IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1612.01624.html
   My bibliography  Save this paper

Exponential Structure of Income Inequality: Evidence from 67 Countries

Author

Listed:
  • Yong Tao
  • Xiangjun Wu
  • Tao Zhou
  • Weibo Yan
  • Yanyuxiang Huang
  • Han Yu
  • Benedict Mondal
  • Victor M. Yakovenko

Abstract

Economic competition between humans leads to income inequality, but, so far, there has been little understanding of underlying quantitative mechanisms governing such a collective behavior. We analyze datasets of household income from 67 countries, ranging from Europe to Latin America, North America and Asia. For all of the countries, we find a surprisingly uniform rule: Income distribution for the great majority of populations (low and middle income classes) follows an exponential law. To explain this empirical observation, we propose a theoretical model within the standard framework of modern economics and show that free competition and Rawls' fairness are the underlying mechanisms producing the exponential pattern. The free parameters of the exponential distribution in our model have an explicit economic interpretation and direct relevance to policy measures intended to alleviate income inequality.

Suggested Citation

  • Yong Tao & Xiangjun Wu & Tao Zhou & Weibo Yan & Yanyuxiang Huang & Han Yu & Benedict Mondal & Victor M. Yakovenko, 2016. "Exponential Structure of Income Inequality: Evidence from 67 Countries," Papers 1612.01624, arXiv.org, revised Dec 2017.
  • Handle: RePEc:arx:papers:1612.01624
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1612.01624
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Lai, T. L. & Robbins, Herbert & Wei, C. Z., 1979. "Strong consistency of least squares estimates in multiple regression II," Journal of Multivariate Analysis, Elsevier, vol. 9(3), pages 343-361, September.
    2. Anthony B. Atkinson & Thomas Piketty & Emmanuel Saez, 2011. "Top Incomes in the Long Run of History," Journal of Economic Literature, American Economic Association, vol. 49(1), pages 3-71, March.
    3. Tao, Yong & Wu, Xiangjun & Li, Changshuai, 2017. "Rawls' fairness, income distribution and alarming level of Gini coefficient," Economics Discussion Papers 2017-67, Kiel Institute for the World Economy (IfW Kiel).
    4. Foster, John & Metcalfe, J. Stan, 2012. "Economic emergence: An evolutionary economic perspective," Journal of Economic Behavior & Organization, Elsevier, vol. 82(2), pages 420-432.
    5. Enrico Moretti, 2013. "Real Wage Inequality," American Economic Journal: Applied Economics, American Economic Association, vol. 5(1), pages 65-103, January.
    6. Foley Duncan K., 1994. "A Statistical Equilibrium Theory of Markets," Journal of Economic Theory, Elsevier, vol. 62(2), pages 321-345, April.
    7. Katz, Lawrence F. & Autor, David H., 1999. "Changes in the wage structure and earnings inequality," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 26, pages 1463-1555, Elsevier.
    8. Thomas Piketty & Nancy Qian, 2009. "Income Inequality and Progressive Income Taxation in China and India, 1986-2015," American Economic Journal: Applied Economics, American Economic Association, vol. 1(2), pages 53-63, April.
    9. 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.
    10. Anand Banerjee & Victor M. Yakovenko, 2009. "Universal patterns of inequality," Papers 0912.4898, arXiv.org, revised Apr 2010.
    11. Charles I. Jones, 2015. "Pareto and Piketty: The Macroeconomics of Top Income and Wealth Inequality," Journal of Economic Perspectives, American Economic Association, vol. 29(1), pages 29-46, Winter.
    12. 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.
    13. Angle, John, 2006. "The Inequality Process as a wealth maximizing process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 388-414.
    14. Adrian Dragulescu & Victor M. Yakovenko, 2000. "Statistical mechanics of money," Papers cond-mat/0001432, arXiv.org, revised Aug 2000.
    15. Thomas Lux & Michele Marchesi, 1999. "Scaling and criticality in a stochastic multi-agent model of a financial market," Nature, Nature, vol. 397(6719), pages 498-500, February.
    16. Jonathan Heathcote & Kjetil Storesletten & Giovanni L. Violante, 2010. "The Macroeconomic Implications of Rising Wage Inequality in the United States," Journal of Political Economy, University of Chicago Press, vol. 118(4), pages 681-722, August.
    17. Thomas Piketty & Emmanuel Saez, 2014. "Inequality in the long run," PSE - Labex "OSE-Ouvrir la Science Economique" halshs-01053609, HAL.
    18. Kurt Dopfer, 2004. "The economic agent as rule maker and rule user: Homo Sapiens Oeconomicus," Journal of Evolutionary Economics, Springer, vol. 14(2), pages 177-195, June.
    19. Mikhail Golosov & Pricila Maziero & Guido Menzio, 2013. "Taxation and Redistribution of Residual Income Inequality," Journal of Political Economy, University of Chicago Press, vol. 121(6), pages 1160-1204.
    20. Akihiro Nishi & Hirokazu Shirado & David G. Rand & Nicholas A. Christakis, 2015. "Inequality and visibility of wealth in experimental social networks," Nature, Nature, vol. 526(7573), pages 426-429, October.
