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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.

Suggested Citation

  • Giulio Bottazzi & Davide Pirino & Federico Tamagni, 2013. "Zipf Law and the Firm Size Distribution: a critical discussion of popular estimators," LEM Papers Series 2013/17, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    • Handle: RePEc:ssa:lemwps:2013/17
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    References listed on IDEAS

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    Cited by:

    1. Lina Cortés & Juan M. Lozada & Javier Perote, 2019. "Firm size and concentration inequality: A flexible extension of Gibrat’s law," Documentos de Trabajo de Valor Público 17205, Universidad EAFIT.
    2. Andrew T. Balthrop, 2021. "Gibrat’s law in the trucking industry," Empirical Economics, Springer, vol. 61(1), pages 339-354, July.
    3. Zakaria Babutsidze, 2016. "Innovation, competition and firm size distribution on fragmented markets," Journal of Evolutionary Economics, Springer, vol. 26(1), pages 143-169, March.
    4. Ruben Dewitte & Michel Dumont & Glenn Rayp & Peter Willemé, 2022. "Unobserved heterogeneity in the productivity distribution and gains from trade," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 55(3), pages 1566-1597, August.
    5. Giulio Bottazzi & Alessandro De Sanctis & Fabio Vanni, 2016. "Non-performing loans, systemic risk and resilience in financial networks," LEM Papers Series 2016/08, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    6. A. B. Atkinson, 2017. "Pareto and the Upper Tail of the Income Distribution in the UK: 1799 to the Present," Economica, London School of Economics and Political Science, vol. 84(334), pages 129-156, April.
    7. Flavio Calvino & Daniele Giachini & Mattia Guerini, 2022. "The age distribution of business firms," Journal of Evolutionary Economics, Springer, vol. 32(1), pages 205-245, January.
    8. Fontanelli, Luca & Guerini, Mattia & Napoletano, Mauro, 2023. "International trade and technological competition in markets with dynamic increasing returns," Journal of Economic Dynamics and Control, Elsevier, vol. 149(C).
    9. Cortés, Lina M. & Mora-Valencia, Andrés & Perote, Javier, 2017. "Measuring firm size distribution with semi-nonparametric densities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 35-47.
    10. Jakub Growiec & Fabio Pammolli & Massimo Riccaboni, 2020. "Innovation and Corporate Dynamics: A Theoretical Framework," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 12(1), pages 1-45, March.
    11. Lina M Cortés & Juan M Lozada & Javier Perote, 2021. "Firm size and economic concentration: An analysis from a lognormal expansion," PLOS ONE, Public Library of Science, vol. 16(7), pages 1-21, July.
    12. J. M. Applegate & Adam Lampert, 2021. "Firm size populations modeled through competition-colonization dynamics," Journal of Evolutionary Economics, Springer, vol. 31(1), pages 91-116, January.
    13. Metzig, Cornelia & Gordon, Mirta B., 2014. "A model for scaling in firms’ size and growth rate distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 264-279.
    14. Luca Fontanelli, 2023. "Theories of market selection: a survey," LEM Papers Series 2023/22, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    15. Vitezić Vanja & Srhoj Stjepan & Perić Marko, 2018. "Investigating Industry Dynamics in a Recessionary Transition Economy," South East European Journal of Economics and Business, Sciendo, vol. 13(1), pages 43-67, June.
    16. Ahmad, Saad & Akgul, Zeynep, 2018. "Using Power Laws to Identify the Structural Parameters of Trade Models with Firm Heterogeneity," Conference papers 332993, Purdue University, Center for Global Trade Analysis, Global Trade Analysis Project.
    17. Marko Petrović & Andrea Teglio & Simone Alfarano, 2022. "Credit allocation and the financial crisis: evidence from Spanish companies," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(4), pages 1069-1114, October.
    18. Ignacio Rosal, 2018. "Power laws in EU country exports," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 45(2), pages 311-337, May.
    19. Ji, Guseon & Dai, Bingcun & Park, Sung-Pil & Ahn, Kwangwon, 2020. "The origin of collective phenomena in firm sizes," Chaos, Solitons & Fractals, Elsevier, vol. 136(C).

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    More about this item

    Keywords

    Firm size distribution; Zipf Law; Power-like distribution;
    All these keywords.

    JEL classification:

    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • D20 - Microeconomics - - Production and Organizations - - - General

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