Advertisement

Modelling the Growth Statistics of Economic Organizations

  • L. A. N. Amaral
  • P. Gopikrishnan
  • V. Plerou
  • H. E. Stanley
Conference paper

Abstract

We apply methods and concepts of statistical physics to the study of economic organizations. We identify robust, universal, characteristics of the time evolution of economic organizations. Specifically, we find the existence of scaling laws describing the growth of the size of these organizations. We study a model assuming a complex evolving internal structure of an organization that is able to reproduce many of the empirical findings.

Keywords

Gross Domestic Product Down Syndrome Annual Growth Rate Economic Organization Business Firm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford, Oxford University Press, 1971)Google Scholar
  2. 1a.
    R. Jackiw, “Introducing Scale Symmetry,” Phys. Today 25(1) (1972) 23–27.Google Scholar
  3. 2.
    C.-K. Peng, S. V. Buldyrev, A. L. Goldberger, S. Havlin, F. Sciortino, M. Simons and H. E. Stanley, “Long-Range Correlations in Nucleotide Sequences,” Nature 356 (1992) 168–171;ADSCrossRefGoogle Scholar
  4. A. Arneodo, E. Bacry, P. V. Graves and J. F. Muzy, “Characterizing Long-Range Correlations in DNA-Sequences from Wavelet Analysis,” Phys. Rev. Lett. 74 (1995) 3293–3296.ADSCrossRefGoogle Scholar
  5. 3.
    B. Suki, A.-L. Barabási, Z. Hantos, F. Peták and H. E. Stanley, “Avalanches and Power Law Behaviour in Lung Inflation,” Nature 368 (1994) 615–618.ADSCrossRefGoogle Scholar
  6. 4.
    B. T. Hyman et al., “Quantitative Analysis of Senile Plaques in Alzheimer Disease: Observation of Log-Normal Size Distribution and of Differences Associated with Apolipoprotein E Genotype and Trisomy 21 (Down Syndrome),” Proc. Natl. Acad. Sci. USA 92 (1995) 3586–3590;ADSCrossRefGoogle Scholar
  7. 4a.
    L. Cruz et al., “Aggregation and Disaggregation of Senile Plaques in Alzheimer Disease,” Proc. Natl. Acad. Sci. USA 94 (1997) 7612–7616;ADSCrossRefGoogle Scholar
  8. 4b.
    R. B. Knowles et al., “Plaque-Induced Neural Network Disruption in Alzheimer’s Disease,” Proc. Natl. Acad. Sci. USA 96 (1999) 5274–5279.ADSCrossRefGoogle Scholar
  9. 5.
    C.-K. Peng, S. Havlin, H. E. Stanley and A. L. Goldberger, “Quantification of Scaling Exponents and Crossover Phenomena in Nonstationary Heartbeat Time Series,” Chaos 5 (1995) 82–87;ADSCrossRefGoogle Scholar
  10. 5a.
    L. A. N. Amaral, A. L. Goldberger, P. Ch. Ivanov, and H. E. Stanley, “Scale-Independent Measures and Pathologic Cardiac Dynamics,” Phys. Rev. Lett. 81 (1998) 2388–2391;ADSCrossRefGoogle Scholar
  11. 5b.
    P. Ch. Ivanov, L. A. N. Amaral, A. L. Goldberger and H. E. Stanley, “Stochastic Feedback and the Regulation of Biological Rhythms,” Europhys. Lett. 43 (1998) 363–369;ADSCrossRefGoogle Scholar
  12. 5c.
    P. Ch. Ivanov, L. A. N. Amaral, A. L. Goldberger, S. Havlin, M. G. Rosenblum, Z. Struzik, and H. E. Stanley, “Multifractality in Human Heartbeat Dynamics,” Nature 399 (1999) 461–465;ADSCrossRefGoogle Scholar
  13. 5d.
    P. Ch. Ivanov, A. Bunde, L. A. N. Amaral, J. Fritsch-Yelle, R. M. Baevsky, S. Havlin, H. E. Stanley, and A. L. Goldberger, “Sleep-wake differences in scaling behavior of the human heartbeat: Analysis of terrestrial and long-term space flight data,” Europhys. Lett. 48 (1999) 594–600;ADSCrossRefGoogle Scholar
  14. 5e.
    A. L. Goldberger, L. A. N. Amaral, L. Glass, S. Havlin, J. M. Hausdorff, P. Ch. Ivanov, R. G. Mark, J. E. Mietus, G. B. Moody, C.-K. Peng, and H. E. Stanley, “Physio Bank, Physio Toolkit, and Physio Net: Components of a new Research Resource for Complex Physiologic Signals,” Circulation 101 (2000) e215–e220;CrossRefGoogle Scholar
  15. 5f.
