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Erschienen in: Journal of Economic Interaction and Coordination 2/2019

27.12.2017 | Regular Article

Exponential structure of income inequality: evidence from 67 countries

verfasst von: Yong Tao, Xiangjun Wu, Tao Zhou, Weibo Yan, Yanyuxiang Huang, Han Yu, Benedict Mondal, Victor M. Yakovenko

Erschienen in: Journal of Economic Interaction and Coordination | Ausgabe 2/2019

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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.

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Fußnoten
1
The emergence of income inequality can be traced back to the pioneering work of Angle (1986, 1992, 1993, 1996, and 2006).
 
2
In the neoclassical economics, monopolistic power implies that the behaviors among firms are highly heterogeneous. Interestingly, Lux and Marchesi (1999) also showed that heterogeneous behaviors among economic agents may lead to a power law in financial markets.
 
3
Here we have considered \({\textit{lim}}_{i \rightarrow \infty } \, y_i \ne 0\).
 
4
When labor L and capital K substitute with each other, we have \({\textit{MRTS}}_{{\textit{LK}}} > 0\).
 
5
Full sample means \(\{x_1, \ldots , x_n\}\), where n denotes the sample size.
 
Literatur
Zurück zum Zitat Acemoglu D, Robinson J (2009) Foundation of societal inequality. Science 326(5953):678–679CrossRef Acemoglu D, Robinson J (2009) Foundation of societal inequality. Science 326(5953):678–679CrossRef
Zurück zum Zitat Angle J (1986) The surplus theory of social stratification and the size distribution of personal wealth. Soc Forces 65:293–326CrossRef Angle J (1986) The surplus theory of social stratification and the size distribution of personal wealth. Soc Forces 65:293–326CrossRef
Zurück zum Zitat Angle J (1992) The inequality process and the distribution of income to blacks and whites. J Math Sociol 17:77–98CrossRef Angle J (1992) The inequality process and the distribution of income to blacks and whites. J Math Sociol 17:77–98CrossRef
Zurück zum Zitat Angle J (1993) Deriving the size distribution of personal wealth from “the rich get richer, the poor get poorer”. J Math Sociol 18:27–46CrossRef Angle J (1993) Deriving the size distribution of personal wealth from “the rich get richer, the poor get poorer”. J Math Sociol 18:27–46CrossRef
Zurück zum Zitat Angle J (1996) How the gamma law of income distribution appears invariant under aggregation. J Math Sociol 31:325–358CrossRef Angle J (1996) How the gamma law of income distribution appears invariant under aggregation. J Math Sociol 31:325–358CrossRef
Zurück zum Zitat Angle J (2006) The inequality process as a wealth maximizing process. Physica A 367:388–414CrossRef Angle J (2006) The inequality process as a wealth maximizing process. Physica A 367:388–414CrossRef
Zurück zum Zitat Arrow KJ (1963) Social choice and individual values. Wiley, New York Arrow KJ (1963) Social choice and individual values. Wiley, New York
Zurück zum Zitat Arrow KJ, Debreu G (1954) Existence of an equilibrium for a competitive economy. Econometrica 22(3):265–290CrossRef Arrow KJ, Debreu G (1954) Existence of an equilibrium for a competitive economy. Econometrica 22(3):265–290CrossRef
Zurück zum Zitat Atkinson AB, Piketty T, Saez E (2011) Top incomes in the long run of history. J Econ Lit 49(1):3–71CrossRef Atkinson AB, Piketty T, Saez E (2011) Top incomes in the long run of history. J Econ Lit 49(1):3–71CrossRef
