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Pareto's Law for Income of Individuals and Debt of Bankrupt Companies

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  • Hideaki Aoyama
  • Yuichi Nagahara
  • Mitsuhiro P. Okazaki
  • Wataru Souma
  • Hideki Takayasu
  • Misako Takayasu

Abstract

We analyze the distribution of income and income tax of individuals in Japan for the fiscal year 1998. From the rank-size plots we find that the accumulated probability distribution of both data obey a power law with a Pareto exponent very close to -2. We also present an analysis of the distribution of the debts owed by bankrupt companies from 1997 to March, 2000, which is consistent with a power law behavior with a Pareto exponent equal to -1. This power law is the same as that of the income distribution of companies. Possible implications of these findings for model building are discussed.

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  • Hideaki Aoyama & Yuichi Nagahara & Mitsuhiro P. Okazaki & Wataru Souma & Hideki Takayasu & Misako Takayasu, 2000. "Pareto's Law for Income of Individuals and Debt of Bankrupt Companies," Papers cond-mat/0006038, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0006038
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    Cited by:

    1. Guo, Qiang & Gao, Li, 2012. "Distribution of individual incomes in China between 1992 and 2009," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(21), pages 5139-5145.
    2. Jean-Philippe Bouchaud, 2000. "Power-laws in economics and finance: some ideas from physics," Science & Finance (CFM) working paper archive 500023, Science & Finance, Capital Fund Management.
    3. Kerim Eser Afc{s}ar & Mehmet Ozyi~git & Yusuf Yuksel & Umit Ak{i}nc{i}, 2021. "Testing the Goodwin Growth Cycles with Econophysics Approach in 2002-2019 Period in Turkey," Papers 2106.02546, arXiv.org.
    4. Atushi Ishikawa & Shouji Fujimoto & Takayuki Mizuno & Tsutomu Watanabe, 2016. "Long-term firm growth properties derived from short-term laws of sales and number of employees in Japan and France," Evolutionary and Institutional Economics Review, Springer, vol. 13(2), pages 409-422, December.
    5. Ausloos, M. & Bronlet, Ph., 2003. "Strategy for investments from Zipf law(s)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 30-37.
    6. Mercik, Szymon & Weron, Rafal, 2002. "Origins of scaling in FX markets," MPRA Paper 2294, University Library of Munich, Germany.
    7. Kaizoji, Taisei, 2003. "Scaling behavior in land markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 326(1), pages 256-264.
    8. Aoyama, Hideaki & Souma, Wataru & Fujiwara, Yoshi, 2003. "Growth and fluctuations of personal and company's income," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 352-358.
    9. Blair Fix, 2018. "Hierarchy and the power-law income distribution tail," Journal of Computational Social Science, Springer, vol. 1(2), pages 471-491, September.
    10. Xin, Xiuying & Jia, Ning & Zheng, Liang & Ma, Shoufeng, 2014. "Power-law in pedestrian crossing flow under the interference of vehicles at an un-signalized midblock crosswalk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 406(C), pages 287-297.
    11. Ignacio González García & Alfonso Mateos Caballero, 2021. "Models of Wealth and Inequality Using Fiscal Microdata: Distribution in Spain from 2015 to 2020," Mathematics, MDPI, vol. 9(4), pages 1-24, February.
    12. Delli Gatti, Domenico & Di Guilmi, Corrado & Gaffeo, Edoardo & Gallegati, Mauro, 2004. "Bankruptcy as an exit mechanism for systems with a variable number of components," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 8-13.
    13. Solomon Sorin & Golo Natasa, 2013. "Minsky Financial Instability, Interscale Feedback, Percolation and Marshall–Walras Disequilibrium," Accounting, Economics, and Law: A Convivium, De Gruyter, vol. 3(3), pages 167-260, October.
    14. Ormerod, Paul & Mounfield, Craig, 2001. "Power law distribution of the duration and magnitude of recessions in capitalist economies: breakdown of scaling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 293(3), pages 573-582.
    15. Clementi, F. & Gallegati, M., 2005. "Power law tails in the Italian personal income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 427-438.
    16. Capehart, Kevin W., 2014. "Is the wealth of the world’s billionaires not Paretian?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 255-260.
    17. Jayadev, Arjun, 2008. "A power law tail in India's wealth distribution: Evidence from survey data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(1), pages 270-276.
    18. 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.
    19. Xu, Yan & Wang, Yougui & Tao, Xiaobo & Ližbetinová, Lenka, 2017. "Evidence of Chinese income dynamics and its effects on income scaling law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 487(C), pages 143-152.
    20. Boris Podobnik & Davor Horvatic & Alexander M. Petersen & Branko Urov{s}evi'c & H. Eugene Stanley, 2010. "Bankruptcy risk model and empirical tests," Papers 1011.2670, arXiv.org.

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