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

Author

Listed:
  • Yang, Jangho
  • Heinrich, Torsten
  • Winkler, Julian
  • Lafond, François
  • Koutroumpis, Pantelis
  • Farmer, J. Doyne

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.

Suggested Citation

  • Yang, Jangho & Heinrich, Torsten & Winkler, Julian & Lafond, François & Koutroumpis, Pantelis & Farmer, J. Doyne, 2019. "Measuring productivity dispersion: a parametric approach using the Lévy alpha-stable distribution," MPRA Paper 96474, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:96474
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    File URL: https://mpra.ub.uni-muenchen.de/96474/1/MPRA_paper_96474.pdf
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    References listed on IDEAS

    as
    1. Cindy Cunningham & Lucia Foster & Cheryl Grim & John Haltiwanger & Sabrina Wulff Pabilonia & Jay Stewart & Zoltan Wolf, 2018. "Dispersion in Dispersion: Measuring Establishment-Level Differences in Productivity," Working Papers 18-25, Center for Economic Studies, U.S. Census Bureau.
    2. Trapani, Lorenzo, 2016. "Testing for (in)finite moments," Journal of Econometrics, Elsevier, vol. 191(1), pages 57-68.
    3. König, Michael & Lorenz, Jan & Zilibotti, Fabrizio, 2016. "Innovation vs. imitation and the evolution of productivity distributions," Theoretical Economics, Econometric Society, vol. 11(3), September.
    4. Philippe Aghion & Nick Bloom & Richard Blundell & Rachel Griffith & Peter Howitt, 2005. "Competition and Innovation: an Inverted-U Relationship," The Quarterly Journal of Economics, Oxford University Press, vol. 120(2), pages 701-728.
    5. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    6. Robert E. Lucas Jr. & Benjamin Moll, 2014. "Knowledge Growth and the Allocation of Time," Journal of Political Economy, University of Chicago Press, vol. 122(1), pages 1-51.
    7. Kalemli-Ozcan, Sebnem & Sorensen, Bent E. & Villegas-Sanchez, Carolina & Volosovych, Vadym & Yesiltas, Sevcan, 2015. "How to construct nationally representative firm level data from the ORBIS global database," CEPR Discussion Papers 10829, C.E.P.R. Discussion Papers.
    8. Ghiglino, Christian, 2012. "Random walk to innovation: Why productivity follows a power law," Journal of Economic Theory, Elsevier, vol. 147(2), pages 713-737.
    9. Mitsukuni Nishida & Amil Petrin & Martin Rotemberg & T. Kirk White, 2016. "Measuring Cross-Country Differences in Misallocation," Working Papers 16-50, Center for Economic Studies, U.S. Census Bureau.
    10. Daron Acemoglu & Melissa Dell, 2010. "Productivity Differences between and within Countries," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(1), pages 169-188, January.
    11. Giulio Bottazzi & Angelo Secchi, 2011. "A new class of asymmetric exponential power densities with applications to economics and finance," Industrial and Corporate Change, Oxford University Press, vol. 20(4), pages 991-1030, August.
    12. repec:hal:journl:hal-00642696 is not listed on IDEAS
    13. Chang-Tai Hsieh & Peter J. Klenow, 2009. "Misallocation and Manufacturing TFP in China and India," The Quarterly Journal of Economics, Oxford University Press, vol. 124(4), pages 1403-1448.
    14. N. Gregory Mankiw & David Romer & David N. Weil, 1992. "A Contribution to the Empirics of Economic Growth," The Quarterly Journal of Economics, Oxford University Press, vol. 107(2), pages 407-437.
    15. Benoit Mandelbrot, 1963. "New Methods in Statistical Economics," Journal of Political Economy, University of Chicago Press, vol. 71, pages 421-421.
    16. Carrasco, Marine & Florens, Jean-Pierre & Renault, Eric, 2007. "Linear Inverse Problems in Structural Econometrics Estimation Based on Spectral Decomposition and Regularization," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 77, Elsevier.
