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Where Gibrat meets Zipf: Scale and Scope of French Firms

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  • MArco Bee
  • Massimo Riccaboni
  • Stefano Schiavo

Abstract

The proper characterization of the size distribution of business firms represents an important issue in economic literature, with the most common reference distribu- tions being the lognormal and the Pareto varieties. This analysis is related to some methodological issues that are rarely properly addressed in applied work, and may significantly affect the results: the major difficulties arise from low power of the tests caused by limited sample size and the common practice of binning the data. In this paper we contribute to this body of literature by analyzing the size distribu- tion of all French companies, strongly rejecting the hypothesis that it is a Pareto distribution. Moreover, we argue that the lognormal distribution is a more reason- able first-cut benchmark for the entire population of firms. This is especially true for single-product firms, while we show the emergence of a Zipf tail for the class of multi-product companies. Our findings are in strong agreement with some recent theoretical contributions, which predict that the size distribution depends on a set of industry specific determinants.

Suggested Citation

  • MArco Bee & Massimo Riccaboni & Stefano Schiavo, 2014. "Where Gibrat meets Zipf: Scale and Scope of French Firms," DEM Discussion Papers 2014/03, Department of Economics and Management.
  • Handle: RePEc:trn:utwpem:2014/03
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    2. Montebruno, Piero & Bennett, Robert J. & van Lieshout, Carry & Smith, Harry, 2019. "A tale of two tails: Do Power Law and Lognormal models fit firm-size distributions in the mid-Victorian era?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 858-875.
    3. Michael Irlacher, 2022. "Multi-product Firms in International Economics," Economics working papers 2022-01, Department of Economics, Johannes Kepler University Linz, Austria.
    4. Asif, Muhammad & Hussain, Zawar & Asghar, Zahid & Hussain, Muhammad Irfan & Raftab, Mariya & Shah, Said Farooq & Khan, Akbar Ali, 2021. "A statistical evidence of power law distribution in the upper tail of world billionaires’ data 2010–20," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    5. Mariasole Banno' & Elisa Pozza & Sandro Trento, 2015. "La famiglia fa male all'internazionalizzazione dell'impresa?," DEM Discussion Papers 2015/03, Department of Economics and Management.
    6. Rashidisabet, Homa & Ajilore, Olusola & Leow, Alex & Demos, Alexander P., 2022. "Revisiting power-law estimation with applications to real-world human typing dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 599(C).
    7. Marco Bee & Stefano Schiavo, 2018. "Powerless: gains from trade when firm productivity is not Pareto distributed," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 154(1), pages 15-45, February.
    8. Lyócsa, Štefan & Výrost, Tomáš, 2018. "Scale-free distribution of firm-size distribution in emerging economies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 501-505.
    9. Letizia Montinari & Massimo Riccaboni & Stefano Schiavo, 2021. "Innovation, trade and multi‐product firms," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 54(1), pages 311-337, February.
    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. Flavio Bazzana & Anna Zadorozhnaya & Roberto Gabriele, 2014. "The role of covenants in bond issue and investment policy. The case of Russian companies," DEM Discussion Papers 2014/05, Department of Economics and Management.
    12. Anna Maria Fiori, 2020. "On firm size distribution: statistical models, mechanisms, and empirical evidence," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(3), pages 447-482, September.
    13. Giuseppe Arbia & Marco Bee & Giuseppe Espa & Flavio Santi, 2014. "Fitting Spatial Econometric Models through the Unilateral Approximation," DEM Discussion Papers 2014/08, Department of Economics and Management.
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    15. Cebreros Alfonso, 2019. "The Micro-economics of Export Supply: Firm-Level Evidence from Mexico," Working Papers 2019-02, Banco de México.
    16. Ricardo González-López & Javier B. Gómez & Amalio F. Pacheco, 2020. "A Minimal Agent-Based Model For The Size-Frequency Distribution Of Firms," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 23(01), pages 1-27, March.

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    More about this item

    Keywords

    Firm size distribution; multi-product firms; Pareto; Zipf’s law; lognormal;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • L25 - Industrial Organization - - Firm Objectives, Organization, and Behavior - - - Firm Performance

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