    P. Bernaola-Galván, P. Ch. Ivanov, L. A. N. Amaral, and H. E. Stanley, “Scale invariance in the nonstationarity of physiologic signals,” arXiv:cond-mat/0005284 (2000).Google Scholar
  16. 6.
    L. A. N. Amaral, and M. Meyer, “Environmental changes, coextinction, and patterns in the fossil record,” Phys. Rev. Lett. 82 (1999) 652–655;ADSCrossRefGoogle Scholar
  17. 6a.
    J. Camacho, R. Guimerà, and L. A. N. Amaral, “Analytical solution of a model for complex food webs,” arXiv:cond-mat/0102127 (2001);Google Scholar
  18. 6b.
    J. Camacho, R. Guimerà, and L. A. N. Amaral, “Robust patterns in food web structure” arXiv:condmat/0103114 (2001).Google Scholar
  19. 7.
    . M. Batty and P. Longley, Fractal Cities (San Diego: Academic Press, 1994);MATHGoogle Scholar
  20. 7a.
    H. Makse, S. Havlin, and H. E. Stanley, “Modeling Urban Growth Patterns,” Nature 377 (1995) 608–612;ADSCrossRefGoogle Scholar
  21. 7b.
    X. Gabaix, “Zipf’s Law for Cities: An Explanation,” Quarterly J. Econ. 114 (1999) 739–767.MATHCrossRefGoogle Scholar
  22. 8.
    L. A. N. Amaral, A. Scala, M. Barthélémy, and H. E. Stanley, “Classes of small-world networks,” Proc. Nat. Acad. Sci. USA 97 (2000) 11149–11152;ADSCrossRefGoogle Scholar
  23. 8a.
    M. Barthélémy, and L. A. N. Amaral, “Small-world networks: Evidence for a crossover picture,” Phys. Rev. Lett. 82 (1999) 3180–3183;ADSCrossRefGoogle Scholar
  24. 8b.
    A. Scala, L. A. N. Amaral, and M. Barthélémy, “Small-world networks and the conformation space of a lattice polymer chain” arXiv:cond-mat/0004380 (2000).Google Scholar
  25. 9.
    B. B. Mandelbrot, “The Variation of Certain Speculative Prices,” J. Business 36 (1963) 394–419;CrossRefGoogle Scholar
  26. 9a.
    A. Pagan, “The Econometrics of Financial Markets,” J. Empirical Finance 3 (1996) 15–102;Google Scholar
  27. 9a.
    R. N. Mantegna and H. E. Stanley, “Scaling Behavior in the Dynamics of an Economic Index” Nature 376 (1995) 46–49;ADSCrossRefGoogle Scholar
  28. 9b.
    R. N. Mantegna and H. E. Stanley, “Turbulence and Exchange Markets,” Nature 383 (1996) 587–588;ADSCrossRefGoogle Scholar
  29. 9c.
    T. Lux, “The Stable Paretian Hypothesis and the Frequency of Large Returns: An Examination of Major German Stocks,” Applied Financial Economics 6 (1996) 463–475;Google Scholar
  30. 9d.
    U. A. Muller, M. M. Dacorogna, and O. V. Pictet, “Heavy Tails in High-Frequency Financial Data,” in A Practical Guide to Heavy Tails, edited by R. J. Adler, R. E. Feldman, and M. S. Taqqu (Birkhäuser Publishers, 1998), pp. 83–311;Google Scholar
  31. 9e.
    V. Plerou, P. Gopikrishnan, L. A. N. Amaral, M. Meyer, and H. E. Stanley, “Scaling of the Distribution of Price Fluctuations of Individual Companies,” Phys. Rev. E 60 (1999) 6519–6529;ADSCrossRefGoogle Scholar
  32. 9f.
    P. Gopikrishnan, V. Plerou, L. A. N. Amaral, M. Meyer, and H. E. Stanley, “Scaling of the Distributions of Fluctuations of Financial Market Indices,” Phys. Rev. E 60 (1999) 5305–5316.ADSCrossRefGoogle Scholar
  33. 10.
    U. A. Muller, M. M. Dacorogna, R. B. Olsen, O. V. Pictet, M. Schwarz, and C. Morgenegg, Journal of Banking and Finance 14 (1990) 1189–1195.CrossRefGoogle Scholar
  34. 11.
    M. H. R. Stanley, L. A. N. Amaral, S. V. Buldyrev, S. Havlin, H. Leschhorn, P. Maass, M. A. Salinger, and H. E. Stanley, “Scaling Behaviour in the Growth of Companies,” Nature 379 (1996) 804–806.ADSCrossRefGoogle Scholar
  35. 12.
    L. A. N. Amaral, S. V. Buldyrev, S. Havlin, H. Leschhorn, P. Maass, M. A. Salinger, H. E. Stanley, and M. H. R. Stanley, “Scaling Behavior in Economics: I. Empirical Results for Company Growth,” J. Phys. I France 7 (1997) 621–633.CrossRefGoogle Scholar
  36. 13.
    Y. Lee, L. A. N. Amaral, D. Canning, M. Meyer, and H. E. Stanley, “Universal Features in the Growth Dynamics of Complex Organizations,” Phys. Lev. Lett. 81 (1998) 3275–3278.ADSCrossRefGoogle Scholar
