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

It is well-known that value added 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 value-added 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 value added per worker using the four parameter L\'evy stable distribution, a natural candidate deriving from the Generalised 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 are at least as useful as interquantile ratios, through case studies on the evolution of dispersion in recent years and the correlation between dispersion and intangible capital intensity.