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Modelling of income distribution in the European Union with the Fokker–Planck equation

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  • Jagielski, Maciej
  • Kutner, Ryszard
Abstract
Herein, we applied statistical physics to study incomes of three (low-, medium- and high-income) society classes instead of the two (low- and medium-income) classes studied so far. In the frame of the threshold nonlinear Langevin dynamics and its threshold Fokker–Planck counterpart, we derived a unified formula for description of income of all society classes, by way of example, of those of the European Union in years 2006 and 2008. Hence, the formula is more general than the well known formula of Yakovenko et al.. That is, our formula well describes not only two regions but simultaneously the third region in the plot of the complementary cumulative distribution function vs. an annual household income. Furthermore, the known stylised facts concerning this income are well described by our formula. Namely, the formula provides the Boltzmann–Gibbs income distribution function for the low-income society class and the weak Pareto law for the medium-income society class, as expected. Importantly, it predicts (to satisfactory approximation) the Zipf law for the high-income society class. Moreover, the region of medium-income society class is now distinctly reduced because the bottom of high-income society class is distinctly lowered. This reduction made, in fact, the medium-income society class an intermediate-income society class.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:392:y:2013:i:9:p:2130-2138
    DOI: 10.1016/j.physa.2013.01.028
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    Citations

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    Cited by:

    1. Yong Tao & Xiangjun Wu & Tao Zhou & Weibo Yan & Yanyuxiang Huang & Han Yu & Benedict Mondal & Victor M. Yakovenko, 2019. "Exponential structure of income inequality: evidence from 67 countries," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(2), pages 345-376, June.
    2. Aktaev, Nurken E. & Bannova, K.A., 2022. "Mathematical modeling of probability distribution of money by means of potential formation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).
    3. Hernández-Ramírez, E. & del Castillo-Mussot, M. & Hernández-Casildo, J., 2021. "World per capita gross domestic product measured nominally and across countries with purchasing power parity: Stretched exponential or Boltzmann–Gibbs distribution?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 568(C).
    4. Alberto Russo, 2014. "A Stochastic Model of Wealth Accumulation with Class Division," Metroeconomica, Wiley Blackwell, vol. 65(1), pages 1-35, February.
    5. Shaikh, Anwar & Papanikolaou, Nikolaos & Wiener, Noe, 2014. "Race, gender and the econophysics of income distribution in the USA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 54-60.
    6. 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).
    7. Safari, Muhammad Aslam Mohd & Masseran, Nurulkamal & Ibrahim, Kamarulzaman, 2018. "Optimal threshold for Pareto tail modelling in the presence of outliers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 169-180.
    8. Remuzgo, Lorena & Trueba, Carmen & Sarabia, José María, 2016. "Evolution of the global inequality in greenhouse gases emissions using multidimensional generalized entropy measures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 146-157.
    9. Soriano-Hernández, P. & del Castillo-Mussot, M. & Campirán-Chávez, I. & Montemayor-Aldrete, J.A., 2017. "Wealth of the world’s richest publicly traded companies per industry and per employee: Gamma, Log-normal and Pareto power-law as universal distributions?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 733-749.
    10. Santiago Pindado & Carlos Pindado & Javier Cubas, 2017. "Fréchet Distribution Applied to Salary Incomes in Spain from 1999 to 2014. An Engineering Approach to Changes in Salaries’ Distribution," Economies, MDPI, vol. 5(2), pages 1-19, May.
    11. Tao, Yong, 2021. "Boltzmann-like income distribution in low and middle income classes: Evidence from the United Kingdom," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 578(C).
    12. Zoltan Neda & Istvan Gere & Tamas S. Biro & Geza Toth & Noemi Derzsy, 2019. "Scaling in Income Inequalities and its Dynamical Origin," Papers 1911.02449, arXiv.org, revised Mar 2020.
    13. Aydiner, Ekrem & Cherstvy, Andrey G. & Metzler, Ralf, 2018. "Wealth distribution, Pareto law, and stretched exponential decay of money: Computer simulations analysis of agent-based models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 278-288.
    14. Díaz, Juan D. & Gutiérrez Cubillos, Pablo & Tapia Griñen, Pablo, 2021. "The exponential Pareto model with hidden income processes: Evidence from Chile," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    15. Soriano-Hernández, P. & del Castillo-Mussot, M. & Córdoba-Rodríguez, O. & Mansilla-Corona, R., 2017. "Non-stationary individual and household income of poor, rich and middle classes in Mexico," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 465(C), pages 403-413.

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