scholarly journals Income inequality measures and the middle class

2021 ◽  
Vol 114 ◽  
pp. 01019
Author(s):  
Oleg I. Pavlov ◽  
Olga Yu. Pavlova
Keyword(s):  
Income Inequality ◽  
Middle Class ◽  
Lower Bounds ◽  
Gini Coefficient ◽  
Lorenz Curve ◽  
Upper And Lower Bounds ◽  
Inequality Measures ◽  
The Gini Coefficient ◽  
Class 1 ◽  
The Lorenz Curve

We study how the presence of the middle class in the sense of Gevorgyan-Malykhin affects the value of income inequality measures including the Gini coefficient J and the Hoover index H. It is proved that in the presence of the middle class (1) $J \leqslant \frac{1}{2}\frac{{L'\left( 0 \right)}}{2}$ (where L is the Lorenz function), (2) $H \leqslant \frac{1}{2}$, (3) the longest vertical distance between the diagonal and the Lorenz curve (which is equal to H) is attained at ${z_0} < \frac{3}{4}$ A tight upper bound for P90/P10 ratio is found assuming L′(0)>0. Tight upper and lower bounds for the differential deviation in terms of the Gini coefficient are found as well.

The Discovery of the Gini Coefficient

2020 ◽  
pp. 115-141
Author(s):  
Michael Schneider
Keyword(s):  
Twentieth Century ◽  
Income Inequality ◽  
Gini Coefficient ◽  
Lorenz Curve ◽  
The Gini Coefficient ◽  
Early Twentieth Century ◽  
Corrado Gini ◽  
The Lorenz Curve

This article traces the development of the methods of representing the degree of income inequality that were developed in the early twentieth century by Max Otto Lorenz and Corrado Gini. It suggests that Gini’s efforts to perfect the Lorenz curve may well have facilitated his discovery of what came to be known as the Gini coefficient and argues that this coefficient is an important example of a multiple (or chain multiple) discovery.

scholarly journals Modified Lorenz Curve and Its Computation

2020 ◽  
Vol 3 (2) ◽  
pp. 99-108
Author(s):  
Subian Saidi ◽  
Ulfah Muharramah ◽  
La Zakaria ◽  
Yomi Mariska ◽  
Triyono Ruby
Keyword(s):  
Income Distribution ◽  
Gini Coefficient ◽  
Lorenz Curve ◽  
Standard Form ◽  
Computer Software ◽  
Computational Techniques ◽  
Computational Results ◽  
Computational Process ◽  
The Gini Coefficient ◽  
The Lorenz Curve

The Lorenz curve is generally used to find out the inequality of income distribution. Mathematically a standard form of the Lorenz curve can be modified with the aim of simplicity of its symmetric analysis and calculation of the Gini coefficient that usually accompanies it. One way to modify the shape of the Lorenz curve without losing its characteristics but is simple in the analysis of geometric shapes is through a transformation (rotation). To be efficient and effective in computing and analyzing a Lorenz curve it is necessary to consider using computer software. In this article, in addition to describing the development of the concept of using transformations (rotations) of the standard Lorenz curve in an easy-to-do form, the symmetric analysis is also described by computational techniques using Mathematica® software. From the results of the application of the development of the concept of the Lorenz curve which is carried out on a data gives a simpler picture of the computational process with relatively similar computational results.

Poverty Incidence and Income Inequality in the Tribal and Non-tribal Area of Central Gujarat

2021 ◽  
Keyword(s):  
Income Inequality ◽  
Gini Coefficient ◽  
Lorenz Curve ◽  
Farm Households ◽  
Graphical Form ◽  
Poor People ◽  
Tribal Area ◽  
Poor Households ◽  
The Lorenz Curve ◽  
Tribal Areas

The present investigation undertook to study the poverty incidence and income distribution among poor and non-poor in the tribal and non-tribal areas applying headcount index and the Gini index, and Lorenz curve. The headcount index shows the proportion of poor households. It shows that poverty was higher in the tribal area than in non-tribal regions. Incidence of poverty was higher in marginal farm households, followed by landless agricultural labour and small farm households. Income inequalities are depicted by the Gini coefficient and presented in graphical form by the Lorenz curve. It showed that total income was distributed more equally among poor and non-poor people in the tribal area than in non-tribal regions. It also observed that in the tribal district, poor and non-poor households had the same proportion of inequality. It was suggested to focus on creating employment opportunities through programmes like MGNREGA to eliminate poverty in particular tribal areas. Keywords: Gini coefficient, headcount index, income inequality, Lorenz curve, poverty incidence. JEL Codes: D63, I32, I38, O15

scholarly journals Timetable and Headway Adherence Assessment using the Gini Coefficient and the Lorenz Curve

2021 ◽  
Vol 9 ◽  
pp. 137-151
Author(s):  
Neila Bhouri ◽  
Sneha Lakhotia ◽  
Maurice Aron ◽  
Geetam Tiwari
Keyword(s):  
Gini Coefficient ◽  
Lorenz Curve ◽  
New Delhi ◽  
Time Data ◽  
The Gini Coefficient ◽  
Adherence Assessment ◽  
The Lorenz Curve ◽  
Traffic Disturbance ◽  
Bus Schedule ◽  
The Impact

