The fallacy in productivity decomposition

Abstract

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 micro sources 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 firm-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. We find that around 60–80% of four-digit industry results are prone to mismeasurement depending on the definition of accurate log measures. We further find significant 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 affect the validity of studies investigating industry characteristics’ role in productivity growth.