scholarly journals Inequality Measures: The Kolkata Index in Comparison With Other Measures

2020 ◽  
Vol 8 ◽  
Author(s):  
Suchismita Banerjee ◽  
Bikas K. Chakrabarti ◽  
Manipushpak Mitra ◽  
Suresh Mutuswami
Keyword(s):  
Gini Coefficient ◽  
Gini Index ◽  
Empirical Studies ◽  
Nonlinear Function ◽  
Hirsch Index ◽  
Inequality Measures ◽  
Income Distributions ◽  
The Gini Coefficient ◽  
The Rich ◽  
Total Wealth

We provide a survey of the Kolkata index of social inequality, focusing in particular on income inequality. Based on the observation that inequality functions (such as the Lorenz function), giving the measures of income or wealth against that of the population, to be generally nonlinear, we show that the fixed point (like Kolkata index k) of such a nonlinear function (or related, like the complementary Lorenz function) offer better measure of inequality than the average quantities (like Gini index). Indeed the Kolkata index can be viewed as a generalized Hirsch index for a normalized inequality function and gives the fraction k of the total wealth possessed by the rich 1−k fraction of the population. We analyze the structures of the inequality indices for both continuous and discrete income distributions. We also compare the Kolkata index to some other measures like the Gini coefficient and the Pietra index. Lastly, we provide some empirical studies which illustrate the differences between the Kolkata index and the Gini coefficient.

scholarly journals The Robin Hood Index Adjusted for Negatives and Equivalised Incomes

2021 ◽  
Vol 37 (4) ◽  
pp. 1047-1058
Author(s):  
Marion van den Brakel ◽  
Reinder Lok
Keyword(s):  
Gini Coefficient ◽  
Wealth Inequality ◽  
Income Transfer ◽  
Income Share ◽  
Robin Hood ◽  
Inequality Measures ◽  
The Poor ◽  
The Gini Coefficient ◽  
The Rich ◽  
Original Index

Abstract Indisputable figures on income and wealth inequality are indispensable for politics, society and science. Although the Gini coefficient is the most common measure of inequality, the straightforward concept of the Robin Hood index (namely, the income share that has to be transferred from the rich to the poor to make everyone equally well off) makes it a more attractive measure for the general public. In a distribution with many negative values – particularly wealth distributions – the Robin Hood index can take on values larger than 1, indicating an intuitively impossible income transfer of more than 100%. This article proposes a method to normalise the Robin Hood index. In contrast to the original index, the normalised Robin Hood index always takes on values between 0 and 1 and ends up as the original index in a distribution without negatives. As inequality measures are commonly applied to equivalised income, we also introduce a method for adequately transferring equivalised incomes from the rich to the poor within the framework of the (normalised) Robin Hood index. An empirical application shows the effect of normalisation for the Robin Hood index, and compares it to the normalisation of the Gini coefficient from previous research.

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 A comparative study of the Gini coefficient estimators based on the linearization and U-statistics Methods

2017 ◽  
Vol 40 (2) ◽  
pp. 205-221 ◽  
Author(s):  
Shahryar Mirzaei ◽  
Gholam Reza Mohtashami Borzadaran ◽  
Mohammad Amini
Keyword(s):  
Comparative Study ◽  
Simulation Study ◽  
Gini Coefficient ◽  
Gini Index ◽  
Real Data ◽  
Linearization Method ◽  
U Statistics ◽  
The Gini Coefficient

In this paper, we consider two well-known methods for analysis of the Gini index, which are U-statistics and linearization for some incomedistributions. In addition, we evaluate two different methods for some properties of their proposed estimators. Also, we compare two methods with resampling techniques in approximating some properties of the Gini index. A simulation study shows that the linearization method performs 'well' compared to the Gini estimator based on U-statistics. A brief study on real data supports our findings.

Anything Lorenz Curves Can Do, Top Shares Can Do: Assessing the TopBot Family of Inequality Measures

2018 ◽  
Vol 49 (4) ◽  
pp. 947-981 ◽  
Author(s):  
Guillermina Jasso
Keyword(s):  
Gini Coefficient ◽  
Probability Distributions ◽  
The United States ◽  
Current Evidence ◽  
Inequality Measure ◽  
Lorenz Curves ◽  
Inequality Measures ◽  
Top Incomes ◽  
The Gini Coefficient ◽  
And Shifts

Newly precise evidence of the trajectory of top incomes in the United States and around the world relies on shares and ratios, prompting new inquiry into their properties as inequality measures. Current evidence suggests a mathematical link between top shares and the Gini coefficient and empirical links extending as well to the Atkinson measure. The work reported in this article strengthens that evidence, making several contributions: First, it formalizes the shares and ratios, showing that as monotonic transformations of each other, they are different manifestations of a single inequality measure, here called TopBot. Second, it presents two standard forms of TopBot, which satisfy the principle of normalization. Third, it presents a new link between top shares and the Gini coefficient, showing that properties and results associated with the Lorenz curve pertain as well to top shares. Fourth, it investigates TopBot in mathematically specified probability distributions, showing that TopBot is monotonically related to classical measures such as the Gini, Atkinson, and Theil measures and the coefficient of variation. Thus, TopBot appears to be a genuine inequality measure. Moreover, TopBot is further distinguished by its ease of calculation and ease of interpretation, making it an appealing People’s measure of inequality. This work also provides new insights, for example, that, given nonlinearities in the (monotonic) relations among inequality measures, Spearman correlations are more appropriate than Pearson correlations and that weakening of correlations signals differences and shifts in distributional form, themselves signals of income dynamics.

