IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v512y2018icp68-73.html
   My bibliography  Save this article

Granularity of the top 1,000 Brazilian companies

Author

Listed:
  • Da Silva, Sergio
  • Matsushita, Raul
  • Giglio, Ricardo
  • Massena, Gunther

Abstract

“Granularity” refers to the fact that economies are populated by a few large companies (the big “grains”) that coexist with many smaller companies. Such a distribution of firm sizes is modeled by power laws. This study adds to the international evidence of the granularity hypothesis by considering data for the top 1,000 Brazilian companies. We sort the companies from top to bottom in terms of their net revenues. Then, we adjust power laws to the data and estimate Pareto and Gumbel exponents. We find we cannot dismiss the hypothesis of granularity for the Brazilian companies. We also find the Pareto exponent is approximately one (1.070 ± .015), roughly a Zipf’s law. Such a result is in line with the previous one found for American companies where the Pareto exponent = 1.059. We also find a power-law progress curve best fits the data.

Suggested Citation

  • Da Silva, Sergio & Matsushita, Raul & Giglio, Ricardo & Massena, Gunther, 2018. "Granularity of the top 1,000 Brazilian companies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 68-73.
    • Handle: RePEc:eee:phsmap:v:512:y:2018:i:c:p:68-73
    DOI: 10.1016/j.physa.2018.08.027
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437118309531
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2018.08.027?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Andrew T. Foerster & Pierre-Daniel G. Sarte & Mark W. Watson, 2011. "Sectoral versus Aggregate Shocks: A Structural Factor Analysis of Industrial Production," Journal of Political Economy, University of Chicago Press, vol. 119(1), pages 1-38.
    2. 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.
    3. Vasco Carvalho & Xavier Gabaix, 2013. "The Great Diversification and Its Undoing," American Economic Review, American Economic Association, vol. 103(5), pages 1697-1727, August.
    4. Julian di Giovanni & Andrei A. Levchenko & Isabelle Mejean, 2014. "Firms, Destinations, and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 82(4), pages 1303-1340, July.
    5. 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.
    6. Da Silva, Sergio & Matsushita, Raul & Silveira, Eliza, 2013. "Hidden power law patterns in the top European football leagues," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5376-5386.
    7. Xavier Gabaix, 2016. "Power Laws in Economics: An Introduction," Journal of Economic Perspectives, American Economic Association, vol. 30(1), pages 185-206, Winter.
    8. Xavier Gabaix, 2011. "The Granular Origins of Aggregate Fluctuations," Econometrica, Econometric Society, vol. 79(3), pages 733-772, May.
    9. 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.
    10. 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.
    11. Pascoal, Rui & Augusto, Mário & Monteiro, A.M., 2016. "Size distribution of Portuguese firms between 2006 and 2012," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 458(C), pages 342-355.
    12. Robert E. Lucas Jr., 1978. "On the Size Distribution of Business Firms," Bell Journal of Economics, The RAND Corporation, vol. 9(2), pages 508-523, Autumn.
    13. Julian di Giovanni & Andrei A. Levchenko, 2012. "Country Size, International Trade, and Aggregate Fluctuations in Granular Economies," Journal of Political Economy, University of Chicago Press, vol. 120(6), pages 1083-1132.
    14. 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.
    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 & Michiko Miyano, 2017. "Zipf's law for share price and company fundamentals," Papers 1702.00144, arXiv.org.
    17. 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.
    18. 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.
    19. Hall, Bronwyn H, 1987. "The Relationship between Firm Size and Firm Growth in the U.S. Manufacturing Sector," Journal of Industrial Economics, Wiley Blackwell, vol. 35(4), pages 583-606, June.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Petra Štamfestová & Lukáš Sobíšek & Jiří Hnilica, 2023. "Firm Size Distribution in the Central European Context," Central European Business Review, Prague University of Economics and Business, vol. 2023(5), pages 151-175.
    2. Tomaschitz, Roman, 2020. "Multiply broken power-law densities as survival functions: An alternative to Pareto and lognormal fits," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    3. Maia, Adriano & Oliveira, Guilherme De & Matsushita, Raul & Da Silva, Sergio, 2021. "The granularity of the Brazilian banking market," The North American Journal of Economics and Finance, Elsevier, vol. 58(C).

    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. 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.
    2. 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.
    3. 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.
    4. Petra Štamfestová & Lukáš Sobíšek & Jiří Hnilica, 2023. "Firm Size Distribution in the Central European Context," Central European Business Review, Prague University of Economics and Business, vol. 2023(5), pages 151-175.
    5. 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.
    6. Alex Coad, 2007. "Firm Growth: a Survey," Post-Print halshs-00155762, HAL.
    7. 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.
    8. Brownlees, Christian & Mesters, Geert, 2021. "Detecting granular time series in large panels," Journal of Econometrics, Elsevier, vol. 220(2), pages 544-561.
    9. Stefano Costa & Federico Sallusti & Claudio Vicarelli, 2022. "Trade networks and shock transmission capacity: a new taxonomy of Italian industries," Economia e Politica Industriale: Journal of Industrial and Business Economics, Springer;Associazione Amici di Economia e Politica Industriale, vol. 49(1), pages 133-153, March.
    10. Grigoli, Francesco & Luttini, Emiliano & Sandri, Damiano, 2023. "Idiosyncratic shocks and aggregate fluctuations in an emerging market," Journal of Development Economics, Elsevier, vol. 160(C).
    11. Glenn Magerman & Karolien De Bruyne & Emmanuel Dhyne & Jan Van Hove, 2016. "Heterogeneous firms and the micro origins of aggregate fluctuations," Working Paper Research 312, National Bank of Belgium.
    12. David Rezza Baqaee & Emmanuel Farhi, 2019. "The Macroeconomic Impact of Microeconomic Shocks: Beyond Hulten's Theorem," Econometrica, Econometric Society, vol. 87(4), pages 1155-1203, July.
    13. Buldyrev, Sergey V. & Salinger, Michael A. & Stanley, H. Eugene, 2016. "A statistical physics implementation of Coase׳s theory of the firm," Research in Economics, Elsevier, vol. 70(4), pages 536-557.
    14. Kang, Sang Hoon & Jiang, Zhuhua & Cheong, Chongcheul & Yoon, Seong-Min, 2011. "Changes of firm size distribution: The case of Korea," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 319-327.
    15. Stefano Costa & Federico Sallusti & Claudio Vicarelli, 2021. "Trade networks and shock transmission within the Italian production system," LEM Papers Series 2021/15, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    16. 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.
    17. Halvarsson, Daniel, 2013. "Industry Differences in the Firm Size Distribution," Ratio Working Papers 214, The Ratio Institute.
    18. Junho Na & Jeong-dong Lee & Chulwoo Baek, 2017. "Is the service sector different in size heterogeneity?," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 12(1), pages 95-120, April.
    19. Gaubert, Cecile & Itskhoki, Oleg & Vogler, Maximilian, 2021. "Government policies in a granular global economy," Journal of Monetary Economics, Elsevier, vol. 121(C), pages 95-112.
    20. Bremus, Franziska & Ludolph, Melina, 2021. "The nexus between loan portfolio size and volatility: Does bank capital regulation matter?," Journal of Banking & Finance, Elsevier, vol. 127(C).

    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:eee:phsmap:v:512:y:2018:i:c:p:68-73. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.