Zurück zum Zitat Autor DH (2014) Skills, education, and the rise of earnings inequality among the “other 99 percent”. Science 344(6186):843–851CrossRef Autor DH (2014) Skills, education, and the rise of earnings inequality among the “other 99 percent”. Science 344(6186):843–851CrossRef
Zurück zum Zitat Autor DH, Katz LF, Kearney MS (2008) Trends in U.S. wage inequality: revising the revisionists. Rev Econ Stat 90(2):300–323CrossRef Autor DH, Katz LF, Kearney MS (2008) Trends in U.S. wage inequality: revising the revisionists. Rev Econ Stat 90(2):300–323CrossRef
Zurück zum Zitat Axtell RL (2001) Zipf distribution of U.S. firm sizes. Science 293(5536):1818–1820CrossRef Axtell RL (2001) Zipf distribution of U.S. firm sizes. Science 293(5536):1818–1820CrossRef
Zurück zum Zitat Banerjee A, Yakovenko VM (2010) Universal patterns of inequality. New J Phys 12:075032CrossRef Banerjee A, Yakovenko VM (2010) Universal patterns of inequality. New J Phys 12:075032CrossRef
Zurück zum Zitat Banerjee A, Yakovenko VM, Di Matteo T (2006) A study of the personal income distribution in Australia. Physica A 370(1):54–59CrossRef Banerjee A, Yakovenko VM, Di Matteo T (2006) A study of the personal income distribution in Australia. Physica A 370(1):54–59CrossRef
Zurück zum Zitat Chakrabarti AS, Chakrabarti BK (2009) Microeconomics of the ideal gas like market models. Physica A 388(19):4151–4158CrossRef Chakrabarti AS, Chakrabarti BK (2009) Microeconomics of the ideal gas like market models. Physica A 388(19):4151–4158CrossRef
Zurück zum Zitat Chakrabarti BK, Chakraborti A, Chakravarty SR, Chatterjee A (2013) Econophysics of income and wealth distributions. Cambridge University Press, CambridgeCrossRef Chakrabarti BK, Chakraborti A, Chakravarty SR, Chatterjee A (2013) Econophysics of income and wealth distributions. Cambridge University Press, CambridgeCrossRef
Zurück zum Zitat Cho A (2014) Physicists say it’s simple. Science 344(6186):828–828CrossRef Cho A (2014) Physicists say it’s simple. Science 344(6186):828–828CrossRef
Zurück zum Zitat Clementi F, Gallegati M, Kaniadakis G (2010) A model of personal income distribution with application to Italian data. Empir Econ 39:559–591CrossRef Clementi F, Gallegati M, Kaniadakis G (2010) A model of personal income distribution with application to Italian data. Empir Econ 39:559–591CrossRef
Zurück zum Zitat Clementi F, Gallegati M, Kaniadakis G (2012) A new model of income distribution: the \(\kappa \)-generalized distribution. J Econ 105:63–91CrossRef Clementi F, Gallegati M, Kaniadakis G (2012) A new model of income distribution: the \(\kappa \)-generalized distribution. J Econ 105:63–91CrossRef
Zurück zum Zitat Derzsy N, Néda Z, Santos MA (2012) Income distribution patterns from a complete social security database. Physica A 391(22):5611–5619CrossRef Derzsy N, Néda Z, Santos MA (2012) Income distribution patterns from a complete social security database. Physica A 391(22):5611–5619CrossRef
Zurück zum Zitat Dopfer K (2004) The economic agent as rule maker and rule user: Homo Sapiens Oeconomicus. J Evol Econ 14:177–195CrossRef Dopfer K (2004) The economic agent as rule maker and rule user: Homo Sapiens Oeconomicus. J Evol Econ 14:177–195CrossRef
Zurück zum Zitat Dragulescu A, Yakovenko VM (2000) Statistical mechanics of money. Eur Phys J B 17(4):723–729CrossRef Dragulescu A, Yakovenko VM (2000) Statistical mechanics of money. Eur Phys J B 17(4):723–729CrossRef
