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An appraisal of firm size distribution: Does sample size matter?

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  • Segarra, Agustí
  • Teruel, Mercedes

Abstract

Recent empirical evidence based on extensive databases shows that firm size distributions (FSD) vary with the sample. This paper analyses the effect of sample size on the FSD of Spanish manufacturing firms for the years 2001 and 2006. We use a comprehensive dataset that has two measures of firm size: sales and employment. Our database shows a skewed FSD to the right which there are numerous small firms and a few large firms. Applying a rolling regression to control for sample size developed by Peng (2010), we show the existence of a non-constant power-law distribution that depends on the sampling size. Furthermore, the FSD of employees is more sensitive to firm age than the FSD of sales.

Suggested Citation

  • Segarra, Agustí & Teruel, Mercedes, 2012. "An appraisal of firm size distribution: Does sample size matter?," Journal of Economic Behavior & Organization, Elsevier, vol. 82(1), pages 314-328.
    • Handle: RePEc:eee:jeborg:v:82:y:2012:i:1:p:314-328
    DOI: 10.1016/j.jebo.2012.02.012
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    as
    1. de Wit, Gerrit, 2005. "Firm size distributions: An overview of steady-state distributions resulting from firm dynamics models," International Journal of Industrial Organization, Elsevier, vol. 23(5-6), pages 423-450, June.
    2. Paolo Angelini & Andrea Generale, 2008. "On the Evolution of Firm Size Distributions," American Economic Review, American Economic Association, vol. 98(1), pages 426-438, March.
    3. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    4. John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March.
    5. Matteo Richiardi, 2004. "Generalizing Gibrat: Reasonable Multiplicative Models of Firm Dynamics," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 7(1), pages 1-2.
    6. Elena Cefis & Orietta Marsili & Hans Schenk, 2009. "The effects of mergers and acquisitions on the firm size distribution," Journal of Evolutionary Economics, Springer, vol. 19(1), pages 1-20, February.
    7. Cirillo, Pasquale & Hüsler, Jürg, 2009. "On the upper tail of Italian firms’ size distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1546-1554.
    8. L. Crosato & P. Ganugi, 2007. "Statistical regularity of firm size distribution: the Pareto IV and truncated Yule for Italian SCI manufacturing," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 16(1), pages 85-115, June.
    9. Growiec, Jakub & Pammolli, Fabio & Riccaboni, Massimo & Stanley, H. Eugene, 2008. "On the size distribution of business firms," Economics Letters, Elsevier, vol. 98(2), pages 207-212, February.
    10. Blank, Aharon & Solomon, Sorin, 2000. "Power laws in cities population, financial markets and internet sites (scaling in systems with a variable number of components)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(1), pages 279-288.
    11. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 53-82.
    12. Luís M B Cabral & José Mata, 2003. "On the Evolution of the Firm Size Distribution: Facts and Theory," American Economic Review, American Economic Association, vol. 93(4), pages 1075-1090, September.
    13. Fujiwara, Yoshi & Di Guilmi, Corrado & Aoyama, Hideaki & Gallegati, Mauro & Souma, Wataru, 2004. "Do Pareto–Zipf and Gibrat laws hold true? An analysis with European firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 197-216.
    14. Giulio Bottazzi & Angelo Secchi, 2003. "Common Properties and Sectoral Specificities in the Dynamics of U.S. Manufacturing Companies," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 23(3_4), pages 217-232, December.
    15. Toke Reichstein & Morten Berg Jensen, 2005. "Firm size and firm growth rate distributions--The case of Denmark," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 14(6), pages 1145-1166, December.
    16. Emin Dinlersoz & Glenn MacDonald, 2009. "The Industry Life-Cycle of the Size Distribution of Firms," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 12(4), pages 648-667, October.
    17. Rousseau, Peter L. & Wachtel, Paul, 2002. "Inflation thresholds and the finance-growth nexus," Journal of International Money and Finance, Elsevier, vol. 21(6), pages 777-793, November.
    18. Pollock, D. S. G., 2003. "Recursive estimation in econometrics," Computational Statistics & Data Analysis, Elsevier, vol. 44(1-2), pages 37-75, October.
    19. 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.
    20. Sorin Solomon & Moshe Levy, 1996. "Spontaneous Scaling Emergence In Generic Stochastic Systems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 7(05), pages 745-751.
    21. Ishikawa, Atushi, 2008. "Power-Law and Log-Normal Distributions in Firm Size Displacement Data," Economics Discussion Papers 2008-45, Kiel Institute for the World Economy (IfW Kiel).
