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Scaling in income inequalities and its dynamical origin

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  • Néda, Zoltán
  • Gere, István
  • Biró, Tamás S.
  • Tóth, Géza
  • Derzsy, Noemi

Abstract

We provide an analytically treatable model that describes in a unified manner income distribution for all income categories. The approach is based on a master equation with growth and reset terms. The model assumptions on the growth and reset rates are tested on an exhaustive database with incomes on individual level spanning a nine year period in the Cluj county (Romania). In agreement with our theoretical predictions we find that income distributions computed for several years collapse on a master-curve when a properly normalised income is considered. The Beta Prime distribution is appropriate to fit the collapsed data and it is shown that distributions derived for other countries are following similar trends with different fit parameters. The non-universal feature of the fit parameters suggests that for a more realistic modelling the model parameters have to be linked with specific socio-economic regulations.

Suggested Citation

  • Néda, Zoltán & Gere, István & Biró, Tamás S. & Tóth, Géza & Derzsy, Noemi, 2020. "Scaling in income inequalities and its dynamical origin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    • Handle: RePEc:eee:phsmap:v:549:y:2020:i:c:s0378437120302156
    DOI: 10.1016/j.physa.2020.124491
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    as
    1. Soares, Abner D. & Moura Jr., Newton J. & Ribeiro, Marcelo B., 2016. "Tsallis statistics in the income distribution of Brazil," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 158-171.
    2. M. Ali Saif & Prashant M. Gade, 2009. "Effects of introduction of new resources and fragmentation of existing resources on limiting wealth distribution in asset exchange models," Papers 0902.2070, arXiv.org.
    3. Fujiwara, Yoshi & Souma, Wataru & Aoyama, Hideaki & Kaizoji, Taisei & Aoki, Masanao, 2003. "Growth and fluctuations of personal income," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 321(3), pages 598-604.
    4. Pianegonda, S & Iglesias, J.R & Abramson, G & Vega, J.L, 2003. "Wealth redistribution with conservative exchanges," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 667-675.
    5. Sinha, Sitabhra, 2006. "Evidence for power-law tail of the wealth distribution in India," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 555-562.
    6. Ishikawa, Atushi, 2005. "Pareto law and Pareto index in the income distribution of Japanese companies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 597-608.
    7. Chatterjee, Arnab & K. Chakrabarti, Bikas & Manna, S.S, 2004. "Pareto law in a kinetic model of market with random saving propensity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(1), pages 155-163.
    8. D. Garlaschelli & M. I. Loffredo, 2004. "Wealth Dynamics on Complex Networks," Papers cond-mat/0402466, arXiv.org.
    9. Ali Saif, M. & Gade, Prashant M., 2009. "Effects of introduction of new resources and fragmentation of existing resources on limiting wealth distribution in asset exchange models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(5), pages 697-704.
    10. Drăgulescu, Adrian & Yakovenko, Victor M., 2001. "Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 213-221.
    11. Gupta, Abhijit Kar, 2006. "Money exchange model and a general outlook," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 634-640.
    12. Hegyi, Géza & Néda, Zoltán & Augusta Santos, Maria, 2007. "Wealth distribution and Pareto's law in the Hungarian medieval society," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 271-277.
    13. 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.
    14. Sitabhra Sinha, 2005. "The Rich Are Different!: Pareto Law from asymmetric interactions in asset exchange models," Papers physics/0504197, arXiv.org.
    15. F. Clementi & M. Gallegati & G. Kaniadakis, 2007. "κ-generalized statistics in personal income distribution," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 57(2), pages 187-193, May.
    16. Arnab Chatterjee & Bikas K. Chakrabarti & S. S. Manna, 2003. "Pareto Law in a Kinetic Model of Market with Random Saving Propensity," Papers cond-mat/0301289, arXiv.org, revised Jan 2004.
    17. Solomon, Sorin & Richmond, Peter, 2001. "Power laws of wealth, market order volumes and market returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 188-197.
    18. Abreu, Everton M.C. & Moura, Newton J. & Soares, Abner D. & Ribeiro, Marcelo B., 2019. "Oscillations in the Tsallis income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 533(C).
    19. Jagielski, Maciej & Kutner, Ryszard, 2013. "Modelling of income distribution in the European Union with the Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(9), pages 2130-2138.
    20. Jean-Philippe Bouchaud & Marc Mezard, 2000. "Wealth condensation in a simple model of economy," Science & Finance (CFM) working paper archive 500026, Science & Finance, Capital Fund Management.
    21. Derzsy, N. & Néda, Z. & Santos, M.A., 2012. "Income distribution patterns from a complete social security database," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5611-5619.
    22. Biró, T.S. & Néda, Z., 2018. "Unidirectional random growth with resetting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 335-361.
    23. Ali Saif, M. & Gade, Prashant M., 2007. "Emergence of power-law in a market with mixed models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 448-456.
    24. Coelho, Ricardo & Néda, Zoltán & Ramasco, José J. & Augusta Santos, Maria, 2005. "A family-network model for wealth distribution in societies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 353(C), pages 515-528.
    25. Nicola Scafetta & Sergio Picozzi & Bruce West, 2004. "An out-of-equilibrium model of the distributions of wealth," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 353-364.
    26. A. Drăgulescu & V.M. Yakovenko, 2001. "Evidence for the exponential distribution of income in the USA," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 20(4), pages 585-589, April.
    27. Iglesias, J.R. & Gonçalves, S. & Pianegonda, S. & Vega, J.L. & Abramson, G., 2003. "Wealth redistribution in our small world," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 327(1), pages 12-17.
    28. N. Derzsy & Z. Neda & M. A. Santos, 2012. "Income distribution patterns from a complete social security database," Papers 1203.1880, arXiv.org.
    29. Chami Figueira, F. & Moura, N.J. & Ribeiro, M.B., 2011. "The Gompertz–Pareto income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 689-698.
    30. Garlaschelli, Diego & Loffredo, Maria I, 2004. "Wealth dynamics on complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(1), pages 113-118.
    31. Bouchaud, Jean-Philippe & Mézard, Marc, 2000. "Wealth condensation in a simple model of economy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(3), pages 536-545.
    32. repec:cup:cbooks:9781107013445 is not listed on IDEAS
    33. Nicola Scafetta & Sergio Picozzi & Bruce J. West, 2004. "An out-of-equilibrium model of the distributions of wealth," Papers cond-mat/0403045, arXiv.org.
    34. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
    35. Yonatan Berman & Yoash Shapira & Eshel Ben-Jacob, 2015. "Modeling the Origin and Possible Control of the Wealth Inequality Surge," PLOS ONE, Public Library of Science, vol. 10(6), pages 1-21, June.
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    Cited by:

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    4. Ilda Inácio & José Velhinho, 2022. "Comments on Mathematical Aspects of the Biró–Néda Model," Mathematics, MDPI, vol. 10(4), pages 1-10, February.

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