Zurück zum Zitat Dragulescu A, Yakovenko VM (2001a) Evidence for the exponential distribution of income in the USA. Eur Phys J B 20(4):585–589CrossRef Dragulescu A, Yakovenko VM (2001a) Evidence for the exponential distribution of income in the USA. Eur Phys J B 20(4):585–589CrossRef
Zurück zum Zitat Dragulescu A, Yakovenko VM (2001b) Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States. Physica A 299(1–2):213–221CrossRef Dragulescu A, Yakovenko VM (2001b) Exponential and power-law probability distributions of wealth and income in the United Kingdom and the United States. Physica A 299(1–2):213–221CrossRef
Zurück zum Zitat Foley DK (1994) A statistical equilibrium theory of markets. J Econ Theory 62(2):321–345CrossRef Foley DK (1994) A statistical equilibrium theory of markets. J Econ Theory 62(2):321–345CrossRef
Zurück zum Zitat Foster J, Metcalfe JS (2012) Economic emergence: an evolutionary economic perspective. J Econ Behav Organ 82(2–3):420–432CrossRef Foster J, Metcalfe JS (2012) Economic emergence: an evolutionary economic perspective. J Econ Behav Organ 82(2–3):420–432CrossRef
Zurück zum Zitat Golosov M, Maziero P, Menzio G (2013) Taxation and redistribution of residual income inequality. J Polit Econ 121(6):1160–1204CrossRef Golosov M, Maziero P, Menzio G (2013) Taxation and redistribution of residual income inequality. J Polit Econ 121(6):1160–1204CrossRef
Zurück zum Zitat Harte J, Zillio T, Conlisk E, Smith AB (2008) Maximum entropy and the state-variable approach to macroecology. Ecology 89(10):2700–2711CrossRef Harte J, Zillio T, Conlisk E, Smith AB (2008) Maximum entropy and the state-variable approach to macroecology. Ecology 89(10):2700–2711CrossRef
Zurück zum Zitat Heathcote J, Storesletten K, Violante GL (2010) The macroeconomic implications of rising wage inequality in the United States. J Polit Econ 118(4):681–722CrossRef Heathcote J, Storesletten K, Violante GL (2010) The macroeconomic implications of rising wage inequality in the United States. J Polit Econ 118(4):681–722CrossRef
Zurück zum Zitat Hodgson GM (2004) The evolution of institutional economics: agency, structure and Darwinism in American Institutionalism. Routledge, LondonCrossRef Hodgson GM (2004) The evolution of institutional economics: agency, structure and Darwinism in American Institutionalism. Routledge, LondonCrossRef
Zurück zum Zitat Jagielski M, Kutner R (2013) Modelling of income distribution in the European Union with the Kokker–Planck equation. Physica A 392(9):2130–2138CrossRef Jagielski M, Kutner R (2013) Modelling of income distribution in the European Union with the Kokker–Planck equation. Physica A 392(9):2130–2138CrossRef
Zurück zum Zitat Jones CI (2015) Pareto and Piketty: the macroeconomics of top income and wealth inequality. J Econ Perspect 29(1):29–46CrossRef Jones CI (2015) Pareto and Piketty: the macroeconomics of top income and wealth inequality. J Econ Perspect 29(1):29–46CrossRef
Zurück zum Zitat Kakwani N (1980) Income inequality and poverty. Oxford University Press, Oxford Kakwani N (1980) Income inequality and poverty. Oxford University Press, Oxford
Zurück zum Zitat Katz L, Autor D (1999) Changes in the wage structure and earnings inequality. In: Ashenfelter O, Card D (eds) Handbook of labor economics, vol 3A. North-Holland, Amsterdam Katz L, Autor D (1999) Changes in the wage structure and earnings inequality. In: Ashenfelter O, Card D (eds) Handbook of labor economics, vol 3A. North-Holland, Amsterdam
