The fallacy in productivity decomposition - Simon Bruhn; Thomas Grebel; Lionel Nesta (Technische Universität Ilmenau, Institut für Volkswirtschaftslehre, 2021)
This paper argues that the typical practice of performing growth decompositions based on log-transformed productivity values induces fallacious conclusions: using logs may lead to an inaccurate aggregate growth rate, an inaccurate description of the microsources of aggregate growth, or both. We identify the mathematical sources of this log-induced fallacy in decomposition and analytically demonstrate the questionable reliability of log results. Using rm-level data from the French manufacturing sector during the 2009-2018 period, we empirically show that the magnitude of the log-induced distortions is substantial. Depending on the de nition of accurate log measures, we nd that around 60-80% of four-digit industry results are prone to mismeasurement. We further nd signi cant correlations of this mismeasurement with commonly deployed industry characteristics, indicating, among other things, that less competitive industries are more prone to log distortions. Evidently, these correlations also a ect the validity of studies that investigate the role of industry characteristics in productivity growth.
Keywords: 330; productivity decomposition; growth; log approximation; geometric mean; arithmetic mean