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|
|Contact details of provider:|| 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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- 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.
- 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.
- Thomas Chaney, 2008. "Distorted Gravity: The Intensive and Extensive Margins of International Trade," American Economic Review, American Economic Association, vol. 98(4), pages 1707-1721, September.
- 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;EDP Sciences, vol. 77(4), pages 565-580, October.
- Daron Acemoglu & Vasco M. Carvalho & Asuman Ozdaglar & Alireza Tahbaz‐Salehi, 2012. "The Network Origins of Aggregate Fluctuations," Econometrica, 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," 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.
- Daron Acemoglu & Vasco Carvalho & Asuman Ozdaglar & Alireza Tahbaz-Salehi, 2011. "The Network Origins of Aggregate Fluctuations," Working Papers 587, Barcelona Graduate School of Economics.
- François Gourio & Leena Rudanko, 2014. "Customer Capital," Review of Economic Studies, Oxford University Press, vol. 81(3), pages 1102-1136.
- Leena Rudanko & Francois Gourio, 2010. "Customer Capital," 2010 Meeting Papers 121, Society for Economic Dynamics.
- Francois Gourio & Leena Rudanko, 2011. "Customer Capital," NBER Working Papers 17191, National Bureau of Economic Research, Inc.
- 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 253, Society for Economic Dynamics.
- 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.
- Diego Garlaschelli & Stefano Battiston & Maurizio Castri & Vito D. P. Servedio & Guido Caldarelli, 2003. "The scale-free topology of market investments," Papers cond-mat/0310503, arXiv.org, revised Dec 2004.
- 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 580, Research Seminar in International Economics, University of Michigan.
- 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.
- Stella, Andrea, 2015. "Firm dynamics and the origins of aggregate fluctuations," Journal of Economic Dynamics and Control, Elsevier, vol. 55(C), pages 71-88.
- Stella, Andrea, 2015. "Firm Dynamics and the Origins of Aggregate Fluctuations," International Finance Discussion Papers 1133, Board of Governors of the Federal Reserve System (U.S.).
- 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.
- 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.
- SAITO (UMENO) Yukiko & WATANABE Tsutomu & IWAMURA Mitsuru, 2007. "Do Larger Firms Have More Interfirm Relationships?," Discussion papers 07028, Research Institute of Economy, Trade and Industry (RIETI).
- D. Garlaschelli & M. I. Loffredo, 2004. "Fitness-dependent topological properties of the World Trade Web," Papers cond-mat/0403051, arXiv.org, revised Oct 2004.
- 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. Full references (including those not matched with items on IDEAS)
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