Productivity levels and growth are extremely heterogeneous among firms. A vast literature has
developed to explain the origins of productivity shocks, their dispersion, evolution and their relation-
ship to the business cycle. We examine in detail the distribution of labor productivity levels and
growth, and observe that they exhibit heavy tails. We propose to model these distributions using the
four parameter Lévy stable distribution, a natural candidate deriving from the generalised Central
Limit Theorem. We show that it is a better fit than several standard alternatives, and is remarkably
consistent over time, countries and sectors. In all samples considered, the tail parameter is such that
the theoretical variance of the distribution is infinite, so that the sample standard deviation increases
with sample size. We find a consistent positive skewness, a markedly different behaviour between
the left and right tails, and a positive relationship between productivity and size. The distributional
approach allows us to test different measures of dispersion and find that productivity dispersion has
slightly decreased over the past decade.
Oxford Martin Programme on Technological and Economic Change
Yang, J., Heinrich, T., Winkler, J., Lafond, F., Koutroumpis, P & Farmer, J.D. (2019). 'Measuring productivity dispersion: a parametric approach using the Lévy alpha-stable distribution'. INET Oxford Working Paper No. 2019-14.