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Scaling behavior in economics: II. Modeling of company growth

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  • S. V. Buldyrev
  • L. A. N. Amaral
  • S. Havlin
  • H. Leschhorn
  • P. Maass
  • M. A. Salinger
  • H. E. Stanley
  • M. H. R. Stanley

Abstract

In the preceding paper we presented empirical results describing the growth of publicly-traded United States manufacturing firms within the years 1974--1993. Our results suggest that the data can be described by a scaling approach. Here, we propose models that may lead to some insight into these phenomena. First, we study a model in which the growth rate of a company is affected by a tendency to retain an ``optimal'' size. That model leads to an exponential distribution of the logarithm of the growth rate in agreement with the empirical results. Then, we study a hierarchical tree-like model of a company that enables us to relate the two parameters of the model to the exponent $\beta$, which describes the dependence of the standard deviation of the distribution of growth rates on size. We find that $\beta = -\ln \Pi / \ln z$, where $z$ defines the mean branching ratio of the hierarchical tree and $\Pi$ is the probability that the lower levels follow the policy of higher levels in the hierarchy. We also study the distribution of growth rates of this hierarchical model. We find that the distribution is consistent with the exponential form found empirically.

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File URL: http://arxiv.org/pdf/cond-mat/9702085
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number cond-mat/9702085.

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Date of creation: Feb 1997
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Handle: RePEc:arx:papers:cond-mat/9702085

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Web page: http://arxiv.org/

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Cited by:
  1. Pammolli, Fabio & Fu, Dongfeng & Buldyrev, Sergey V. & Riccaboni, Massimo & Matia, Kaushik & Yamasaki, Kazuko & Stanley, H. Eugene, 2006. "A Generalized Preferential Attachment Model for Business Firms Growth Rates: I. Empirical Evidence," MPRA Paper 15983, University Library of Munich, Germany.
  2. Sandro Sapio & Grid Thoma, 2006. "The Growth of Industrial Sectors: Theoretical Insights and Empirical Evidence from U.S. Manufacturing," LEM Papers Series 2006/09, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
  3. Xavier Gabaix, 2009. "The Granular Origins of Aggregate Fluctuations," NBER Working Papers 15286, National Bureau of Economic Research, Inc.
  4. S. V. Buldyrev & F. Pammolli & M. Riccaboni & K. Yamasaki & D. Fu & K. Matia & H. E. Stanley, 2006. "A Generalized Preferential Attachment Model for Business Firms Growth Rates: II. Mathematical Treatment," Papers physics/0609020, arXiv.org.
  5. 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.
  6. Canning, D. & Amaral, L. A. N. & Lee, Y. & Meyer, M. & Stanley, H. E., 1998. "Scaling the volatility of GDP growth rates," Economics Letters, Elsevier, vol. 60(3), pages 335-341, September.
  7. Fioretti, Guido, 2007. "The production function," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 707-714.
  8. Stanley, H. Eugene & Plerou, Vasiliki & Gabaix, Xavier, 2008. "A statistical physics view of financial fluctuations: Evidence for scaling and universality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3967-3981.
  9. Chakrabarti, Anindya S., 2012. "Effects of the turnover rate on the size distribution of firms: An application of the kinetic exchange models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6039-6050.
  10. Guido Fioretti, 2005. "The Production Function," Papers physics/0511191, arXiv.org.
  11. Anindya S. Chakrabarti, 2011. "Firm dynamics in a closed, conserved economy: A model of size distribution of employment and related statistics," Papers 1112.2168, arXiv.org.
  12. Xavier Gabaix, 2004. "Power laws and the origins of aggregate fluctuations," Econometric Society 2004 North American Summer Meetings 484, Econometric Society.
  13. Anindya S. Chakrabarti, 2013. "Bimodality in the firm size distributions: a kinetic exchange model approach," Papers 1302.3818, arXiv.org, revised May 2013.
  14. Xie, Wen-Jie & Gu, Gao-Feng & Zhou, Wei-Xing, 2010. "On the growth of primary industry and population of China’s counties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3876-3882.
  15. Fu, Dongfeng & Pammolli, Fabio & Buldyrev, Sergey V. & Riccaboni, Massimo & Matia, Kaushik & Yamasaki, Kazuko & Stanley, H. Eugene, 2005. "The Growth of Business Firms: Theoretical Framework and Empirical Evidence," MPRA Paper 15905, University Library of Munich, Germany.
  16. repec:ebl:ecbull:v:15:y:2003:i:6:p:1-7 is not listed on IDEAS
  17. Stanley, H.E. & Gabaix, Xavier & Gopikrishnan, Parameswaran & Plerou, Vasiliki, 2007. "Economic fluctuations and statistical physics: Quantifying extremely rare and less rare events in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 286-301.

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