Scaling in income inequalities and its dynamical origin

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A mean-field type model with random growth and reset terms is considered. The stationary distributions resulting from the corresponding master equation are relatively easy to obtain; however, for practical applications one also needs to know the convergence to stationarity. The present work contributes to this direction, studying the transient dynamics in the discrete version of the model by two different approaches. The first method is based on mathematical induction by the recursive integration of the coupled differential equations for the discrete states. The second method transforms the coupled ordinary differential equation system into a partial differential equation for the generating function. We derive analytical results for some important, practically interesting cases and discuss the obtained results for the transient dynamics.

Section: Introductionmentioning

confidence: 99%

Transient Dynamics in the Random Growth and Reset Model

Bı́ró

Csillag

Néda

2021

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“…Several other PDFs have been suggested to describe income or wealth distributions in terms of time [ 17 , 26 , 27 , 28 , 29 ]. Many of them are not treatable analytically, so the

relation can only be explored numerically.…”

Section: Discussionmentioning

confidence: 99%

“…For part of the PDF, exponential fits can also be done [ 16 ]. As an overall fit to the whole income distribution curve recently, it has been shown that a Tsallis–Pareto cut power-law or some special beta prime distribution works well [ 17 ].…”

Section: Introductionmentioning

confidence: 99%

Gintropy: Gini Index Based Generalization of Entropy

Bı́ró

Néda

2020

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Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini index, on the other hand, is an established measure for social and economical inequalities in a society. In this paper, we explore the mathematical similarities and connections in these two quantities and introduce a new measure that is capable of connecting these two at an interesting analogy level. This supports the idea that a generalization of the Gibbs–Boltzmann–Shannon entropy, based on a transformation of the Lorenz curve, can properly serve in quantifying different aspects of complexity in socio- and econo-physics.

“…As already mentioned, since its introduction, a plethora of empirical investigations have found the Pareto distribution to be consistent with income data. To focus on the most recent related publication, Néda et al [132] used income data from Japan (2015), USA (2013), Russia (2015), Australia (2011), Finland (2017), Hungary (2015) and a county in Romania (2005), fitting a simple and elegant model to them, and identified a beta prime distribution, which has a Pareto tail with tail index ξ = 1/3. The same research team, in a follow-up publication [133], examined the wealth data for the USA and Russia and again reported a Pareto tail.…”

Section: Hyperbolic Background Measure and The Pareto Distributionmentioning

confidence: 99%

Entropy and Wealth

Koutsoyiannis

Sargentis

2021

While entropy was introduced in the second half of the 19th century in the international vocabulary as a scientific term, in the 20th century it became common in colloquial use. Popular imagination has loaded “entropy” with almost every negative quality in the universe, in life and in society, with a dominant meaning of disorder and disorganization. Exploring the history of the term and many different approaches to it, we show that entropy has a universal stochastic definition, which is not disorder. Hence, we contend that entropy should be used as a mathematical (stochastic) concept as rigorously as possible, free of metaphoric meanings. The accompanying principle of maximum entropy, which lies behind the Second Law, gives explanatory and inferential power to the concept, and promotes entropy as the mother of creativity and evolution. As the social sciences are often contaminated by subjectivity and ideological influences, we try to explore whether maximum entropy, applied to the distribution of a wealth-related variable, namely annual income, can give an objective description. Using publicly available income data, we show that income distribution is consistent with the principle of maximum entropy. The increase in entropy is associated to increases in society’s wealth, yet a standardized form of entropy can be used to quantify inequality. Historically, technology has played a major role in the development of and increase in the entropy of income. Such findings are contrary to the theory of ecological economics and other theories that use the term entropy in a Malthusian perspective.