    21. Venkatasubramanian, Venkat & Luo, Yu & Sethuraman, Jay, 2015. "How much inequality in income is fair? A microeconomic game theoretic perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 120-138.
    22. Fabio Clementi & Mauro Gallegati & Giorgio Kaniadakis, 2010. "A model of personal income distribution with application to Italian data," Empirical Economics, Springer, vol. 39(2), pages 559-591, October.
    23. Banerjee, Anand & Yakovenko, Victor M. & Di Matteo, T., 2006. "A study of the personal income distribution in Australia," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 54-59.
    24. Thomas Piketty & Emmanuel Saez, 2003. "Income Inequality in the United States, 1913–1998," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 118(1), pages 1-41.
    25. Mas-Colell, Andreu & Whinston, Michael D. & Green, Jerry R., 1995. "Microeconomic Theory," OUP Catalogue, Oxford University Press, number 9780195102680.
    26. 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.
    27. Chakrabarti, Anindya S. & Chakrabarti, Bikas K., 2009. "Microeconomics of the ideal gas like market models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(19), pages 4151-4158.
    28. N. Derzsy & Z. Neda & M. A. Santos, 2012. "Income distribution patterns from a complete social security database," Papers 1203.1880, arXiv.org.
    29. Tao, Yong, 2015. "Universal laws of human society’s income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 89-94.
    30. Chakrabarti,Bikas K. & Chakraborti,Anirban & Chakravarty,Satya R. & Chatterjee,Arnab, 2013. "Econophysics of Income and Wealth Distributions," Cambridge Books, Cambridge University Press, number 9781107013445.
    31. Yong Tao, 2015. "Universal Laws of Human Society's Income Distribution," Papers 1506.05418, arXiv.org.
    32. Emmanuel Saez & Gabriel Zucman, 2016. "Editor's Choice Wealth Inequality in the United States since 1913: Evidence from Capitalized Income Tax Data," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 131(2), pages 519-578.
    33. Yong Tao, 2010. "Competitive market for multiple firms and economic crisis," Papers 1010.1413, arXiv.org.
    34. Jason Potts, 2001. "Knowledge and markets," Journal of Evolutionary Economics, Springer, vol. 11(4), pages 413-431.
    35. Makoto Nirei & Wataru Souma, 2007. "A Two Factor Model Of Income Distribution Dynamics," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 53(3), pages 440-459, September.
    36. Thomas Piketty, 2003. "Income Inequality in France, 1901-1998," Journal of Political Economy, University of Chicago Press, vol. 111(5), pages 1004-1042, October.
    37. Victor M. Yakovenko & J. Barkley Rosser, 2009. "Colloquium: Statistical mechanics of money, wealth, and income," Papers 0905.1518, arXiv.org, revised Dec 2009.
    38. Yong Tao, 2016. "Spontaneous economic order," Journal of Evolutionary Economics, Springer, vol. 26(3), pages 467-500, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Anwar Shaikh & Amr Ragab, 2023. "Some universal patterns in income distribution: An econophysics approach," Metroeconomica, Wiley Blackwell, vol. 74(1), pages 248-264, February.
    2. Gregor Semieniuk & Isabella M. Weber, 2019. "Inequality in Energy Consumption: Statistical Equilibrium or a Question of Accounting Conventions?," Working Papers 228, Department of Economics, SOAS University of London, UK.
    3. Tao, Yong & Wu, Xiangjun & Li, Changshuai, 2017. "Rawls' fairness, income distribution and alarming level of Gini coefficient," Economics Discussion Papers 2017-67, Kiel Institute for the World Economy (IfW Kiel).
    4. Danial Ludwig & Victor M. Yakovenko, 2021. "Physics-inspired analysis of the two-class income distribution in the USA in 1983-2018," Papers 2110.03140, arXiv.org, revised Jan 2022.
    5. Saurabh Mishra & Bilal M. Ayyub, 2019. "Shannon Entropy for Quantifying Uncertainty and Risk in Economic Disparity," Risk Analysis, John Wiley & Sons, vol. 39(10), pages 2160-2181, October.
    6. Tao, Yong, 2020. "Self-referential Boltzmann machine," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    7. 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).
    8. Kumar, Rishabh, 2021. "Personal income inequality in USA from a two-class perspective: 2004-2018," SocArXiv fmkj3, Center for Open Science.
    9. Gandzha, I.S. & Kliushnichenko, O.V. & Lukyanets, S.P., 2021. "Modeling and controlling the spread of epidemic with various social and economic scenarios," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    10. Mayerhoffer, Daniel & Schulz-Gebhard, Jan, 2023. "Social segregation, misperceptions, and emergent cyclical choice patterns," BERG Working Paper Series 186, Bamberg University, Bamberg Economic Research Group.
    11. Tao, Yong, 2018. "Swarm intelligence in humans: A perspective of emergent evolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 436-446.
