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

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Listed:
  • Jangho Yang
  • Torsten Heinrich
  • Julian Winkler
  • Franc{c}ois Lafond
  • Pantelis Koutroumpis
  • J. Doyne Farmer

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 relationship 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 L\'{e}vy 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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  • Jangho Yang & Torsten Heinrich & Julian Winkler & Franc{c}ois Lafond & Pantelis Koutroumpis & J. Doyne Farmer, 2019. "Measuring productivity dispersion: a parametric approach using the L\'{e}vy alpha-stable distribution," Papers 1910.05219, arXiv.org.
  • Handle: RePEc:arx:papers:1910.05219
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    Cited by:

    1. Torsten Heinrich & Jangho Yang & Shuanping Dai, 2020. "Growth, development, and structural change at the firmlevel: The example of the PR China," Chemnitz Economic Papers 040, Department of Economics, Chemnitz University of Technology.
    2. Goldin, Ian & Koutroumpis, Pantelis & Lafond, François & Winkler, Julian, 2020. "Why is productivity slowing down?," MPRA Paper 99172, University Library of Munich, Germany.
    3. Heinrich, Torsten & Yang, Jangho & Dai, Shuanping, 2020. "Levels of structural change: An analysis of China's development push 1998-2014," MPRA Paper 100106, University Library of Munich, Germany.
    4. Heinrich, Torsten & Yang, Jangho & Dai, Shuanping, 2020. "Growth, development, and structural change at the firm-level: The example of the PR China," MPRA Paper 105011, University Library of Munich, Germany.
    5. Heinrich, Torsten & Yang, Jangho & Dai, Shuanping, 2021. "Growth, development, and structural change at the firm level: The example of the PR China," Working Papers on East Asian Studies 128/2021, University of Duisburg-Essen, Institute of East Asian Studies IN-EAST.
    6. Torsten Heinrich & Jangho Yang & Shuanping Dai, 2020. "Growth, development, and structural change at the firm-level: The example of the PR China," Papers 2012.14503, arXiv.org.

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    More about this item

    JEL classification:

    • D2 - Microeconomics - - Production and Organizations
    • J24 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Human Capital; Skills; Occupational Choice; Labor Productivity
    • O3 - Economic Development, Innovation, Technological Change, and Growth - - Innovation; Research and Development; Technological Change; Intellectual Property Rights
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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