Exponential Structure of Income Inequality: Evidence from 67 Countries
📝 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.
💡 Analysis
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.
📄 Content
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Exponential Structure of Income Inequality: Evidence from 67 Countries
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.
Keywords Income Inequality · General Equilibrium · Rawls’ Fairness · Technological Progress·Entropy JEL Classification D31·D51·D63·E14
Authors: Yong Tao1, Xiangjun Wu3, Tao Zhou4, Weibo Yan5, Yanyuxiang Huang2, Han Yu2, Benedict Mondal6, Victor M. Yakovenko7
Author affiliations: 1College of Economics and Management, Southwest University, Chongqing 400715, China 2College of Hanhong, Southwest University, Chongqing 400715, China 3College of Economics, Hangzhou Dianzi University, Hangzhou 310018, China 4Big Data Research Center, University of Electronic Science and Technology of China, Chengdu 611731, China 5School of Economics and Finance, Xi’an Jiaotong University, Xi’an 710049, China 6Department of Physics, University of Maryland, College Park, MD 20742-4111, USA 7Department of Physics, CMTC and JQI, University of Maryland, College Park, MD 20742-4111, USA
Acknowledgments: The authors would like to thank two anonymous referees and the editorial board for valuable comments and suggestions. All errors remain ours. Victor Yakovenko was supported by grant “Statistical Physics Approach to Income and Wealth Distribution” from the Institute for New Economic Thinking (INET), and Yong Tao by the Fundamental Research Funds for the Central Universities of China (Grant No. SWU1409444).
To whom correspondence should be addressed. Email: taoyingyong@yahoo.com (Yong Tao) or yakovenk@physics.umd.edu (Victor M. Yakovenko) 2
- Introduction
Economic inequality is a universal phenomenon in human societies. Although there are broad patterns of economic inequality between countries, their sources are poorly understood and hotly debated (Kuznets 1955; Acemoglu and Robinson 2009; Autor 2014; Piketty and Saez 2014; Ravallion 2014; Nishi et al. 2015). To explain the origin of economic inequality, researchers put forward different mechanisms, such as institutional structures (Acemoglu and Robinson 2009; Piketty and Saez 2014), technological progress (Acemoglu and Robinson 2009; Autor 2014), economic growth (Ravallion 2014), psychological factor (Nishi et al. 2015), and so on. In fact, because economic inequality involves many different aspects (e.g. income, wealth, social status, and so on) in human societies, seeking a universal pattern of economic inequality seems an impossible task. Nevertheless, some researchers tried to find universal patterns in income inequality. An influential economist Vilfredo Pareto proposed that income distribution in a society is well described by a power law (Pareto 1897). Although many studies have confirmed that the high-income class of populations follows a power law (Mandelbrot 1960; Kakwani 1980), there is increasing evidence showing that it does not apply to the majority of population with lower income. Using income data for USA, Yakovenko and Rosser (2009) have shown that the US society has a well-defined two-class structure (Dragulescu and Yakovenko 2001a, 2001b; Silva and Yakovenko 2005; Yakovenko and Rosser 2009; Banerjee and Yakovenko 2010): The great majority of population (low and middle income class) follows an exponential law, while the remaining part (high income class) follows a power law. Dragulescu and Yakovenko proposed a thermal equilibrium theory based on statistical mechanics to explain the exponential pattern of income distribution (Dragulescu and Yakovenko 2000), which has won more and more support from recent empirical studies (Nirei and Souma 2007; Derzsy, Néda, and Santos 2012; Jagielski and Kutner 2013; Shaikh, Papanikolaou, and Wiener 2014; Shaikh 2016; Oancea, Andrei, and Pirjol 2016). However, it should be noted that the exponential law does not fit the super-low income data, which are usually fitted by log-normal or gamma distributions (Banerjee, Yakovenko, and Di Matteo 2006; Chakrabarti et al. 2013). Moreover, although the exponential law is quite successful in describing the low and middle income data, the mec
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