IDEAS home Printed from https://ideas.repec.org/p/ssa/lemwps/2007-10.html
   My bibliography  Save this paper

On the Irreconcilability of Pareto and Gibrat Laws

Author

Listed:
  • Giulio Bottazzi

Abstract

If business firms face a multiplicative growth process in which their growth rates are independent from their sizes, then these sizes cannot be distributed according to a stationary Pareto distribution. At the same time , the Laplace distribution of growth rates cannot be easily reconciled with a Pareto distribution of firm sizes. Recent contributions, using formal arguments, seems to contrast these statements. We prove that the proposed formal results are wrong.

Suggested Citation

  • Giulio Bottazzi, 2007. "On the Irreconcilability of Pareto and Gibrat Laws," LEM Papers Series 2007/10, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  • Handle: RePEc:ssa:lemwps:2007/10
    as

    Download full text from publisher

    File URL: http://www.lem.sssup.it/WPLem/files/2007-10.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Scalas, Enrico, 2006. "The application of continuous-time random walks in finance and economics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 362(2), pages 225-239.
    2. John Sutton, 1997. "Gibrat's Legacy," Journal of Economic Literature, American Economic Association, vol. 35(1), pages 40-59, March.
    3. Giovanni Dosi, 2008. "Statistical Regularities in the Evolution of Industries. A Guide through Some Evidence and Challenges for the Theory," L'industria, Società editrice il Mulino, issue 2, pages 185-220.
    4. Aoyama, Hideaki & Souma, Wataru & Fujiwara, Yoshi, 2003. "Growth and fluctuations of personal and company's income," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 352-358.
    5. 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.
    6. Malerba,Franco & Brusoni,Stefano (ed.), 2007. "Perspectives on Innovation," Cambridge Books, Cambridge University Press, number 9780521685610, October.
    7. Giulio Bottazzi & Angelo Secchi, 2006. "Explaining the distribution of firm growth rates," RAND Journal of Economics, RAND Corporation, vol. 37(2), pages 235-256, June.
    8. Fujiwara, Yoshi & Souma, Wataru & Aoyama, Hideaki & Kaizoji, Taisei & Aoki, Masanao, 2003. "Growth and fluctuations of personal income," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 321(3), pages 598-604.
    9. 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.
    10. Gatti, Domenico Delli & Guilmi, Corrado Di & Gaffeo, Edoardo & Giulioni, Gianfranco & Gallegati, Mauro & Palestrini, Antonio, 2005. "A new approach to business fluctuations: heterogeneous interacting agents, scaling laws and financial fragility," Journal of Economic Behavior & Organization, Elsevier, vol. 56(4), pages 489-512, April.
    11. 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.
    12. Franco Malerba, 2007. "Innovation and the evolution of industries," Springer Books, in: Uwe Cantner & Franco Malerba (ed.), Innovation, Industrial Dynamics and Structural Transformation, pages 7-27, Springer.
    13. Malerba,Franco & Brusoni,Stefano (ed.), 2007. "Perspectives on Innovation," Cambridge Books, Cambridge University Press, number 9780521866644, October.
    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. Hernan Mondani & Petter Holme & Fredrik Liljeros, 2014. "Fat-Tailed Fluctuations in the Size of Organizations: The Role of Social Influence," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-9, July.
    2. Ishikawa, Atushi, 2007. "The uniqueness of firm size distribution function from tent-shaped growth rate distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 79-84.
    3. Davide Provenzano, 2017. "On the World Distribution of Income," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 63(1), pages 189-196, March.
    4. 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.
    5. Cirillo, Pasquale, 2010. "An analysis of the size distribution of Italian firms by age," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(3), pages 459-466.
    6. Xu, Yan & Wang, Yougui & Tao, Xiaobo & Ližbetinová, Lenka, 2017. "Evidence of Chinese income dynamics and its effects on income scaling law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 487(C), pages 143-152.

