IDEAS home Printed from https://ideas.repec.org/a/eee/dyncon/v37y2013i6p1195-1212.html
   My bibliography  Save this article

Zipf's law and maximum sustainable growth

Author

Listed:
  • Malevergne, Y.
  • Saichev, A.
  • Sornette, D.

Abstract

Zipf's law states that the number of firms with size greater than S is inversely proportional to S. Most explanations start with Gibrat's rule of proportional growth but require additional constraints. We show that Gibrat's rule, at all firm levels, yields Zipf's law under a balance condition between the effective growth rate of incumbent firms (which includes their possible demise) and the growth rate of investments in entrant firms. Under the additional assumption that firms do not consume more resources than available, we show that Zipf's law is the signature that firms grow at the maximum reachable long-term rate.

Suggested Citation

  • Malevergne, Y. & Saichev, A. & Sornette, D., 2013. "Zipf's law and maximum sustainable growth," Journal of Economic Dynamics and Control, Elsevier, vol. 37(6), pages 1195-1212.
    • Handle: RePEc:eee:dyncon:v:37:y:2013:i:6:p:1195-1212
    DOI: 10.1016/j.jedc.2013.02.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165188913000341
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jedc.2013.02.004?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    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. Esteban Rossi-Hansberg & Mark L. J. Wright, 2007. "Urban Structure and Growth," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 597-624.
    3. Mark Gertler & Simon Gilchrist, 1994. "Monetary Policy, Business Cycles, and the Behavior of Small Manufacturing Firms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 109(2), pages 309-340.
    4. Bonaccorsi di Patti, Emilia & Dell'Ariccia, Giovanni, 2004. "Bank Competition and Firm Creation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 36(2), pages 225-251, April.
    5. Da Rin, Marco & Di Giacomo, Marina & Sembenelli, Alessandro, 2011. "Entrepreneurship, firm entry, and the taxation of corporate income: Evidence from Europe," Journal of Public Economics, Elsevier, vol. 95(9), pages 1048-1066.
    6. Alex Coad, 2010. "The Exponential Age Distribution and the Pareto Firm Size Distribution," Journal of Industry, Competition and Trade, Springer, vol. 10(3), pages 389-395, September.
    7. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    8. John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March.
    9. Eric Bartelsman & Stefano Scarpetta & Fabiano Schivardi, 2003. "Comparative Analysis of Firm Demographics and Survival: Micro-Level Evidence for the OECD Countries," OECD Economics Department Working Papers 348, OECD Publishing.
    10. Reed, William J., 2001. "The Pareto, Zipf and other power laws," Economics Letters, Elsevier, vol. 74(1), pages 15-19, December.
    11. Peretto, Pietro F., 1999. "Firm size, rivalry and the extent of the market in endogenous technological change," European Economic Review, Elsevier, vol. 43(9), pages 1747-1773, October.
    12. Klapper, Leora & Laeven, Luc & Rajan, Raghuram, 2006. "Entry regulation as a barrier to entrepreneurship," Journal of Financial Economics, Elsevier, vol. 82(3), pages 591-629, December.
    13. Galor, Oded, 2005. "From Stagnation to Growth: Unified Growth Theory," Handbook of Economic Growth, in: Philippe Aghion & Steven Durlauf (ed.), Handbook of Economic Growth, edition 1, volume 1, chapter 4, pages 171-293, Elsevier.
    14. Acs,Zoltan J. & Carlsson,Bo & Karlsson,Charlie (ed.), 1999. "Entrepreneurship, Small and Medium-Sized Enterprises and the Macroeconomy," Cambridge Books, Cambridge University Press, number 9780521621052.
    15. 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.
    16. Eric Bartelsman & Stefano Scarpetta & Fabiano Schivardi, 2005. "Comparative analysis of firm demographics and survival: evidence from micro-level sources in OECD countries," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 14(3), pages 365-391, June.
    17. Davis, Steven J & Haltiwanger, John & Schuh, Scott, 1996. "Small Business and Job Creation: Dissecting the Myth and Reassessing the Facts," Small Business Economics, Springer, vol. 8(4), pages 297-315, August.
    18. Zhang, Qunzhi & Sornette, Didier, 2011. "Empirical test of the origin of Zipf’s law in growing social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4124-4130.
    19. 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.
    20. Marco Da Rin & Marina Di Giacomo & Alessandro Sembenelli, 2010. "Corporate Taxation and the Size of New Firms: Evidence from Europe," Journal of the European Economic Association, MIT Press, vol. 8(2-3), pages 606-616, 04-05.
    21. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    22. Giesen, Kristian & Zimmermann, Arndt & Suedekum, Jens, 2010. "The size distribution across all cities - Double Pareto lognormal strikes," Journal of Urban Economics, Elsevier, vol. 68(2), pages 129-137, September.
    23. Reinhold Grotz & Udo Brixy, 2003. "Regional Patterns and Determinants of the Success of New Firms in Western Germany," ERSA conference papers ersa03p270, European Regional Science Association.
    24. Erzo G. J. Luttmer, 2011. "On the Mechanics of Firm Growth," Review of Economic Studies, Oxford University Press, vol. 78(3), pages 1042-1068.
    25. Esteban Rossi-Hansberg & Mark L. J. Wright, 2007. "Establishment Size Dynamics in the Aggregate Economy," American Economic Review, American Economic Association, vol. 97(5), pages 1639-1666, December.
