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Modeling the joint distribution of firm size and firm age based on grouped data

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  • Chen Ge
  • Shu-Guang Zhang
  • Bin Wang

Abstract

The firm size distribution is highly skewed to the right and often follows a power law. In practice, it is common that firm size and firm age data are aggregated and released as grouped data to avoid disclosure of confidential information. We investigate multiple parametric methods for firm size and firm age modeling based on grouped data, and propose to estimate the joint distribution of firm size and firm age using the Plackett copula. The goodness-of-fit of the estimated marginal distributions are benchmarked with respect to the fit to the whole data and to the upper tails, respectively. The utilization of the proposed methods are demonstrated via an application to the 1977-2014 US firm data. Results show that the generalized lambda distribution has overall better performance in modeling both firm size and firm age data. The exponentiated Weibull distribution also works well in modeling the firm size data. As a by-product, the estimated parameter of the Plackett copula provides a measure of the association between firm size and firm age.

Suggested Citation

  • Chen Ge & Shu-Guang Zhang & Bin Wang, 2020. "Modeling the joint distribution of firm size and firm age based on grouped data," PLOS ONE, Public Library of Science, vol. 15(7), pages 1-19, July.
    • Handle: RePEc:plo:pone00:0235282
    DOI: 10.1371/journal.pone.0235282
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    References listed on IDEAS

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    1. Evans, David S, 1987. "The Relationship between Firm Growth, Size, and Age: Estimates for 100 Manufacturing Industries," Journal of Industrial Economics, Wiley Blackwell, vol. 35(4), pages 567-581, June.
    2. 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.
    3. Ibhagui, Oyakhilome W. & Olokoyo, Felicia O., 2018. "Leverage and firm performance: New evidence on the role of firm size," The North American Journal of Economics and Finance, Elsevier, vol. 45(C), pages 57-82.
    4. Doi, Noriyuki & Cowling, Marc, 1998. "The Evolution of Firm Size and Employment Share Distribution in Japanese and UK Manufacturing: A Study of Small Business Presence," Small Business Economics, Springer, vol. 10(3), pages 283-292, May.
    5. Evans, David S, 1987. "Tests of Alternative Theories of Firm Growth," Journal of Political Economy, University of Chicago Press, vol. 95(4), pages 657-674, August.
    6. 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.
    7. Variyam, Jayachandran N. & Kraybill, David S., 1992. "Empirical evidence on determinants of firm growth," Economics Letters, Elsevier, vol. 38(1), pages 31-36, January.
    8. Taisei Kaizoji & Hiroshi Iyetomi & Yuichi Ikeda, 2005. "Re-examination of the size distribution of firms," Papers physics/0512124, arXiv.org, revised Mar 2006.
    9. 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.
    10. 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.
    11. Stanley, Michael H. R. & Buldyrev, Sergey V. & Havlin, Shlomo & Mantegna, Rosario N. & Salinger, Michael A. & Eugene Stanley, H., 1995. "Zipf plots and the size distribution of firms," Economics Letters, Elsevier, vol. 49(4), pages 453-457, October.
    12. Guiso, Luigi & Rustichini, Aldo, 2018. "Understanding the size and profitability of firms: The role of a biological factor," Research in Economics, Elsevier, vol. 72(1), pages 65-85.
    13. repec:bla:jindec:v:46:y:1998:i:4:p:453-88 is not listed on IDEAS
    14. Dietmar Harhoff & Konrad Stahl & Michaerl Woywode, 1998. "Legal Form, Growth and Exit of West German Firms—Empirical Results for Manufacturing, Construction, Trade and Service Industries," Journal of Industrial Economics, Wiley Blackwell, vol. 46(4), pages 453-488, December.
    15. Patrizio Pagano & Fabiano Schivardi, 2003. "Firm Size Distribution and Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 105(2), pages 255-274, June.
    16. Dunne, Paul & Hughes, Alan, 1994. "Age, Size, Growth and Survival: UK Companies in the 1980s," Journal of Industrial Economics, Wiley Blackwell, vol. 42(2), pages 115-140, June.
    17. Bin Wang, 2020. "A Zipf-plot based normalization method for high-throughput RNA-seq data," PLOS ONE, Public Library of Science, vol. 15(4), pages 1-15, April.
    18. Takehiko Yasuda, 2005. "Firm Growth, Size, Age and Behavior in Japanese Manufacturing," Small Business Economics, Springer, vol. 24(1), pages 1-15, December.
    19. Audretsch, David B & Klomp, Luuk & Thurik, A R Roy, 1997. "Do Services Differ From Manufacturing? The Post-Entry Performance of Firms in Dutch Services," CEPR Discussion Papers 1718, C.E.P.R. Discussion Papers.
    20. 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.
    21. 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.
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