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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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
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
J. Zhang, Q. Chen, Y. Wang, “Zipf distribution in top Chinese firms and an economic explanation”, Physica A, vol. 388, pp. 2020-2024. 2009.
Firm Size Distribution in China
Variations in rank indicate it seems move randomly over time .
Aggregate variation in rank can not be simply figure out by putting all individuals’ evolutions together.
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.
Absolute mobility covers changes of all firm sizes and is somewhat independent of scale.
The ranks of individuals can be derived from attributes of them.
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.
Michael Batty, “Rank clocks”, Nature, vol. 444, pp. 592–596, 2006.
Seven firms ranked in top 500 of the world during the thirteen years
Many firms ranked in 500 firms in USA
Eight firms ranked in top 500 in USA
Rank Shift Clocks of Firms
Validation of the Gibrat Model