Adherence to the schedule is of prime importance in public transport. This paper presents a specific application of the Gini coefficient, well known indicator in economics, for the headway adherence assessment. The paper shows that Lorenz curve, which is usually used to define mathematically the Gini coefficient, is a good indicator of the users' waiting time when it is based on the bus schedule. When it is computed on the basis of the ratio of observed headway to the schedule, it is a powerful visual tool that can be used by operators to detect the existence of irregularities on a bus line at a glance. An equation gives, in an idealistic case, the impact of any single traffic disturbance on the Gini coefficient, making this coefficient comprehensive. A detailed analysis is developed, based on the bus proportions according to the headway adherence level. These proportions are obtained from new indices coming from the derivative of the Lorenz curve. The values of these indexes alert the operator of any adherence disturbance. The examination of the Lorenz curve takes more time, but is worthwhile, giving the types of the irregularities The application of these indicators is carried on real-time data from the New Delhi bus network.

scholarly journals MODELS OF DISTRIBUTION OF GDP AT THE GLOBAL LEVEL

2018 ◽  
pp. 177
Author(s):  
Zoran Tomić ◽  
Ognjen Radović
Keyword(s):  
Gini Coefficient ◽  
Lorenz Curve ◽  
Statistical Physics ◽  
Gibbs Distribution ◽  
Global Level ◽  
The Gini Coefficient ◽  
Pareto Model ◽  
The Lorenz Curve

Problem of distribution gathers the attention of researchers for years. In their research they analyze the uniformity of distribution using Pareto model of distribution, the Lorenz curve and the Gini coefficient. Also some authors are testing the applicability of models from statistical physics to the problem of distribution to better describe it. In addition to the analysis of distribution at the level of states and certain groups such as the Forbes list, the problem is spreading to the global level, where we analyze the distribution of GDP as a measure of the wealth of individual countries.In this paper we analyzed the distribution of GDP of countries applying the Pareto model, Lorenz curve, Gini coefficient and Boltzmann Gibbs distribution from statistical physics. The analysis was done for 2015, while the Gini coefficient analysis was done during the period from 1990 to 2015.

The Contest for Olympic Success as a Public Good

2013 ◽  
Author(s):  
Loek Groot
Keyword(s):  
Lorenz Curve ◽  
Gini Index ◽  
World Population ◽  
Level Playing Field ◽  
Actual Distribution ◽  
Playing Field ◽  
Inequality Measures ◽  
The Rich ◽  
The Lorenz Curve ◽  
Rich Countries

In this study it is demonstrated that standard income inequality measures, such as the Lorenz curve and the Gini index, can successfully be applied to the distribution of Olympic success. Olympic success is distributed very unevenly, with the rich countries capturing a disproportionately higher share compared to their world population share, which suggests that the Olympic Games do not provide a level playing field. The actual distribution of Olympic success is compared with alternative hypothetical distributions, among which are chosen the distribution according to population shares, the welfare optimal distribution under the assumption of zero government expenditures, and the non-cooperating Nash-Cournot distribution. By way of conclusion, a device is proposed to make the distribution of Olympic success more equitable.

scholarly journals Financialization and Income Inequality in Selected European Countries, 2004–2013

e-Finanse ◽  
2017 ◽  
Vol 12 (4) ◽  
pp. 20-32
Author(s):  
Grzegorz Golebiowski ◽  
Piotr Szczepankowski ◽  
Dorota Wisniewska
Keyword(s):  
Income Inequality ◽  
Eastern Europe ◽  
Gini Coefficient ◽  
Central And Eastern Europe ◽  
Value Added ◽  
European Countries ◽  
Total Employment ◽  
The Gini Coefficient ◽  
Synthetic Indicator ◽  
The Impact

Abstract The article examines the impact of financialization on income inequality between 2004 and 2013, through a panel analysis of seven European countries. Moreover, it attempts to examine differences in the perception of the phenomenon between the selected European countries belonging to the G-7 and countries from Central and Eastern Europe. The results demonstrate the existence of individual effects, which means that the level of inequality under examination is influenced predominantly by country-specific factors. The most significant correlation is noticeable between the level of unemployment and the degree of income inequality. An increase in unemployment is accompanied by a rise in the disproportions in the level of income that individual citizens have at their disposal whereas a decrease in the unemployment level contributes to an improvement of the GINI coefficient. Simultaneously, the results confirm the existence of significant correlations between the level of the GINI coefficient and such financialization indicators as the share of employment in finance in total employment and the contribution of the financial sector to total value added creation. The most prominent dependency was discovered when a constructed synthetic indicator was adopted as an indicator of financialization. At the same time, analysis of the synthetic country financialization indicator points to a conclusion that the level of financialization is higher in European countries belonging to the G-7 (especially Great Britain) than in countries from Central and Eastern Europe.

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