Measuring productivity dispersion: a parametric approach using the Lévy alpha-stable distribution

It is well known that value added (VA) per worker is extremely heterogeneous among firms, but relatively little has been done to characterize this heterogeneity more precisely. Here, we show that the distribution of VA per worker exhibits heavy tails, a very large support, and consistently features a proportion of negative values, which prevents log transformation. We propose to model the distribution of VA per worker using the four-parameter Lévy stable distribution, a natural candidate deriving from the generalized central limit theorem, and we show that it is a better fit than key alternatives. Fitting a distribution allows us to capture dispersion through the tail exponent and scale parameters separately. We show that these parametric measures of dispersion can be useful to characterize the evolution of dispersion in recent years.