    17. Xavier Gabaix, 2011. "The Granular Origins of Aggregate Fluctuations," Econometrica, Econometric Society, vol. 79(3), pages 733-772, May.
    18. Eric Bartelsman & John Haltiwanger & Stefano Scarpetta, 2013. "Cross-Country Differences in Productivity: The Role of Allocation and Selection," American Economic Review, American Economic Association, vol. 103(1), pages 305-334, February.
    19. repec:nbr:nberch:13889 is not listed on IDEAS
    20. Robert E. Hall & Charles I. Jones, 1999. "Why do Some Countries Produce So Much More Output Per Worker than Others?," The Quarterly Journal of Economics, Oxford University Press, vol. 114(1), pages 83-116.
    21. repec:eee:ecolet:v:166:y:2018:i:c:p:76-78 is not listed on IDEAS
    22. Jesse Perla & Christopher Tonetti, 2014. "Equilibrium Imitation and Growth," Journal of Political Economy, University of Chicago Press, vol. 122(1), pages 52-76.
    23. Sean Holly & Ivan Petrella & Emiliano Santoro, 2013. "Aggregate fluctuations and the cross-sectional dynamics of firm growth," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 176(2), pages 459-479, February.
    24. Calvino, Flavio & Criscuolo, Chiara & Menon, Carlo & Secchi, Angelo, 2018. "Growth volatility and size: A firm-level study," Journal of Economic Dynamics and Control, Elsevier, vol. 90(C), pages 390-407.
    25. Giuseppe Berlingieri & Patrick Blanchenay & Sara Calligaris & Chiara Criscuolo, 2017. "The Multiprod project: A comprehensive overview," OECD Science, Technology and Industry Working Papers 2017/04, OECD Publishing.
    26. Cette, Gilbert & Corde, Simon & Lecat, Rémy, 2018. "Firm-level productivity dispersion and convergence," Economics Letters, Elsevier, vol. 166(C), pages 76-78.
    27. Gaffeo, Edoardo, 2011. "The distribution of sectoral TFP growth rates: International evidence," Economics Letters, Elsevier, vol. 113(3), pages 252-255.
    28. Lucia Foster & Cheryl Grim & John Haltiwanger & Zoltan Wolf, 2018. "Innovation, Productivity Dispersion, and Productivity Growth," NBER Chapters, in: Measuring and Accounting for Innovation in the 21st Century, National Bureau of Economic Research, Inc.
    29. Samuelson, Paul A., 1967. "Efficient Portfolio Selection for Pareto-Lévy Investments*," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 2(2), pages 107-122, June.
    30. Asquith, William H., 2014. "Parameter estimation for the 4-parameter Asymmetric Exponential Power distribution by the method of L-moments using R," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 955-970.
    31. Eugene F. Fama, 1965. "Portfolio Analysis in a Stable Paretian Market," Management Science, INFORMS, vol. 11(3), pages 404-419, January.
    32. Gaffeo, Edoardo, 2008. "Lã‰Vy-Stable Productivity Shocks," Macroeconomic Dynamics, Cambridge University Press, vol. 12(3), pages 425-443, June.
    33. Hideaki Aoyama & Hiroshi Yoshikawa & Hiroshi Iyetomi & Yoshi Fujiwara, 2010. "Productivity dispersion: facts, theory, and implications," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 5(1), pages 27-54, June.
    34. Nolan, John P., 1998. "Parameterizations and modes of stable distributions," Statistics & Probability Letters, Elsevier, vol. 38(2), pages 187-195, June.
    35. G. Bottazzi & E. Cefis & G. Dosi & A. Secchi, 2007. "Invariances and Diversities in the Patterns of Industrial Evolution: Some Evidence from Italian Manufacturing Industries," Small Business Economics, Springer, vol. 29(1), pages 137-159, June.
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    More about this item

    Keywords

    productivity; dispersion; distribution; heavy-tail; Lévy stable distribution;

    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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