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Universal Structure of the Personal Income Distribution

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  • Wataru Souma

Abstract

We investigate the Japanese personal income distribution in the high income range over the 112 years 1887-1998, and that in the middle income range over the 44 years 1955-98. It is observed that the distribution pattern of the lognormal with power law tail is the universal structure. However the indexes specifying the distribution differ from year to year. One of the index characterizing the distribution is the mean value of the lognormal distribution; the mean income in the middle income range. It is found that this value correlates linearly with the Gross Domestic Product (GDP). To clarify the temporal change of the equality or inequality of the distribution, we analyze Pareto and Gibrat indexes, which characterize the distribution in the high income range and that in the middle income range respectively. It is found for some years that there is no correlation between the high income and the middle income. It is also shown that the mean value of Pareto index equals to 2, and the change of this index is effected by the change of the asset price. From these analysis we derive four constraints that must be satisfied by mathematical models.

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  • Wataru Souma, 2000. "Universal Structure of the Personal Income Distribution," Papers cond-mat/0011373, arXiv.org.
    • Handle: RePEc:arx:papers:cond-mat/0011373
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    Cited by:

    1. Willis, Geoff, 2011. "Why money trickles up – wealth & income distributions," MPRA Paper 30851, University Library of Munich, Germany.
    2. Jiandong Chen & Dai Dai & Ming Pu & Wenxuan Hou & Qiaobin Feng, 2010. "The trend of the Gini coefficient of China," Global Development Institute Working Paper Series 10910, GDI, The University of Manchester.
    3. Borges, Ernesto P, 2004. "Empirical nonextensive laws for the county distribution of total personal income and gross domestic product," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 255-266.
    4. Geoff Willis & Juergen Mimkes, 2004. "Evidence for the Independence of Waged and Unwaged Income, Evidence for Boltzmann Distributions in Waged Income, and the Outlines of a Coherent Theory of Income Distribution," Microeconomics 0408001, University Library of Munich, Germany.
    5. Geoff Willis, 2004. "Laser Welfare: First Steps in Econodynamic Engineering," Microeconomics 0408003, University Library of Munich, Germany.
    6. Chakrabarti, Anindya S. & Chakrabarti, Bikas K., 2010. "Statistical theories of income and wealth distribution," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 4, pages 1-31.
    7. Wataru Souma, 2002. "Physics of Personal Income," Papers cond-mat/0202388, arXiv.org.
    8. 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.

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