    12. Tao, Yong & Sornette, Didier & Lin, Li, 2021. "Emerging social brain: A collective self-motivated Boltzmann machine," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    13. Cui, Lijie & Lin, Chuandong, 2021. "A simple and efficient kinetic model for wealth distribution with saving propensity effect: Based on lattice gas automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    14. Anwar Shaikh, 2018. "Some Universal Patterns in Income Distribution: An Econophysics Approach," Working Papers 1808, New School for Social Research, Department of Economics.
    15. Tian, Songtao & Liu, Zhirong, 2020. "Emergence of income inequality: Origin, distribution and possible policies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    16. Tao, Yong & Lin, Li & Wang, Hanjie & Hou, Chen, 2023. "Superlinear growth and the fossil fuel energy sustainability dilemma: Evidence from six continents," Structural Change and Economic Dynamics, Elsevier, vol. 66(C), pages 39-51.
    17. Kenji Itao & Kunihiko Kaneko, 2021. "Evolution of family systems and resultant socio-economic structures," Palgrave Communications, Palgrave Macmillan, vol. 8(1), pages 1-11, December.
    18. Maia, Adriano & Matsushita, Raul & Da Silva, Sergio, 2020. "Earnings distributions of scalable vs. non-scalable occupations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    19. Bogdan Oancea & Dan Pirjol, 2019. "Extremal properties of the Theil and Gini measures of inequality," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(2), pages 859-869, March.
    20. 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).
    21. 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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    2. Tao, Yong & Wu, Xiangjun & Li, Changshuai, 2017. "Rawls' fairness, income distribution and alarming level of Gini coefficient," Economics Discussion Papers 2017-67, Kiel Institute for the World Economy (IfW Kiel).
    3. Costas Efthimiou & Adam Wearne, 2016. "Household Income Distribution in the USA," Papers 1602.06234, arXiv.org.
    4. Alberto Russo, 2014. "A Stochastic Model of Wealth Accumulation with Class Division," Metroeconomica, Wiley Blackwell, vol. 65(1), pages 1-35, February.
    5. Scott Lawrence & Qin Liu & Victor M. Yakovenko, 2013. "Global inequality in energy consumption from 1980 to 2010," Papers 1312.6443, arXiv.org, revised Mar 2014.
    6. 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).
    7. Victor M. Yakovenko, 2012. "Applications of statistical mechanics to economics: Entropic origin of the probability distributions of money, income, and energy consumption," Papers 1204.6483, arXiv.org.
    8. Tao, Yong, 2018. "Swarm intelligence in humans: A perspective of emergent evolution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 436-446.
    9. Yuri Biondi & Simone Righi, 2019. "Inequality, mobility and the financial accumulation process: a computational economic analysis," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 14(1), pages 93-119, March.
    10. Smerlak, Matteo, 2016. "Thermodynamics of inequalities: From precariousness to economic stratification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 441(C), pages 40-50.
    11. Atanu Ghoshray & Issam Malki & Javier Ordóñez, 2022. "On the long-run dynamics of income and wealth inequality," Empirical Economics, Springer, vol. 62(2), pages 375-408, February.
    12. Tao, Yong, 2015. "Universal laws of human society’s income distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 435(C), pages 89-94.
    13. Yang, Xiaoliang & Zhou, Peng, 2022. "Wealth inequality and social mobility: A simulation-based modelling approach," Journal of Economic Behavior & Organization, Elsevier, vol. 196(C), pages 307-329.
    14. Shaikh, Anwar & Jacobo, Juan Esteban, 2020. "Economic Arbitrage and the Econophysics of Income Inequality," Review of Behavioral Economics, now publishers, vol. 7(4), pages 299–315-2, December.
    15. Thomas Piketty & Emmanuel Saez & Gabriel Zucman, 2018. "Distributional National Accounts: Methods and Estimates for the United States," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 133(2), pages 553-609.
    16. Istvan Gere & Szabolcs Kelemen & Geza Toth & Tamas Biro & Zoltan Neda, 2021. "Wealth distribution in modern societies: collected data and a master equation approach," Papers 2104.04134, arXiv.org.
    17. Markus P. A. Schneider, 2018. "Revisiting the thermal and superthermal two-class distribution of incomes: A critical perspective," Papers 1804.06341, arXiv.org.
    18. Garbinti, Bertrand & Goupille-Lebret, Jonathan & Piketty, Thomas, 2018. "Income inequality in France, 1900–2014: Evidence from Distributional National Accounts (DINA)," Journal of Public Economics, Elsevier, vol. 162(C), pages 63-77.
    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. 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.

    More about this item

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • E14 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Austrian; Evolutionary; Institutional

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1612.01624. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.