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Zipf's law and maximum sustainable growth

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  • Y. Malevergne
  • A. Saichev
  • D. Sornette

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. Remarkably, Zipf's law is the signature of the long-term optimal allocation of resources that ensures the maximum sustainable growth rate of an economy.

Suggested Citation

  • Y. Malevergne & A. Saichev & D. Sornette, 2010. "Zipf's law and maximum sustainable growth," Papers 1012.0199, arXiv.org.
  • Handle: RePEc:arx:papers:1012.0199
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    1. Patrizio Pagano & Fabiano Schivardi, 2003. "Firm Size Distribution and Growth," Scandinavian Journal of Economics, Wiley Blackwell, vol. 105(2), pages 255-274, June.
    2. Mark Gertler & Simon Gilchrist, 1994. "Monetary Policy, Business Cycles, and the Behavior of Small Manufacturing Firms," The Quarterly Journal of Economics, Oxford University Press, vol. 109(2), pages 309-340.
    3. 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.
    4. Esteban Rossi-Hansberg & Mark L. J. Wright, 2007. "Urban Structure and Growth," Review of Economic Studies, Oxford University Press, vol. 74(2), pages 597-624.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Jan Eeckhout, 2004. "Gibrat's Law for (All) Cities," American Economic Review, American Economic Association, vol. 94(5), pages 1429-1451, December.
    10. John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March.
    11. 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.
    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. Erzo G. J. Luttmer, 2007. "Selection, Growth, and the Size Distribution of Firms," The Quarterly Journal of Economics, Oxford University Press, vol. 122(3), pages 1103-1144.
    14. Reed, William J., 2001. "The Pareto, Zipf and other power laws," Economics Letters, Elsevier, vol. 74(1), pages 15-19, December.
    15. Jan Eeckhout, 2009. "Gibrat's Law for (All) Cities: Reply," American Economic Review, American Economic Association, vol. 99(4), pages 1676-1683, September.
    16. 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.
    17. 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.
    18. 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.
    19. 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.
    20. 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.
    21. 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.
    22. 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, vol. 14(3), pages 365-391, June.
    23. Erzo G. J. Luttmer, 2011. "On the Mechanics of Firm Growth," Review of Economic Studies, Oxford University Press, vol. 78(3), pages 1042-1068.
    24. 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.
    25. Dale Jorgenson & Masahiro Kuroda & Kazuyuki Motohashi, 2007. "Introduction," Chapters,in: Productivity in Asia, chapter 1 Edward Elgar Publishing.
    26. Xavier Gabaix, 2009. "Power Laws in Economics and Finance," Annual Review of Economics, Annual Reviews, vol. 1(1), pages 255-294, May.
    27. 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.
    28. 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.
    29. 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.
    30. Agarwal, Rajshree & Audretsch, David B, 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.
    31. Moshe Levy, 2009. "Gibrat's Law for (All) Cities: Comment," American Economic Review, American Economic Association, vol. 99(4), pages 1672-1675, September.
    32. 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.
    33. 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.
    34. Xavier Gabaix, 1999. "Zipf's Law for Cities: An Explanation," The Quarterly Journal of Economics, Oxford University Press, vol. 114(3), pages 739-767.
    35. 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.
    36. 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.
    37. Xavier Gabaix, 1999. "Zipf's Law and the Growth of Cities," American Economic Review, American Economic Association, vol. 89(2), pages 129-132, May.
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    2. 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.
    3. Xavier Gabaix & Jean‐Michel Lasry & Pierre‐Louis Lions & Benjamin Moll, 2016. "The Dynamics of Inequality," Econometrica, Econometric Society, vol. 84, pages 2071-2111, November.
    4. Charles I. Jones & Jihee Kim, 2014. "A Schumpeterian Model of Top Income Inequality," NBER Working Papers 20637, National Bureau of Economic Research, Inc.
    5. Gregor Semieniuk & Ellis Scharfenaker, 2014. "A Bayesian Latent Variable Mixture Model for Filtering Firm Profit Rate," SCEPA working paper series. SCEPA's main areas of research are macroeconomic policy, inequality and poverty, and globalization. 2014-1, Schwartz Center for Economic Policy Analysis (SCEPA), The New School.
    6. 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.
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    8. Davide Fiaschi & Imre Kondor & Matteo Marsili, 2013. "The Interrupted Power Law and The Size of Shadow Banking," Discussion Papers 2013/166, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
    9. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    10. Edouard Ribes, 2018. "Growth patterns of professional services firms," Working Papers hal-01762381, HAL.

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    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

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