Measuring productivity dispersion: a parametric approach using the L\'{e}vy alpha-stable distribution

TL;DR

This paper models the heterogeneity in value added per worker across firms using a four-parameter Lévy alpha-stable distribution, capturing heavy tails, negative values, and dispersion more effectively than alternatives.

Contribution

It introduces a novel parametric approach employing Lévy stable distributions to characterize firm-level productivity heterogeneity, including negative values and heavy tails.

Findings

Lévy stable distribution fits productivity data better than alternatives.

Dispersion measures derived from the distribution are as useful as interquantile ratios.

The approach reveals insights into the evolution of productivity heterogeneity and its relation to intangible capital.

Abstract

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.