  37. 14.
    V. Plerou, L. A. N. Amaral, P. Gopikrishnan, M. Meyer, and H. E. Stanley, “Similarities between the Growth Dynamics of University Research and of Competitive Economic Activities,” Nature 400 (1999) 433–437.ADSCrossRefGoogle Scholar
  38. 15.
    H. F. Moed and M. Luwel, “Science Policy: the Business of Research,” Nature 400 (1999) 411–412.ADSCrossRefGoogle Scholar
  39. 16.
    H. E. Stanley, “Power Laws and Universality,” Nature 378 (1995) 554–555.ADSCrossRefGoogle Scholar
  40. 17.
    H. E. Stanley, “Scaling, Universality, and Renormalization: Three Pillars of Modern Critical Phenomena,” Rev. Mod. Phys. 71 (1999) S358-S366 [Special Issue for the Centennial of the American Physical Society].CrossRefGoogle Scholar
  41. 18.
    R. Gibrat, Les Inégalités Economiques (Sirey, Paris, 1931);MATHGoogle Scholar
  42. 18a.
    Y. Ijiri and H. A. Simon, Skew Distributions and the Sizes of Business Firms (North Holland, Amsterdam, 1977);MATHGoogle Scholar
  43. 18b.
    B. H. Hall, “The Relationship between Firm Size and Firm Growth in the U.S. Manufacturing Sector,” The J. Indust. Econ. 35 (1987) 583–606;CrossRefGoogle Scholar
  44. 18c.
    J. Sutton, “Gibrat’s Legacy,” J. Econ. Lit. 35 (1997) 40–59.Google Scholar
  45. 19.
    V. Pareto, Cours d’Economie Politique (Lausanne and Paris, 1897);Google Scholar
  46. 19a.
    P. Levy, Théorie de l’Addition des Variables Aléatoires (Gauthier-Villars, Paris, 1937);Google Scholar
  47. 19b.
    G. K. Zipf, Human Behavior and the Principle of Least Effort (Addison-Wesley, Cambridge MA, 1949);Google Scholar
  48. 19c.
    G. R. Carroll, “National city-size distribution: What do we know after 67 years of research?” Progress in Human Geography VI (1982) 1–43;Google Scholar
  49. 19d.
    M. Levy and S. Solomon, “Power Laws are Logarithmic Boltz-mann Laws,” Int. J. Mod. Phys. C 7 (1996) 595;ADSCrossRefGoogle Scholar
  50. 19e.
    O. Malcai O. Biham and S. Solomon, “Power-law distributions and Lévy-stable intermittent fluctuations in stochastic systems of many autocatalytic elements,” Phys. Rev. E 60 (1999) 1299;ADSGoogle Scholar
  51. 19f.
    A. Blank and S. Solomon, “Power laws in cities population, financial markets and internet sites (scaling in systems with a variable number of components),” Physica A 287 (2000) 279–288.MathSciNetADSCrossRefGoogle Scholar
  52. 20.
    S. N. Durlauf, “On the Convergence and Divergence of Growth Rates,” The Economic J. 106 (1996) 1016–1018.CrossRefGoogle Scholar
  53. 21.
    R. Summers and A. Heston, “The Penn World Tables (Mark 5): An expanded set of international comparisons, 1950–1988,” Quarterly J. Economics 106 (1991) 327–368.CrossRefGoogle Scholar
  54. 22.
    Press, W. H., et al. Numerical Recipes 2nd ed. (Cambridge University Press, Cambridge, 1992).Google Scholar
  55. 23.
    J. Sutton, “The Variance of Firm Growth Rates: The ‘Scaling’ Puzzle,” working paper, London School of Economics (2000).Google Scholar
  56. 24.
    L. A. N. Amaral, S. V. Buldyrev, S. Havlin, M. A. Salinger, and H. E. Stanley, “Power Law Scaling for a System of Interacting Units with Complex Internal Structure,” Phys. Rev. Letters 80 (1998) 1385–1388.ADSCrossRefGoogle Scholar
  57. 25.
    A. Chandler, Strategy and Structure (MIT Press, Cambridge, 1962).Google Scholar
  58. 26.
    M. Gort, Diversification and Integration in American Industry (Princeton University Press, Princeton, 1962).Google Scholar

Copyright information

© Springer Japan 2002

Authors and Affiliations

  • L. A. N. Amaral
    • 1
  • P. Gopikrishnan
    • 1
  • V. Plerou
    • 1
    • 2
  • H. E. Stanley
    • 1
  1. 1.Center for Polymer Studies and Department of PhysicsBoston UniversityBostonUSA
  2. 2.Department of PhysicsBoston CollegeBostonUSA

Personalised recommendations