Analytical Derivation of Power Laws in Firm Size Variables from Gibrat’s Law and Quasi-inversion Symmetry: A Geomorphological Approach
AbstractWe 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.
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Bibliographic InfoPaper provided by University of Tokyo, Graduate School of Economics in its series UTokyo Price Project Working Paper Series with number 019.
Length: 22 pages
Date of creation: Jan 2014
Date of revision:
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Postal: University of Tokyo 702 Faculty of Economics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan
Web page: http://www.e.u-tokyo.ac.jp/
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econophysics; power law; Gibrat’s law;
This paper has been announced in the following NEP Reports:
- NEP-ALL-2014-06-28 (All new papers)
- NEP-BEC-2014-06-28 (Business Economics)
- NEP-COM-2014-06-28 (Industrial Competition)
- NEP-IND-2014-06-28 (Industrial Organization)
- NEP-NET-2014-06-28 (Network Economics)
- NEP-TID-2014-06-28 (Technology & Industrial Dynamics)
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- D. Garlaschelli & M. I. Loffredo, 2004. "Fitness-dependent topological properties of the World Trade Web," Papers cond-mat/0403051, arXiv.org, revised Oct 2004.
- SAITO (UMENO) Yukiko & WATANABE Tsutomu & IWAMURA Mitsuru, 2007.
"Do Larger Firms Have More Interfirm Relationships?,"
Discussion papers, Research Institute of Economy, Trade and Industry (RIETI)
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, Elsevier, vol. 383(1), pages 158-163.
- Leena Rudanko & Francois Gourio, 2011. "Customer capital and the business cycle," 2011 Meeting Papers 120, Society for Economic Dynamics.
- Daron Acemoglu & Vasco M. Carvalho & Asuman Ozdaglar & Alireza Tahbazâ€Salehi, 2012.
"The Network Origins of Aggregate Fluctuations,"
Econometrica, Econometric Society,
Econometric Society, vol. 80(5), pages 1977-2016, 09.
- 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.
- 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.
- 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, Elsevier, vol. 31(6), pages 2061-2084, June.
- Leena Rudanko & Francois Gourio, 2010.
2010 Meeting Papers, Society for Economic Dynamics
121, Society for Economic Dynamics.
- Thomas Chaney, 2008. "Distorted Gravity: The Intensive and Extensive Margins of International Trade," American Economic Review, American Economic Association, American Economic Association, vol. 98(4), pages 1707-21, September.
- 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, University of Chicago Press, vol. 119(1), pages 1 - 38.
- Bryan Kelly & Hanno Lustig & Stijn Van Nieuwerburgh, 2013.
"Firm Volatility in Granular Networks,"
NBER Working Papers
19466, National Bureau of Economic Research, Inc.
- Stijn Van Nieuwerburgh & Hanno Lustig & Bryan Kelly, 2014. "Firm Volatility in Granular Networks," 2014 Meeting Papers, Society for Economic Dynamics 253, Society for Economic Dynamics.
- 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, Elsevier, vol. 392(4), pages 741-756.
- 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.
- Julian di Giovanni & Andrei A. Levchenko, 2008. "Putting the Parts Together: Trade, Vertical Linkages, and Business Cycle Comovement," Working Papers, Research Seminar in International Economics, University of Michigan 580, Research Seminar in International Economics, University of Michigan.
- 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,
Elsevier, vol. 350(2), pages 491-499.
- 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.
- 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, Springer, vol. 77(4), pages 565-580, October.
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