The fallacy in productivity decomposition

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 mea-
sures. We further find significant correlations of this mismeasurement with commonly
deployed industry characteristics, indicating, among other things, that less compet-
itive industries are more prone to log distortions. Evidently, these correlations also
affect the validity of studies investigating industry characteristics’ role in productivity
growth.