scholarly journals Intersecting Lorenz curves and aversion to inverse downside inequality

2020 ◽  
Author(s):  
W. Henry Chiu
Keyword(s):  
Gini Coefficient ◽  
Linear Inequality ◽  
The Other ◽  
Inequality Aversion ◽  
Inequality Index ◽  
Lorenz Curves ◽  
Income Distributions ◽  
The Gini Coefficient ◽  
Precise Condition

Abstract This paper defines and characterizes the concept of an increase in inverse downside inequality and show that, when the Lorenz curves of two income distributions intersect, how the change from one distribution to the other is judged by an inequality index exhibiting inverse downside inequality aversion often depends on the relative strengths of its aversion to inverse downside inequality and inequality aversion. For the class of linear inequality indices, of which the Gini coefficient is a member, a measure characterizing the strength of an index’s aversion to inverse downside inequality against its own inequality aversion is shown to determine the ranking by the index of two distributions whose Lorenz curves cross once. The precise condition under which the same result generalizes to the case of multiple-crossing Lorenz curves is also identified.

scholarly journals Analyzing the Relationship between the PM2.5 Concentration and the Gini Coefficient Using the Grey Model

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Lifeng Wu ◽  
Kai Cai ◽  
Yan Chen
Keyword(s):  
Gini Coefficient ◽  
Northwest China ◽  
Grey Model ◽  
Effective Control ◽  
Grey Prediction ◽  
Gini Coefficients ◽  
The Gini Coefficient ◽  
The Rich ◽  
The Relationship ◽  
Pm2.5 Concentration

To explore the relationship between the PM2.5 concentration and the gap between the rich and the poor, the PM2.5 concentration in 26 provincial regions of China is predicted by using the Gini coefficient as the independent variable. The nonequigap fractional grey prediction model (CFNGM (1, 1)) is used for data fitting and predicting. The validity of the model is verified by comparing with the traditional nonequidistant grey model. The predicting results show that the PM2.5 concentration in many provinces of China presents a roughly downward trend. In the past nine years, the Gini coefficients have declined in more than 70% of the 26 provinces. However, the development of the Gini coefficient in Northwest China fluctuates greatly and even has an upward trend in recent years. According to the predictive results, reasonable suggestions can be put forward for the effective control of PM2.5 emission in China.

scholarly journals Getting to a feasible income equality

PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0249204
Author(s):  
Ji-Won Park ◽  
Chae Un Kim
Keyword(s):  
Income Inequality ◽  
Income Distribution ◽  
Economic System ◽  
Gini Coefficient ◽  
Government Policies ◽  
Government Interventions ◽  
Income Equality ◽  
Income Distributions ◽  
The Gini Coefficient ◽  
Negative Impacts

Income inequality is known to have negative impacts on an economic system, thus has been debated for a hundred years past or more. Numerous ideas have been proposed to quantify income inequality, and the Gini coefficient is a prevalent index. However, the concept of perfect equality in the Gini coefficient is rather idealistic and cannot provide realistic guidance on whether government interventions are needed to adjust income inequality. In this paper, we first propose the concept of a more realistic and ‘feasible’ income equality that maximizes total social welfare. Then we show that an optimal income distribution representing the feasible equality could be modeled using the sigmoid welfare function and the Boltzmann income distribution. Finally, we carry out an empirical analysis of four countries and demonstrate how optimal income distributions could be evaluated. Our results show that the feasible income equality could be used as a practical guideline for government policies and interventions.

scholarly journals Income Inequality in Pakistan: An Analysis of Existing Evidence

1984 ◽  
Vol 23 (2-3) ◽  
pp. 365-379 ◽  
Author(s):  
Zafar Mahmood
Keyword(s):  
Standard Deviation ◽  
Income Distribution ◽  
Gini Coefficient ◽  
Coefficient Of Variation ◽  
Single Measure ◽  
Lorenz Curves ◽  
Inequality Measures ◽  
Income Distributions ◽  
Income Inequalities ◽  
Rank Distributions

To study the consequences of an economic change on income distribution we rank distributions of income at different points in time and quantify the degree of income inequalities. Changes in income distribution can be ascertained either through drawing the Lorenz curves or through estimating different inequality indices, such as Gini Coefficient, coefficient of variation, standard deviation of logs of in• comes, Theil's Index and Atkinson's Index. Ranking the distributions of income through Lorenz curves is, of course, possible only as long as they do not intersect. Moreover, when Lorenz curves do not intersect each other, all inequality measures rank income distributions uniformly. However, if the Lorenz curves do intersect each other. different inequality measures may rank income distributions differently and thus the direction of change cannot be determined unambiguously. For this reason , the use of a single measure would be misleading. Accordingly , the use of a 'package' of inequality measures becomes essential.

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.

Measuring and Explaining Economic Inequality

2013 ◽  
pp. 87-101
Author(s):  
C. Chameni Nembua
Keyword(s):  
Case Studies ◽  
Gini Coefficient ◽  
Gini Index ◽  
Economic Inequality ◽  
Transfer Principle ◽  
New Class ◽  
The Gini Coefficient ◽  
The One ◽  
Theoretical Results ◽  
Subgroup Decomposition

This chapter proposes a new class of inequality indices based on the Gini coefficient (or index). The properties of the indices are studied and are found to be regular, relative, and to satisfy the Pigou-Dalton transfer principle. A subgroup decomposition is performed, and the method is found to be similar to the one used by Dagum when decomposing the Gini index. The theoretical results are illustrated by case studies, using Cameroonian data.

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