Analytical Derivation of Power Laws in Firm Size Variables from Gibrat’s Law and Quasi-inversion Symmetry: A Geomorphological Approach
We start from Gibrat’s law and quasi-inversion symmetry for three firm size variables (i.e., tangible fixed assets K, number of employees L, and sales Y) and derive a partial differential equation to be satisfied by the joint probability density function of K and L.We then transform K and L, which are correlated, into two independent variables by applying surface openness used in geomorphology and provide an analytical solution to the partial differential equation. Using worldwide data on the firm size variables for companies, we confirm that the estimates on the power-law exponents of K, L, and Y satisfy a relationship implied by the theory.
|Date of creation:||Jan 2014|
|Date of revision:|
|Contact details of provider:|| Postal: |
Web page: http://www.e.u-tokyo.ac.jp/Email:
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Stijn Van Nieuwerburgh & Hanno Lustig & Bryan Kelly, 2014.
"Firm Volatility in Granular Networks,"
2014 Meeting Papers
253, Society for Economic Dynamics.
- Y. Fujiwara & H. Aoyama, 2010. "Large-scale structure of a nation-wide production network," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 77(4), pages 565-580, October.
- D. Garlaschelli & M. I. Loffredo, 2004. "Fitness-dependent topological properties of the World Trade Web," Papers cond-mat/0403051, arXiv.org, revised Oct 2004.
- Daron Acemoglu & Vasco M. Carvalho & Asuman Ozdaglar & Alireza Tahbaz‐Salehi, 2012.
"The Network Origins of Aggregate Fluctuations,"
Econometric Society, vol. 80(5), pages 1977-2016, 09.
- Daron Acemoglu & Vasco M. Carvalho & Asuman E. Ozdaglar & Alireza Tahbaz-Salehi, 2012. "The Network Origins of Aggregate Fluctuations," Levine's Working Paper Archive 786969000000000359, David K. Levine.
- Daron Acemoglu & Vasco Carvalho & Asuman Ozdaglar & Alireza Tahbaz-Salehi, 2011. "The Network Origins of Aggregate Fluctuations," Working Papers 587, Barcelona Graduate School of Economics.
- Daron Acemoglu & Vasco Carvalho & Asuman Ozdaglar & Alireza Tahbaz-Salehi, 2011. "The network origins of aggregate fluctuations," Economics Working Papers 1291, Department of Economics and Business, Universitat Pompeu Fabra.
- Garlaschelli, Diego & Battiston, Stefano & Castri, Maurizio & Servedio, Vito D.P. & Caldarelli, Guido, 2005.
"The scale-free topology of market investments,"
Physica A: Statistical Mechanics and its Applications,
Elsevier, vol. 350(2), pages 491-499.
- Francois Gourio & Leena Rudanko, 2011.
NBER Working Papers
17191, National Bureau of Economic Research, Inc.
- Battiston, Stefano & Delli Gatti, Domenico & Gallegati, Mauro & Greenwald, Bruce & Stiglitz, Joseph E., 2007. "Credit chains and bankruptcy propagation in production networks," Journal of Economic Dynamics and Control, Elsevier, vol. 31(6), pages 2061-2084, June.
- Julian di Giovanni & Andrei A. Levchenko, 2008.
"Putting the Parts Together: Trade, Vertical Linkages, and Business Cycle Comovement,"
580, Research Seminar in International Economics, University of Michigan.
- Julian di Giovanni & Andrei A. Levchenko, 2010. "Putting the Parts Together: Trade, Vertical Linkages, and Business Cycle Comovement," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(2), pages 95-124, April.
- Andrei A. Levchenko & Julian di Giovanni, 2009. "Putting the Parts together; Trade, Vertical Linkages, and Business Cycle Comovement," IMF Working Papers 09/181, International Monetary Fund.
- Andrew T. Foerster & Pierre-Daniel G. Sarte & Mark W. Watson, 2011. "Sectoral versus Aggregate Shocks: A Structural Factor Analysis of Industrial Production," Journal of Political Economy, University of Chicago Press, vol. 119(1), pages 1 - 38.
- Vasco Carvalho, 2007.
"Aggregate fluctuations and the network structure of intersectoral trade,"
Economics Working Papers
1206, Department of Economics and Business, Universitat Pompeu Fabra, revised Oct 2010.
- Vasco M Carvalho, 2008. "Aggregate Fluctuations and the Network Structure of Intersectoral Trade," 2008 Meeting Papers 1062, Society for Economic Dynamics.
- SAITO (UMENO) Yukiko & WATANABE Tsutomu & IWAMURA Mitsuru, 2007.
"Do Larger Firms Have More Interfirm Relationships?,"
07028, Research Institute of Economy, Trade and Industry (RIETI).
- Saito, Yukiko Umeno & Watanabe, Tsutomu & Iwamura, Mitsuru, 2007. "Do larger firms have more interfirm relationships?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 383(1), pages 158-163.
- Thomas Chaney, 2008. "Distorted Gravity: The Intensive and Extensive Margins of International Trade," American Economic Review, American Economic Association, vol. 98(4), pages 1707-21, September.
- Watanabe, Hayafumi & Takayasu, Hideki & Takayasu, Misako, 2013. "Relations between allometric scalings and fluctuations in complex systems: The case of Japanese firms," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 741-756.
- Leena Rudanko & Francois Gourio, 2011. "Customer capital and the business cycle," 2011 Meeting Papers 120, Society for Economic Dynamics.
When requesting a correction, please mention this item's handle: RePEc:upd:utppwp:019. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Yayoi Hatano)
If references are entirely missing, you can add them using this form.