    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. Heinrich, Torsten, 2016. "The Narrow and the Broad Approach to Evolutionary Modeling in Economics," MPRA Paper 75797, University Library of Munich, Germany.
    2. Heinrich, Torsten & Dai, Shuanping, 2016. "Diversity of firm sizes, complexity, and industry structure in the Chinese economy," Structural Change and Economic Dynamics, Elsevier, vol. 37(C), pages 90-106.
    3. Marco Capasso & Elena Cefis & Alessandro Sapio, 2013. "Reconciling quantile autoregressions of firm size and variance–size scaling," Small Business Economics, Springer, vol. 41(3), pages 609-632, October.
    4. Giovanni Dosi & Mauro Napoletano & Andrea Roventini & Tania Treibich, 2017. "Micro and macro policies in the Keynes+Schumpeter evolutionary models," Journal of Evolutionary Economics, Springer, vol. 27(1), pages 63-90, January.
    5. Dosi, Giovanni & Fagiolo, Giorgio & Roventini, Andrea, 2010. "Schumpeter meeting Keynes: A policy-friendly model of endogenous growth and business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1748-1767, September.
    6. Dosi, Giovanni & Nelson, Richard R., 2010. "Technical Change and Industrial Dynamics as Evolutionary Processes," Handbook of the Economics of Innovation, in: Bronwyn H. Hall & Nathan Rosenberg (ed.), Handbook of the Economics of Innovation, edition 1, volume 1, chapter 0, pages 51-127, Elsevier.
    7. Werner Hölzl & Peter Huber, 2014. "Firm Level Job Creation Rates Over The Business Cycle," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 4(6), pages 837-852, June.
    8. 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.
    9. Mauro Napoletano & Eric Guerci & Nobuyuki Hanaki, 2018. "Recent advances in financial networks and agent-based model validation," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 13(1), pages 1-7, April.
    10. Carolina Castaldi & Giovanni Dosi, 2009. "The patterns of output growth of firms and countries: Scale invariances and scale specificities," Empirical Economics, Springer, vol. 37(3), pages 475-495, December.
    11. Halvarsson, Daniel, 2013. "Industry Differences in the Firm Size Distribution," Ratio Working Papers 214, The Ratio Institute.
    12. Giovanni Dosi & Mauro Napoletano & Andrea Roventini & Tania Treibich, 2019. "Debunking the granular origins of aggregate fluctuations: from real business cycles back to Keynes," Journal of Evolutionary Economics, Springer, vol. 29(1), pages 67-90, March.
    13. Dosi, Giovanni & Fagiolo, Giorgio & Napoletano, Mauro & Roventini, Andrea & Treibich, Tania, 2015. "Fiscal and monetary policies in complex evolving economies," Journal of Economic Dynamics and Control, Elsevier, vol. 52(C), pages 166-189.
    14. Fontanelli, Luca & Guerini, Mattia & Napoletano, Mauro, 2023. "International trade and technological competition in markets with dynamic increasing returns," Journal of Economic Dynamics and Control, Elsevier, vol. 149(C).
    15. Dosi, Giovanni & Fagiolo, Giorgio & Napoletano, Mauro & Roventini, Andrea, 2013. "Income distribution, credit and fiscal policies in an agent-based Keynesian model," Journal of Economic Dynamics and Control, Elsevier, vol. 37(8), pages 1598-1625.
    16. Giovanni Dosi & Mauro Napoletano & Andrea Roventini & Joseph E. Stiglitz & Tania Treibich, 2020. "Rational Heuristics? Expectations And Behaviors In Evolving Economies With Heterogeneous Interacting Agents," Economic Inquiry, Western Economic Association International, vol. 58(3), pages 1487-1516, July.
    17. repec:spo:wpecon:info:hdl:2441/eu4vqp9ompqllr09j0h130d0n is not listed on IDEAS
    18. Ítalo Pedrosa & Dany Lang, 2018. "Heterogeneity, distribution and financial fragility of non-financial firms: an agent-based stock-flow consistent (AB-SFC) model," Working Papers hal-01937186, HAL.
    19. Klaus Friesenbichler & Werner Hölzl, 2020. "High-growth firm shares in Austrian regions: the role of economic structures," Regional Studies, Taylor & Francis Journals, vol. 54(11), pages 1585-1595, November.
    20. Nanditha Mathew, 2017. "Drivers of firm growth: micro-evidence from Indian manufacturing," Journal of Evolutionary Economics, Springer, vol. 27(3), pages 585-611, July.
    21. Francesco Lamperti & Giovanni Dosi & Mauro Napoletano & Andrea Roventini & Alessandro Sapio, 2018. "And then he wasn't a she : Climate change and green transitions in an agent-based integrated assessment model," Working Papers hal-03443464, HAL.

    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:ssa:lemwps:2007/10. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/labssit.html .

    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.