    22. L. A. N. Amaral & S. V. Buldyrev & S. Havlin & H. Leschhorn & P. Maass & M. A. Salinger & H. E. Stanley & M. H. R. Stanley, 1997. "Scaling behavior in economics: I. Empirical results for company growth," Papers cond-mat/9702082, arXiv.org.
    23. repec:bla:jfinan:v:43:y:1988:i:4:p:933-48 is not listed on IDEAS
    24. Urzua, Carlos M., 2000. "A simple and efficient test for Zipf's law," Economics Letters, Elsevier, vol. 66(3), pages 257-260, March.
    25. Sutton, John, 2007. "Market Structure: Theory and Evidence," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 35, pages 2301-2368, Elsevier.
    26. Gabaix, Xavier & Ioannides, Yannis M., 2004. "The evolution of city size distributions," Handbook of Regional and Urban Economics, in: J. V. Henderson & J. F. Thisse (ed.), Handbook of Regional and Urban Economics, edition 1, volume 4, chapter 53, pages 2341-2378, Elsevier.
    27. Gabaix, Xavier & Ibragimov, Rustam, 2011. "Rank − 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 24-39.
    28. Xavier Gabaix & Rustam Ibragimov, 2006. "Log(Rank-1/2): A Simple Way to Improve the OLS Estimation of Tail Exponents," Harvard Institute of Economic Research Working Papers 2106, Harvard - Institute of Economic Research.
    29. Gupta, Hari M. & Campanha, José R. & de Aguiar, Daniela R. & Queiroz, Gabriel A. & Raheja, Charu G., 2007. "Gradually truncated log-normal in USA publicly traded firm size distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 643-650.
    30. Giulio Bottazzi & Angelo Secchi & Federico Tamagni, 2008. "Productivity, profitability and financial performance," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 17(4), pages 711-751, August.
    31. Meese, R. & Rogoff, K., 1988. "Was It Real? The Exchange Rate-Interest Differential Ralation Over The Modern Floating-Rate Period," Working papers 368, Wisconsin Madison - Social Systems.
    32. Alex Coad, 2009. "The Growth of Firms," Books, Edward Elgar Publishing, number 13424.
    33. Zhang, Jianhua & Chen, Qinghua & Wang, Yougui, 2009. "Zipf distribution in top Chinese firms and an economic explanation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(10), pages 2020-2024.
    34. Xavier Gabaix & Rustam Ibragimov, 2011. "Rank - 1 / 2: A Simple Way to Improve the OLS Estimation of Tail Exponents," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 24-39, January.
    35. Mansor H. Ibrahim & Hassanuddeen Aziz, 2003. "Macroeconomic variables and the Malaysian equity market: A view through rolling subsamples," Journal of Economic Studies, Emerald Group Publishing, vol. 30(1), pages 6-27, January.
    36. Reed, William J., 2003. "The Pareto law of incomes—an explanation and an extension," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 469-486.
    37. Jovanovic, Boyan, 1982. "Selection and the Evolution of Industry," Econometrica, Econometric Society, vol. 50(3), pages 649-670, May.
    38. Taisei Kaizoji & Hiroshi Iyetomi & Yuichi Ikeda, 2005. "Re-examination of the size distribution of firms," Papers physics/0512124, arXiv.org, revised Mar 2006.
    39. Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
    40. Gallegati, M. & Palestrini, A., 2010. "The complex behavior of firms' size dynamics," Journal of Economic Behavior & Organization, Elsevier, vol. 75(1), pages 69-76, July.
    41. Peter Hart & Nicholas Oulton, 1997. "Zipf and the size distribution of firms," Applied Economics Letters, Taylor & Francis Journals, vol. 4(4), pages 205-206.
    42. Peng, Guohua, 2010. "Zipf’s law for Chinese cities: Rolling sample regressions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3804-3813.
    43. Johannes Voit, 2001. "The Growth Dynamics Of German Business Firms," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 149-162.
    44. Orietta Marsili, 2005. "Technology and the Size Distribution of Firms: Evidence from Dutch Manufacturing," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 27(4), pages 303-328, December.
    45. Pavitt, Keith & Robson, Michael & Townsend, Joe, 1987. "The Size Distribution of Innovating Firms in the UK: 1945-1983," Journal of Industrial Economics, Wiley Blackwell, vol. 35(3), pages 297-316, March.
    46. J. Aitchison & J. A. C. Brown, 1954. "A Synthesis of Engel Curve Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 22(1), pages 35-46.
    Full references (including those not matched with items on IDEAS)

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    11. 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.
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    20. Hassan Aly & Yousef Daoud & Amr Ragab & Ayhab Saad, 2017. "Young Gazelles and Aging Turtles: Understanding the Determinants of Employment Creation in the Labor Market in MENA Countries," Working Papers 1121, Economic Research Forum, revised 07 2017.
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    More about this item

    Keywords

    Firm size distribution; Power-laws; Truncation point;
    All these keywords.

    JEL classification:

    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions

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