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

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Document pages: 64 pages

Abstract: Productivity levels and growth are extremely heterogeneous among firms. Avast literature has developed to explain the origins of productivity shocks,their dispersion, evolution and their relationship to the business cycle. Weexamine in detail the distribution of labor productivity levels and growth, andobserve that they exhibit heavy tails. We propose to model these distributionsusing the four parameter Lévy stable distribution, a natural candidatederiving from the generalised Central Limit Theorem. We show that it is abetter fit than several standard alternatives, and is remarkably consistentover time, countries and sectors. In all samples considered, the tail parameteris such that the theoretical variance of the distribution is infinite, so thatthe sample standard deviation increases with sample size. We find a consistentpositive skewness, a markedly different behaviour between the left and righttails, and a positive relationship between productivity and size. Thedistributional approach allows us to test different measures of dispersion andfind that productivity dispersion has slightly decreased over the past decade.

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