Firm size mobility and validity of the gibrat model
Download
1 / 31

Firm Size Mobility and Validity of the Gibrat Model - PowerPoint PPT Presentation


  • 62 Views
  • Uploaded on

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.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Firm Size Mobility and Validity of the Gibrat Model' - urbain


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
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 4th China-Europe Summer School on Complexity Science, Shanghai, August 14, 2010


Acknowledgments
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.


Outline of this talk
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


Firm size distribution
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.


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


Firm size distribution in china
Firm Size Distribution in China Economics Letters 49 (1995) 453-457

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 usa
Firm Size Distribution in USA Economics Letters 49 (1995) 453-457


Firm size distribution in world
Firm Size Distribution in World Economics Letters 49 (1995) 453-457


Changes under stable distributions
Changes under Stable Distributions Economics Letters 49 (1995) 453-457

Time


Changes under stable distributions1
Changes under Stable Distributions Economics Letters 49 (1995) 453-457

Firm Size Distribution in China


Individual evolution
Individual Evolution Economics Letters 49 (1995) 453-457

Variations in rank indicate it seems move randomly over time .


All individuals evolutions
All Individuals’ Evolutions Economics Letters 49 (1995) 453-457

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


Mobility of firm size
Mobility of Firm Size Economics Letters 49 (1995) 453-457

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
Absolute Mobility Economics Letters 49 (1995) 453-457

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


Relative mobility
Relative Mobility Economics Letters 49 (1995) 453-457

The ranks of individuals can be derived from attributes of them.


Zipf plot
Zipf Plot Economics Letters 49 (1995) 453-457


Relative mobility1
Relative Mobility Economics Letters 49 (1995) 453-457

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.


Rank clock of top 100 cities in usa
Rank Clock Economics Letters 49 (1995) 453-457 of Top 100 Cities in USA

Michael Batty, “Rank clocks”, Nature, vol. 444, pp. 592–596, 2006.


Rank Clocks of Firms Economics Letters 49 (1995) 453-457

Seven firms ranked in top 500 of the world during the thirteen years


Rank Clocks of Firms Economics Letters 49 (1995) 453-457

Many firms ranked in 500 firms in USA

Eight firms ranked in top 500 in USA


Rank-shift Clocks of Firm Size Economics Letters 49 (1995) 453-457

Rank Shift Clocks of Firms


The measurements of mobility
The Measurements of Mobility Economics Letters 49 (1995) 453-457


The law of proportional effect
The Law of Proportional Effect Economics Letters 49 (1995) 453-457

  • 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.


The gibrat model
The Gibrat Model Economics Letters 49 (1995) 453-457

  • 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.




Validity of gibrat s model
Validity of Gibrat’s model Distribution

Validation of the Gibrat Model




Conclusions
Conclusions Distribution

  • 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.


Many thanks
Many Thanks! Distribution


ad