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Firm Size Mobility and Validity of the Gibrat Model

Firm Size Mobility and Validity of the Gibrat Model. Yougui Wang Department of Systems Science School of Management, Beijing Normal University A talk @ the 4 th China-Europe Summer School on Complexity Science, Shanghai, August 14, 2010. Acknowledgments.

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Firm Size Mobility and Validity of the Gibrat Model

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  1. Firm Size Mobility and Validity of the Gibrat Model Yougui Wang Department of Systems Science School of Management, Beijing Normal University A talk @ the 4th China-Europe Summer School on Complexity Science, Shanghai, August 14, 2010

  2. Acknowledgments • The works referred in this talk were carried out under collaborations with Jinzhong Guo, Beishan Xu, Jianhua Zhang and Qinghua Chen. • Thanks to all organizers of this summer school. • The invitation from Professor Yi-Cheng Zhang and Professor Binghong Wang is appreciated. • I am grateful to Professor Shlomo Havlin and Paul Ormerod for his valuable suggestions and comments.

  3. Outline of This Talk • Background and Motivations • Firm size distribution • Firm Size Mobility • Rank clock of firm size • The validity of the Gibrat Model • Conclusions

  4. Firm Size distribution • Firm size distribution has long been a topic in economics. Robert Gibrat carried out the pioneer work in this issue. • In recent years, many works have been done on the firm size distribution such as Simon 1977,B.H.Hall 1987, Michael H. R. Stanley 1995, Robert L. Axtell 2001,J,Zhang 2009.

  5. M.H.Stanley. Zipf plots and the size distribution of firms, Economics Letters 49 (1995) 453-457 Robert L. Axtell. Zipf Distribution of U.S. Firm Sizes, 1818 (2001); 293 Science

  6. Firm Size Distribution in China J. Zhang, Q. Chen, Y. Wang, “Zipf distribution in top Chinese firms and an economic explanation”, Physica A, vol. 388, pp. 2020-2024. 2009.

  7. Firm Size Distribution in USA

  8. Firm Size Distribution in World

  9. Changes under Stable Distributions Time

  10. Changes under Stable Distributions Firm Size Distribution in China

  11. Individual Evolution Variations in rank indicate it seems move randomly over time .

  12. All Individuals’ Evolutions Aggregate variation in rank can not be simply figure out by putting all individuals’ evolutions together.

  13. Mobility of Firm Size G. S. Fields and E. A. Ok, “The meaning and measurement of income mobility”, Journal of Economic Theory, vol. 71, pp. 349–377. 1996. where, N is the number of firms, xk0 andxk1are the sizes of firm i at time 0 and 1 respectively.

  14. Absolute Mobility Absolute mobility covers changes of all firm sizes and is somewhat independent of scale.

  15. Relative Mobility The ranks of individuals can be derived from attributes of them.

  16. Zipf Plot

  17. Relative Mobility Shlomo Havlin, “The distance between Zipf plots”, Physica A, vol. 216, pp. 148-150，1995. where, N is the number of firms, rk0 andrk1are the rank of firm i at time 0 and 1 respectively.

  18. Rank Clockof Top 100 Cities in USA Michael Batty, “Rank clocks”, Nature, vol. 444, pp. 592–596, 2006.

  19. Rank Clocks of Firms Seven firms ranked in top 500 of the world during the thirteen years

  20. Rank Clocks of Firms Many firms ranked in 500 firms in USA Eight firms ranked in top 500 in USA

  21. Rank-shift Clocks of Firm Size Rank Shift Clocks of Firms

  22. The Measurements of Mobility

  23. The Law of Proportional Effect • The rate of growth of size X between period (t-1) and period t is a random variable, so that • Then after a series of periods, the evolution of size can be integrated as • Taking log and making some approximations, we thus obtain • The distribution can be approximated by a normal distribution.

  24. The Gibrat Model • The change in size for firm i follows the proportional effect plus a steady growth, so that • There is a minimum value of firm size and the firms whose size is less than it will be replaced by the current average one.

  25. Simulation Results on the Evolution of US Firm Size Distribution

  26. Validation of the Gibrat Model

  27. Validity of Gibrat’s model Validation of the Gibrat Model

  28. Growth Rate of Firm Size

  29. Comparisons Between Simulations and Measurements

  30. Conclusions • The firm size distribution has a unified pattern over time and regions. • Behind the stable Zipf distributions, the firm size mobility exhibit various characteristics. • Gibrat model can reproduce both the distribution and mobility of firm size.

  31. Many Thanks!

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