa’s output deviation cycles.

Methods: We extract deviation cycles at standard high- and medium-frequency ranges (denoted as short- and medium-term deviation cycles respectively) and analyse their informational overlap with the components of an alternative theory-based estimate of the business cycle, decomposed into demand, supply, domestic and foreign sources of business cycle dynamics.

Results: Our findings suggest that the contents of deviation cycles extracted over a high-frequency range do not neatly correspond to the transitory ‘demand-driven’ business cycle, while cycles extracted over a medium-frequency range correspond closely to the combined path of permanent output shocks.

Conclusion: One should thus be cautious of drawing strong conclusions about the nature of business cycles from filter-based deviation cycle estimates, particularly if the objective of the study relies on assuming that high-frequency deviation cycles correspond to transitory demand shocks.