Zurück zum Zitat Kuznets S (1955) Economic growth and income inequality. Am Econ Rev 45(1):1–28 Kuznets S (1955) Economic growth and income inequality. Am Econ Rev 45(1):1–28
Zurück zum Zitat Lai TL, Robbins H, Wei CZ (1979) Strong consistency of least squares estimates in multiple regression II. J Multivar Anal 9(3):343–361CrossRef Lai TL, Robbins H, Wei CZ (1979) Strong consistency of least squares estimates in multiple regression II. J Multivar Anal 9(3):343–361CrossRef
Zurück zum Zitat Lambert PJ (1993) The distribution and redistribution of income: a mathematical analysis, 2nd edn. Manchester University Press, Manchester Lambert PJ (1993) The distribution and redistribution of income: a mathematical analysis, 2nd edn. Manchester University Press, Manchester
Zurück zum Zitat Lux T, Marchesi M (1999) Scaling and criticality in a stochastic multi-agent model of a financial market. Nature 397:498–500CrossRef Lux T, Marchesi M (1999) Scaling and criticality in a stochastic multi-agent model of a financial market. Nature 397:498–500CrossRef
Zurück zum Zitat Mandelbrot B (1960) The Pareto–Levy law and the distribution of income. Int Econ Rev 1(2):79–106CrossRef Mandelbrot B (1960) The Pareto–Levy law and the distribution of income. Int Econ Rev 1(2):79–106CrossRef
Zurück zum Zitat Mas-Collel A, Whinston MD, Green JR (1995) Microeconomic theory. Oxford University Press, Oxford Mas-Collel A, Whinston MD, Green JR (1995) Microeconomic theory. Oxford University Press, Oxford
Zurück zum Zitat Moretti E (2013) Real wage inequality. Am Econ J Appl Econ 5(1):65–103CrossRef Moretti E (2013) Real wage inequality. Am Econ J Appl Econ 5(1):65–103CrossRef
Zurück zum Zitat Nelson RR, Winter SG (1982) An evolutionary theory of economic change. The Belknap Press of Harvard University Press, Cambridge Nelson RR, Winter SG (1982) An evolutionary theory of economic change. The Belknap Press of Harvard University Press, Cambridge
Zurück zum Zitat Nirei M, Souma W (2007) A two factor model of income distribution dynamics. Rev Income Wealth 53(3):440–459CrossRef Nirei M, Souma W (2007) A two factor model of income distribution dynamics. Rev Income Wealth 53(3):440–459CrossRef
Zurück zum Zitat Nishi A, Shirado H, Rand DG, Christakis NA (2015) Inequality and visibility of wealth in experimental social networks. Nature 526(7573):426–429CrossRef Nishi A, Shirado H, Rand DG, Christakis NA (2015) Inequality and visibility of wealth in experimental social networks. Nature 526(7573):426–429CrossRef
Zurück zum Zitat Pareto V (1897) Cours d’ Economie Politique. L’ Universite de Lausanne, Lausanne Pareto V (1897) Cours d’ Economie Politique. L’ Universite de Lausanne, Lausanne
Zurück zum Zitat Piketty T (2003) Income inequality in France, 1901–1998. J Polit Econ 111:1004–1042CrossRef Piketty T (2003) Income inequality in France, 1901–1998. J Polit Econ 111:1004–1042CrossRef
Zurück zum Zitat Piketty T, Qian N (2009) Income inequality and progressive income taxation in China and India, 1986–2015. Am Econ J Appl Econ 1(2):53–63CrossRef Piketty T, Qian N (2009) Income inequality and progressive income taxation in China and India, 1986–2015. Am Econ J Appl Econ 1(2):53–63CrossRef
Zurück zum Zitat Piketty T, Saez E (2003) Income inequality in the United States, 1913–1998. Q J Econ 118:1–39CrossRef Piketty T, Saez E (2003) Income inequality in the United States, 1913–1998. Q J Econ 118:1–39CrossRef