    26. Moshe Levy, 2009. "Gibrat's Law for (All) Cities: Comment," American Economic Review, American Economic Association, vol. 99(4), pages 1672-1675, September.
    27. Richard E. Caves, 1998. "Industrial Organization and New Findings on the Turnover and Mobility of Firms," Journal of Economic Literature, American Economic Association, vol. 36(4), pages 1947-1982, December.
    28. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 114(3), pages 739-767.
    29. Alfarano, Simone & Milaković, Mishael & Irle, Albrecht & Kauschke, Jonas, 2012. "A statistical equilibrium model of competitive firms," Journal of Economic Dynamics and Control, Elsevier, vol. 36(1), pages 136-149.
    30. Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
    31. Patrizio Pagano & Fabiano Schivardi, 2003. "Firm Size Distribution and Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 105(2), pages 255-274, June.
    32. Foss, Nicolai & Mahnke, Volker (ed.), 2000. "Competence, Governance, and Entrepreneurship: Advances in Economic Strategy Research," OUP Catalogue, Oxford University Press, number 9780198297178, Decembrie.
    33. Timothy Dunne & Mark J. Roberts & Larry Samuelson, 1988. "Patterns of Firm Entry and Exit in U.S. Manufacturing Industries," RAND Journal of Economics, The RAND Corporation, vol. 19(4), pages 495-515, Winter.
    34. Erzo G. J. Luttmer, 2007. "Selection, Growth, and the Size Distribution of Firms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 122(3), pages 1103-1144.
    35. 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.
    36. Jan Eeckhout, 2009. "Gibrat's Law for (All) Cities: Reply," American Economic Review, American Economic Association, vol. 99(4), pages 1676-1683, September.
    37. Silvia Ardagna & Annamaria Lusardi, 2010. "Heterogeneity in the Effect of Regulation on Entrepreneurship and Entry Size," Journal of the European Economic Association, MIT Press, vol. 8(2-3), pages 594-605, 04-05.
    38. Timothy Dunne & Mark J. Roberts & Larry Samuelson, 1989. "The Growth and Failure of U. S. Manufacturing Plants," The Quarterly Journal of Economics, Oxford University Press, vol. 104(4), pages 671-698.
    39. Rajshree Agarwal & David B. Audretsch, 2001. "Does Entry Size Matter? The Impact of the Life Cycle and Technology on Firm Survival," Journal of Industrial Economics, Wiley Blackwell, vol. 49(1), pages 21-43, March.
    40. Udo Brixy & Reinhold Grotz, 2007. "Regional patterns and determinants of birth and survival of new firms in Western Germany," Entrepreneurship & Regional Development, Taylor & Francis Journals, vol. 19(4), pages 293-312, July.
    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. Vandermarliere, B. & Ryckebusch, J. & Schoors, K. & Cauwels, P. & Sornette, D., 2017. "Discrete hierarchy of sizes and performances in the exchange-traded fund universe," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 111-123.
    2. Corrado Di Guilmi & Yoshi Fujiwara, 2020. "Does the supply network shape the firm size distribution? The Japanese case," CAMA Working Papers 2020-66, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    3. Toda, Alexis Akira, 2016. "Zipf's Law: A Microfoundation," MPRA Paper 78985, University Library of Munich, Germany.
    4. Anindya S. Chakrabarti, 2017. "Scale-free distribution as an economic invariant: a theoretical approach," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 12(1), pages 1-26, April.
    5. Christian Schluter & Mark Trede, 2019. "Size distributions reconsidered," Econometric Reviews, Taylor & Francis Journals, vol. 38(6), pages 695-710, July.
    6. Xavier Gabaix & Jean‐Michel Lasry & Pierre‐Louis Lions & Benjamin Moll, 2016. "The Dynamics of Inequality," Econometrica, Econometric Society, vol. 84, pages 2071-2111, November.
    7. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    8. Ke Wu & Spencer Wheatley & Didier Sornette, 2018. "Classification of cryptocurrency coins and tokens by the dynamics of their market capitalisations," Papers 1803.03088, arXiv.org, revised May 2018.
    9. Charles I. Jones & Jihee Kim, 2018. "A Schumpeterian Model of Top Income Inequality," Journal of Political Economy, University of Chicago Press, vol. 126(5), pages 1785-1826.
    10. Davide Fiaschi & Imre Kondor & Matteo Marsili & Valerio Volpati, 2014. "The Interrupted Power Law and the Size of Shadow Banking," PLOS ONE, Public Library of Science, vol. 9(4), pages 1-8, April.
    11. Jo~ao Pedro Jerico & Franc{c}ois P. Landes & Matteo Marsili & Isaac P'erez Castillo & Valerio Volpati, 2016. "When does inequality freeze an economy?," Papers 1602.07300, arXiv.org, revised Apr 2016.
    12. Didier Sornette & Thomas Maillart & Giacomo Ghezzi, 2014. "How Much Is the Whole Really More than the Sum of Its Parts? 1 ⊞ 1 = 2.5: Superlinear Productivity in Collective Group Actions," PLOS ONE, Public Library of Science, vol. 9(8), pages 1-15, August.
    13. Sandro Claudio Lera & Didier Sornette, 2017. "Quantification of the evolution of firm size distributions due to mergers and acquisitions," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-16, August.
    14. Didier SORNETTE, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based Models," Swiss Finance Institute Research Paper Series 14-25, Swiss Finance Institute.
    15. Gregor Semieniuk & Ellis Scharfenaker, 2014. "A Bayesian Latent Variable Mixture Model for Filtering Firm Profit Rate," SCEPA working paper series. 2014-1, Schwartz Center for Economic Policy Analysis (SCEPA), The New School.
    16. Edouard Ribes, 2018. "Growth patterns of US professional services firms," Working Papers hal-01762381, HAL.

