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.

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.

Cooperation dynamics of polycentric climate governance

2015 ◽  
Vol 25 (13) ◽  
pp. 2503-2517 ◽  
Author(s):  
Vítor V. Vasconcelos ◽  
Francisco C. Santos ◽  
Jorge M. Pacheco
Keyword(s):  
Common Good ◽  
Evolutionary Game ◽  
Wealth Inequality ◽  
Small Scale ◽  
The Poor ◽  
Viable Solution ◽  
The Rich ◽  
Global Coordination ◽  
The Impact ◽  
Climate Change Governance

Global coordination for the preservation of a common good, such as climate, is one of the most prominent challenges of modern societies. In this manuscript, we use the framework of evolutionary game theory to investigate whether a polycentric structure of multiple small-scale agreements provides a viable solution to solve global dilemmas as climate change governance. We review a stochastic model which incorporates a threshold game of collective action and the idea of risky goods, capturing essential features unveiled in recent experiments. We show how reducing uncertainty both in terms of the perception of disaster and in terms of goals induce a transition to cooperation. Taking into account wealth inequality, we explore the impact of the homophily, potentially present in the network of influence of the rich and the poor, in the different contributions of the players. Finally, we discuss the impact of polycentric sanctioning institutions, showing how such a scenario also proves to be more efficient than a single global institution.

How to Boost the Payoff from Innovation While Shrinking its Destructive Side Effects

2021 ◽  
Vol 95 (4) ◽  
pp. 823-840
Author(s):  
Robert J. Gordon
Keyword(s):  
Climate Change ◽  
Economic Growth ◽  
Side Effects ◽  
Wealth Inequality ◽  
Profit Margins ◽  
Income Share ◽  
The Rich ◽  
Human Costs ◽  
Deaths Of Despair

Gather a group of economists together and ask what most concerns them, and a wide variety of topics would soon emerge: slowing economic growth in the rich nations, the inability of many poor nations to converge toward the rich, rising income and wealth inequality, the increasing dominance of superstar firms, growing profit margins and the decline in labor's income share, globalization and the human costs of outsourcing, deaths of despair, and the threat of climate change. Decade after decade, numerous books have been written about each of these issues. But here we have in one compact package a blockbuster book that deals with all of them.

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 A Meta-Analysis of the Association between Income Inequality and Intergenerational Mobility

2019 ◽  
Vol 5 ◽  
pp. 237802311988128 ◽  
Author(s):  
Ernesto F. L. Amaral ◽  
Shih-Keng Yen ◽  
Sharron Xuanren Wang-Goodman
Keyword(s):  
Income Inequality ◽  
Gini Coefficient ◽  
Intergenerational Mobility ◽  
Meta Analysis ◽  
The United States ◽  
Income Share ◽  
Income Elasticities ◽  
Great Gatsby ◽  
The Gini Coefficient ◽  
Over Time

We provide an overview of associations between income inequality and intergenerational mobility in the United States, Canada, and eight European countries. We analyze whether this correlation is observed across and within countries over time. We investigate Great Gatsby curves and perform metaregression analyses based on several papers on this topic. Results suggest that countries with high levels of inequality tend to have lower levels of mobility. Intergenerational income elasticities have stronger associations with the Gini coefficient compared to associations with the top 1 percent income share. Once models are controlled for methodological variables, country indicators, and paper indicators, correlations of mobility with the Gini coefficient lose significance but not with the top 1 percent income share. This result is an indication that recent increases in inequality at the top of the distribution might be negatively affecting mobility on a greater magnitude compared to variations across the income distribution.

Introduction

2018 ◽  
Author(s):  
Børge Bakken
Keyword(s):  
Gini Coefficient ◽  
Relative Income ◽  
Income Differences ◽  
The Poor ◽  
The Gini Coefficient ◽  
The People ◽  
The World ◽  
The Chinese Dream ◽  
Party Ideology ◽  
Strong Inequality

Børge Bakken explains that the Party ideology of the “Chinese Dream” is not the alleged dream of the people as presented by the propaganda, but rather the dream of the emperor. The “Dream” is instead building on a strategy of “betting on the strong”. Inequality in China as measured by the Gini coefficient of relative income differences has reached world top levels, making China one of the most unequal societies in the world today. It is virtually impossible for poor migrants to achieve any kind of prosperity under circumstances disfavouring them. In coping with this problem, the poor and the destitute employ illegal strategies and employ certain “weapons of the weak” in order to cope with the strain created by the unequal framework they are operating within.

The case for welfare state universalism, or the lasting relevance of the paradox of redistribution

2018 ◽  
Vol 28 (1) ◽  
pp. 70-85 ◽  
Author(s):  
Olivier Jacques ◽  
Alain Noël
Keyword(s):  
Welfare State ◽  
Institutional Design ◽  
Welfare States ◽  
Cross Sectional ◽  
Robin Hood ◽  
The Poor ◽  
Provision Of Services ◽  
Original Argument ◽  
The Rich ◽  
Cross Sectional Design

In 1998, Walter Korpi and Joakim Palme proposed a political and institutional explanation to account for the greater redistributive success of welfare states that relied more on universal than on targeted programmes. Effective redistribution, they argued, resulted less from a Robin Hood logic – taking from the rich to give to the poor – than from a broad and egalitarian provision of services and transfers. Hence, the paradox: a country obtained more redistribution when it took from all to give to all than when it sought to take from the rich to help the poor. Recent studies, however, failed to confirm the existence of this paradox. This article suggests that the original argument was theoretically sound but inadequately operationalized. Korpi and Palme measured universalism indirectly, not by the design or character of social programmes, but rather by their outcomes, namely, by their income effects. These outcomes, however, are influenced by exogenous factors. We use two new Organisation for Economic Co-operation and Development (OECD) indicators to capture universalism directly, through the institutional design of social programmes: (1) the percentage of social benefits that are means or income tested and (2) the proportion of private spending in total social expenditures. These two indicators are combined into a universalism index and tested with a time-series cross-sectional design for 20 OECD countries between 2000 and 2011. This approach, we argue, better captures institutional design, in a way that is consistent with Korpi and Palme’s original argument, and it suggests that there is still a paradox of redistribution in the 21st-century welfare state.

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 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.

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