Exponential structure of income inequality: evidence from 67 countries

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

doi:10.1007/s11403-017-0211-6

Cited by 62 publications

(48 citation statements)

References 64 publications

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“…Among them, the distribution of income and wealth in a society was known to follow a power-law by V. Pareto in 1897 [ 1 ] and, since then, many empirical and numerical studies have been performed and newly discovered facts are reported over the whole range distribution functions [ 2 , 3 , 4 , 5 , 6 , 7 , 8 ]. The so-called Pareto law is valid only for the high rich people [ 9 , 10 , 11 , 12 ] and for the majority of non-rich people different distributions such as exponential and/or gamma-like functions are well fitted to the empirical statistics [ 13 , 14 , 15 ]. To explain the observed features of distributions of income and wealth, several agent-based models have been proposed on the basis of stochasticity and statistical mechanics.…”

Section: Introductionmentioning

confidence: 99%

Analysis of Solidarity Effect for Entropy, Pareto, and Gini Indices on Two-Class Society Using Kinetic Wealth Exchange Model

Lim

Min

2020

Entropy

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It is well known that two different underlying dynamics lead to different patterns of income/wealth distribution such as the Boltzmann–Gibbs form for the lower end and the Pareto-like power-law form for the higher-end. The Boltzmann–Gibbs distribution is naturally derived from maximizing the entropy of random interactions among agents, whereas the Pareto distribution requires a rational approach of economics dependent on the wealth level. More interestingly, the Pareto regime is very dynamic, whereas the Boltzmann–Gibbs regime is stable over time. Also, there are some cases in which the distributions of income/wealth are bimodal or polymodal. In order to incorporate the dynamic aspects of the Pareto regime and the polymodal forms of income/wealth distribution into one stochastic model, we present a modified agent-based model based on classical kinetic wealth exchange models. First, we adopt a simple two-class society consisting of the rich and the poor where the agents in the same class engage in random exchanges while the agents in the different classes perform a wealth-dependent winner-takes-all trading. This modification leads the system to an extreme polarized society with preserving the Pareto exponent. Second, we incorporate a solidarity formation among agents belonging to the lower class in our model, in order to confront a super-rich agent. This modification leads the system to a drastic bimodal distribution of wealth with a varying Pareto exponent over varying the solidarity parameter, that is, the Pareto-regime becomes narrower and the Pareto exponent gets larger as the solidarity parameter increases. We argue that the solidarity formation is the key ingredient in the varying Pareto exponent and the polymodal distribution. Lastly, we take two approaches to evaluate the level of inequality of wealth such as Gini coefficients and the entropy measure. According to the numerical results, the increasing solidarity parameter leads to a decreasing Gini coefficient not linearly but nonlinearly, whereas the entropy measure is robust over varying solidarity parameters, implying that there is a trade-off between the intermediate party and the high end.

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Section: Introductionmentioning

confidence: 99%

Analysis of Solidarity Effect for Entropy, Pareto, and Gini Indices on Two-Class Society Using Kinetic Wealth Exchange Model

Lim

Min

2020

Entropy

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“…Evidence from advanced economies shows a well‐defined two‐class structure. The majority of the population (about 97%) belongs to the lower class characterized by the exponential (“thermal”) distribution, whereas the upper class (about 3% of the population) is characterized by the Pareto power‐law (“superthermal”) distribution, and its share of the total income expands and contracts dramatically during booms and busts in financial markets (Tao et al., ).…”

Section: Uncertainty Measurement In Economic Disparitymentioning

confidence: 99%

Shannon Entropy for Quantifying Uncertainty and Risk in Economic Disparity

Mishra¹,

Ayyub

2019

Risk Analysis

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The rise in economic disparity presents significant risks to global social order and the resilience of local communities. However, existing measurement science for economic disparity (e.g., the Gini coefficient) does not explicitly consider a probability distribution with information, deficiencies, and uncertainties associated with the underlying income distribution. This article introduces the quantification of Shannon entropy for income inequality across scales, including national-, subnational-, and city-level data. The probabilistic principles of Shannon entropy provide a new interpretation for uncertainty and risk related to economic disparity. Entropy and information-based conflict rise as world incomes converge. High-entropy instances can resemble both happy and prosperous societies as well as a socialist-communist social structure. Low entropy signals high-risk tipping points for anomaly and conflict detection with higher confidence. Finally, spatial-temporal entropy maps for U.S. cities offer a city risk profiling framework. The results show polarization of household incomes within and across Baltimore, Washington, DC, and San Francisco. Entropy produces reliable results at significantly reduced computational costs than Gini coefficients.

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“…A jövedelmek eloszlása ettől lényegesen eltérő, exponenciális (hat-vány)eloszlást követ, melynek kumulatív eloszlásfüggvényét a 3.b ábra mutatja. A jövedelmi egyenlőtlenség exponenciális struktúráját egy, a közelmúltban megjelent, hatvanhét országra kiterjedő elemzés is igazolta (Tao et al, 2017).…”

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Egészségegyenlőtlenségek az egyenlőtlenségek globális kontextusában

Kósa¹,

Kőmüves²

2019

Ma.Tud.

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1 PhD, mD, egyetemi tanár, igazgató, Debreceni Egyetem Népegészségügyi Kar magatartástudományi Intézet kosa.karolina@sph.unideb.hu 2 PhD, adjunktus, Debreceni Egyetem Népegészségügyi Kar magatartástudományi Intézet komuves.sandor@sph.unideb.hu öSSZEFoGlalÁS A tanulmány első lépésben definiálja az egyenlőtlenséget, ennek kontextusában az egészségegyenlőtlenségeket, ismerteti az egészségegyenlőtlenségek méréséhez és elemzéséhez használt legfontosabb mutatókat, illetve utal azok morális aspektusára. Ezt követően a magyar lakosság lelki egészségében megfigyelhető egyik egészségegyenlőtlenség ismertetésén keresztül vezeti fel annak a nemzetközi diskurzusnak a rövid leírását, melyben hosszú évtizedek óta fókuszban állnak az egészségegyenlőtlenségek lényegi kérdései. Külön fejezet utal az egyenlőtlenség globális jelenségére, hangsúlyozva, hogy a globális egészségegyenlőtlenségek az egyenlőtlenségek legtágabb kontextusában értelmezendők. Az egyenlőtlenség komplex szemléleti igényű magyarázatának hangsúlyozása során a hatványtörvény mint lehetséges magyarázó erő hosszabb részben kerül ismertetésre. A tanulmány az egyenlőtlenség morális kontextusának illusztrálásával zárul.aBSTraCTThe manuscript defines health inequalities in the framework of general inequalities; presents variables used to measure and analyse health inequalities, and refers to their moral aspects. Starting with data regarding mental health inequalities in the Hungarian population, the international discourse of past decades on global inequalities and health inequalities is presented. Power law as one potential determinant of inequalities is discussed by referring to recent publications in the international and Hungarian scientific literature. Finally, the moral context of inequalities is pointed out.

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Exponential structure of income inequality: evidence from 67 countries

Cited by 62 publications

References 64 publications

Analysis of Solidarity Effect for Entropy, Pareto, and Gini Indices on Two-Class Society Using Kinetic Wealth Exchange Model

Analysis of Solidarity Effect for Entropy, Pareto, and Gini Indices on Two-Class Society Using Kinetic Wealth Exchange Model

Shannon Entropy for Quantifying Uncertainty and Risk in Economic Disparity

Egészségegyenlőtlenségek az egyenlőtlenségek globális kontextusában

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