    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. 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.
    2. Costas Arkolakis, 2016. "A Unified Theory of Firm Selection and Growth," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(1), pages 89-155.
    3. Halvarsson, Daniel, 2013. "Industry Differences in the Firm Size Distribution," Ratio Working Papers 214, The Ratio Institute.
    4. Acemoglu, Daron & Cao, Dan, 2015. "Innovation by entrants and incumbents," Journal of Economic Theory, Elsevier, vol. 157(C), pages 255-294.
    5. Ramos, Arturo, 2015. "Log-growth distributions of US city sizes and non-Lévy processes," MPRA Paper 66561, University Library of Munich, Germany.
    6. Ruben Dewitte & Michel Dumont & Glenn Rayp & Peter Willemé, 2022. "Unobserved heterogeneity in the productivity distribution and gains from trade," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 55(3), pages 1566-1597, August.
    7. Rafael González-Val, 2019. "US city-size distribution and space," Spatial Economic Analysis, Taylor & Francis Journals, vol. 14(3), pages 283-300, July.
    8. 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.
    9. Erzo G.J. Luttmer, 2010. "Models of Growth and Firm Heterogeneity," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 547-576, September.
    10. Ramos, Arturo & Sanz-Gracia, Fernando & González-Val, Rafael, 2013. "A new framework for the US city size distribution: Empirical evidence and theory," MPRA Paper 52190, University Library of Munich, Germany.
    11. Giesen, Kristian & Suedekum, Jens, 2014. "City age and city size," European Economic Review, Elsevier, vol. 71(C), pages 193-208.
    12. Sandro Claudio Lera & Didier Sornette, 2017. "Quantification of the evolution of firm size distributions due to mergers and acquisitions," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-16, August.
    13. Marco Vivarelli, 2013. "Is entrepreneurship necessarily good? Microeconomic evidence from developed and developing countries," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 22(6), pages 1453-1495, December.
    14. Enrico Santarelli & Marco Vivarelli, 2007. "Entrepreneurship and the process of firms’ entry, survival and growth," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 16(3), pages 455-488, June.
    15. Monika Mrázová & J. Peter Neary & Mathieu Parenti, 2021. "Sales and Markup Dispersion: Theory and Empirics," Econometrica, Econometric Society, vol. 89(4), pages 1753-1788, July.
    16. Bee, Marco & Riccaboni, Massimo & Schiavo, Stefano, 2017. "Where Gibrat meets Zipf: Scale and scope of French firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 265-275.
    17. Ronan Lyons & Elisa Maria Tirindelli, 2022. "The Rise & Fall of Urban Concentration in Britain: Zipf, Gibrat and Gini across two centuries," Trinity Economics Papers tep0522, Trinity College Dublin, Department of Economics.
    18. Arturo, Ramos, 2019. "Have the log-population processes stationary and independent increments? Empirical evidence for Italy, Spain and the USA along more than a century," MPRA Paper 93562, University Library of Munich, Germany.
    19. Valente J. Matlaba & Mark J. Holmes & Philip McCann & Jacques Poot, 2013. "A Century Of The Evolution Of The Urban System In Brazil," Review of Urban & Regional Development Studies, Wiley Blackwell, vol. 25(3), pages 129-151, November.
    20. Ramos, Arturo & Sanz-Gracia, Fernando, 2015. "US city size distribution revisited: Theory and empirical evidence," MPRA Paper 64051, University Library of Munich, Germany.

    More about this item

    Keywords

    Firm growth; Gibrat's law; Zipf's law;
    All these keywords.

    JEL classification:

    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

    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:eee:dyncon:v:37:y:2013:i:6:p:1195-1212. 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.elsevier.com/locate/jedc .

    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.