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

Yang, Jangho and Heinrich, Torsten and Winkler, Julian and Lafond, François and Koutroumpis, Pantelis and Farmer, J. Doyne (2019): Measuring productivity dispersion: a parametric approach using the Lévy alpha-stable distribution.

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Abstract

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.

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