IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0235282.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0235282
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0235282&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0235282?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    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. 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.
    3. Variyam, Jayachandran N. & Kraybill, David S., 1992. "Empirical evidence on determinants of firm growth," Economics Letters, Elsevier, vol. 38(1), pages 31-36, January.
    4. 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.
    5. 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.
    6. Harhoff, Dietmar & Stahl, Konrad & Woywode, Michael, 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.
    7. Patrizio Pagano & Fabiano Schivardi, 2003. "Firm Size Distribution and Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 105(2), pages 255-274, June.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. 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.
    14. 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.
    15. 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.
    16. Taisei Kaizoji & Hiroshi Iyetomi & Yuichi Ikeda, 2005. "Re-examination of the size distribution of firms," Papers physics/0512124, arXiv.org, revised Mar 2006.
    17. 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.
    18. 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.
    19. 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.
    20. Takehiko Yasuda, 2005. "Firm Growth, Size, Age and Behavior in Japanese Manufacturing," Small Business Economics, Springer, vol. 24(1), pages 1-15, December.
    21. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Alex Coad, 2007. "Firm Growth: a Survey," Post-Print halshs-00155762, HAL.
    2. Daria Ciriaci & Pietro Moncada-Paternò-Castello & Peter Voigt, 2016. "Innovation and job creation: a sustainable relation?," Eurasian Business Review, Springer;Eurasia Business and Economics Society, vol. 6(2), pages 189-213, August.
    3. Lina Cortés & Juan M. Lozada & Javier Perote, 2019. "Firm size and concentration inequality: A flexible extension of Gibrat’s law," Documentos de Trabajo CIEF 17205, Universidad EAFIT.
    4. Gao, Baojun & Chan, Wai Kin (Victor) & Li, Hongyi, 2015. "On the increasing inequality in size distribution of China's listed companies," China Economic Review, Elsevier, vol. 36(C), pages 25-41.
    5. 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.
    6. 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.
    7. D.B. Audretsch & L. Klomp & E. Santarelli & A.R. Thurik, 2004. "Gibrat's Law: Are the Services Different?," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 24(3), pages 301-324, May.
    8. Anna Giunta & Domenico Scalera & Annamaria Nifo, 2008. "Divisione del lavoro, crescita e divari di performance nell'industria italiana degli anni '90," Departmental Working Papers of Economics - University 'Roma Tre' 0097, Department of Economics - University Roma Tre.
    9. Alex Coad & Werner Hölzl, 2012. "Firm Growth: Empirical Analysis," Chapters, in: Michael Dietrich & Jackie Krafft (ed.), Handbook on the Economics and Theory of the Firm, chapter 24, Edward Elgar Publishing.
    10. Bergner, Sören Martin & Bräutigam, Rainer & Evers, Maria Theresia & Spengel, Christoph, 2017. "The use of SME tax incentives in the European Union," ZEW Discussion Papers 17-006, ZEW - Leibniz Centre for European Economic Research.
    11. Dirk Burghardt & Marco Helm, 2015. "Firm growth in the course of mergers and acquisitions," Small Business Economics, Springer, vol. 44(4), pages 889-904, April.
    12. Byeongyong Paul Choi, 2010. "The U.S. Property and Liability Insurance Industry: Firm Growth, Size, and Age," Risk Management and Insurance Review, American Risk and Insurance Association, vol. 13(2), pages 207-224, September.
    13. Habermann, Harald, 2017. "Business takeovers and firm growth: Empirical evidence from a German panel," Working Papers 01/17, Institut für Mittelstandsforschung (IfM) Bonn.
    14. Takehiko Yasuda, 2005. "Firm Growth, Size, Age and Behavior in Japanese Manufacturing," Small Business Economics, Springer, vol. 24(1), pages 1-15, December.
    15. Gavin Reid & Zhibin Xu, 2012. "Generalising Gibrat: using Chinese evidence founded on fieldwork," Small Business Economics, Springer, vol. 39(4), pages 1017-1028, November.
    16. Jaana Lappalainen & Mervi Niskanen, 2009. "Does Board Composition and Ownership Structure Affect Firm Growth? Evidence from Finnish SMEs," Research in Economics and Business: Central and Eastern Europe, Tallinn School of Economics and Business Administration, Tallinn University of Technology, vol. 1(1).
    17. ŠEmsa ÖZAR & Gökhan ÖZERTAN & Zeynep Burcu İRFANOĞLU, 2008. "Micro And Small Enterprise Growth In Turkey: Under The Shadow Of Financial Crisis," The Developing Economies, Institute of Developing Economies, vol. 46(4), pages 331-362, December.
    18. Ferrando, Annalisa & Martinez-Carrascal, Carmen & Coluzzi, Chiara, 2009. "Financing obstacles and growth: an analysis for euro area non-financial corporations," Working Paper Series 997, European Central Bank.
    19. 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.
    20. Nuno Silva & Pedro Dias Moreira, 2023. "On the forecasting power of corporate sales growth determinants," Economic Bulletin and Financial Stability Report Articles and Banco de Portugal Economic Studies, Banco de Portugal, Economics and Research Department.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:plo:pone00:0235282. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.