Zurück zum Zitat Piketty T, Saez E (2014) Inequality in the long run. Science 344(6186):838–843CrossRef Piketty T, Saez E (2014) Inequality in the long run. Science 344(6186):838–843CrossRef
Zurück zum Zitat Ravallion M (2014) Income inequality in the developing world. Science 344(6186):851–855CrossRef Ravallion M (2014) Income inequality in the developing world. Science 344(6186):851–855CrossRef
Zurück zum Zitat Rawls J (1999) A theory of justice (revised edition). Harvard University Press, Cambridge Rawls J (1999) A theory of justice (revised edition). Harvard University Press, Cambridge
Zurück zum Zitat Rudin W (1976) Principles of mathematical analysis, 3rd edn. McGraw-Hill, Inc, New York Rudin W (1976) Principles of mathematical analysis, 3rd edn. McGraw-Hill, Inc, New York
Zurück zum Zitat Saez E, Zucman G (2016) Wealth inequality in the United States since 1913: evidence from capitalized income tax data. Q J Econ 131:519–578CrossRef Saez E, Zucman G (2016) Wealth inequality in the United States since 1913: evidence from capitalized income tax data. Q J Econ 131:519–578CrossRef
Zurück zum Zitat Shaikh A, Papanikolaou N, Wiener N (2014) Race, gender and the econophysics of income distribution in the USA. Physica A 415:54–60CrossRef Shaikh A, Papanikolaou N, Wiener N (2014) Race, gender and the econophysics of income distribution in the USA. Physica A 415:54–60CrossRef
Zurück zum Zitat Silva AC, Yakovenko VM (2005) Temporal evolution of the “thermal” and “superthermal” income classes in the USA during 1983–2001. Europhys Lett 69(2):304–310CrossRef Silva AC, Yakovenko VM (2005) Temporal evolution of the “thermal” and “superthermal” income classes in the USA during 1983–2001. Europhys Lett 69(2):304–310CrossRef
Zurück zum Zitat Tao Y (2010) Competitive market for multiple firms and economic crisis. Phys Rev E 82(3):036118CrossRef Tao Y (2010) Competitive market for multiple firms and economic crisis. Phys Rev E 82(3):036118CrossRef
Zurück zum Zitat Tao Y (2015) Universal laws of human society’s income distribution. Physica A 435:89–94CrossRef Tao Y (2015) Universal laws of human society’s income distribution. Physica A 435:89–94CrossRef
Zurück zum Zitat Venkatasubramanian V, Luo Y, Sethuraman J (2015) How much inequality in income is fair? A microeconomic game theoretic perspective. Physica A 435:120–138CrossRef Venkatasubramanian V, Luo Y, Sethuraman J (2015) How much inequality in income is fair? A microeconomic game theoretic perspective. Physica A 435:120–138CrossRef
Zurück zum Zitat Walras L (2003) Elements of pure economics or the theory of social wealth. Routledge, London Walras L (2003) Elements of pure economics or the theory of social wealth. Routledge, London
Zurück zum Zitat Yakovenko VM, Rosser JB Jr (2009) Statistical mechanics of money, wealth, and income. Rev Mod Phys 81(4):1703–1717CrossRef Yakovenko VM, Rosser JB Jr (2009) Statistical mechanics of money, wealth, and income. Rev Mod Phys 81(4):1703–1717CrossRef
Metadaten
Titel
Exponential structure of income inequality: evidence from 67 countries
verfasst von
Yong Tao
Xiangjun Wu
Tao Zhou
Weibo Yan
Yanyuxiang Huang
Han Yu
Benedict Mondal
Victor M. Yakovenko
Publikationsdatum
27.12.2017
Verlag
Springer Berlin Heidelberg
Erschienen in
Journal of Economic Interaction and Coordination / Ausgabe 2/2019
Print ISSN: 1860-711X
Elektronische ISSN: 1860-7128
DOI
https://doi.org/10.1007/s11403-017-0211-6

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