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Zipf Law and the Firm Size Distribution: a critical discussion of popular estimators

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  • Giulio Bottazzi
  • Davide Pirino
  • Federico Tamagni

Abstract

The upper tail of the firm size distribution is often assumed to follow a Power Law behavior. Recently, using different estimators and on different data sets, several papers conclude that this distribution follows the Zipf Law, meaning that the fraction of firms whose size is above a given value is inversely proportional to the value itself. We compare the different methods through which this conclusion has been reached. We find that the family of estimators most widely adopted, based on an OLS regression, is in fact unreliable and basically useless for appropriate inference. This finding rises some doubts about previously identified Zipf Laws. In general, when individual observations are available, we recommend the adoption of the Hill estimator over any other method.

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Bibliographic Info

Paper provided by Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy in its series LEM Papers Series with number 2013/17.

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Date of creation: 12 Jul 2013
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Handle: RePEc:ssa:lemwps:2013/17

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Related research

Keywords: Firm size distribution; Zipf Law; Power-like distribution;

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  1. Okuyama, K & Takayasu, M & Takayasu, H, 1999. "Zipf's law in income distribution of companies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 125-131.
  2. Nunes Amaral, Luís A & Buldyrev, Sergey V & Havlin, Shlomo & Maass, Philipp & Salinger, Michael A & Eugene Stanley, H & Stanley, Michael H.R, 1997. "Scaling behavior in economics: The problem of quantifying company growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 244(1), pages 1-24.
  3. Giulio Bottazzi & Alex Coad & Nadia Jacoby & Angelo Secchi, 2005. "Corporate Growth and Industrial Dynamics: Evidence from French Manufacturing," LEM Papers Series 2005/21, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  4. Rafal Weron, 2001. "Levy-stable distributions revisited: tail index > 2 does not exclude the Levy-stable regime," HSC Research Reports HSC/01/01, Hugo Steinhaus Center, Wroclaw University of Technology.
  5. Julian di Giovanni & Andrei A. Levchenko, 2009. "Firm Entry, Trade, and Welfare in Zipf's World," Working Papers 591, Research Seminar in International Economics, University of Michigan.
  6. Xavier Gabaix & Augustin Landier, 2008. "Why Has CEO Pay Increased So Much?," The Quarterly Journal of Economics, MIT Press, vol. 123(1), pages 49-100, 02.
  7. Xavier Gabaix, 2008. "Power Laws in Economics and Finance," NBER Working Papers 14299, National Bureau of Economic Research, Inc.
  8. Julian di Giovanni & Andrei A. Levchenko & Romain Ranciere, 2010. "Power Laws in Firm Size and Openness to Trade: Measurement and Implications," Working Papers 598, Research Seminar in International Economics, University of Michigan.
  9. Boris Podobnik & Davor Horvatic & Alexander M. Petersen & Branko Uro\v{s}evi\'c & H. Eugene Stanley, 2010. "Bankruptcy risk model and empirical tests," Papers 1011.2670, arXiv.org.
  10. Xavier Gabaix & Rustam Ibragimov, 2007. "Rank-1/2: A Simple Way to Improve the OLS Estimation of Tail Exponents," NBER Technical Working Papers 0342, National Bureau of Economic Research, Inc.
  11. Erzo G. J. Luttmer, 2007. "Selection, Growth, and the Size Distribution of Firms," The Quarterly Journal of Economics, MIT Press, vol. 122(3), pages 1103-1144, 08.
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