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.

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 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 Equality in Income and Sustainability in Economic Growth: Agent-Based Simulations on OECD Data.

2019 ◽  
Vol 11 (20) ◽  
pp. 5803 ◽  
Author(s):  
Sakaki
Keyword(s):  
Economic Growth ◽  
Income Distribution ◽  
Gini Coefficient ◽  
The Other ◽  
Agent Based ◽  
The Gini Coefficient ◽  
Marginal Propensity To Consume ◽  
Marginal Propensity ◽  
Stable Growth

In countries that have developed under the current market economy, inequalities in income distribution tend to increase with three different trends, i.e., high (United States, United Kingdom, Japan), low (North Europe countries), and medium Gini coefficient levels. On the other hand, the relationship between income distribution and social welfare is generally a difficult problem to solve in economics. So, this paper discusses the impact of income distribution on the macroeconomy, limiting the scope to consistency with long-term economic growth. We attempt to answer these economic policy issues by simulation using an agent-based model based on replicator dynamics. As a result of the simulation in this paper, in general, in countries with the high marginal propensity to consume, long-term growth can be maintained by inducing equality in income distribution. On the other hand, a mature country with a low marginal propensity to consume can sustain not so high but stable growth despite increasing inequality in income distribution. According to simulation results based on OECD (Organisation for Economic Co-operation and Development) data, in the former UK, US, and Japan, the lower the Gini coefficient is, the higher the growth potential is, while in the latter Norway and Luxembourg, relatively stable growth is maintained even if the Gini coefficient increases.

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 Group averaging and the Gini deviation

2021 ◽  
Vol 29 (3) ◽  
pp. 595-605
Author(s):  
Oleg I. Pavlov ◽  
Olga Yu. Pavlova
Keyword(s):  
Gini Coefficient ◽  
Upper Bound ◽  
Lorenz Curve ◽  
Piecewise Linear ◽  
Geometric Parameters ◽  
Natural Question ◽  
Lorenz Curves ◽  
The Gini Coefficient ◽  
The Difference ◽  
Group Averaging

It is known that partitioning a society into groups with subsequent averaging in each group decreases the Gini coefficient. The resulting Lorenz function is piecewise linear. This study deals with a natural question: by how much the Gini coefficient could decrease when passing to a piecewise linear Lorenz function? Obtained results are quite illustrative (since they are expressed in terms of the geometric parameters of the polygon Lorenz curve, such as the lengths of its segments and the angles between successive segments) upper bound estimates for the maximum possible change in the Gini coefficient with a restriction on the group shares, or on the difference between the averaged values of the attribute for consecutive groups. It is shown that there exist Lorenz curves with the Gini coefficient arbitrarily close to one, and at the same time with the Gini coefficient of the averaged society arbitrarily close to zero.

scholarly journals How do mean division shares affect growth and development

2017 ◽  
Vol 64 (5) ◽  
pp. 525-545 ◽  
Author(s):  
Liang Shao
Keyword(s):  
Panel Data ◽  
Gini Coefficient ◽  
Growth And Development ◽  
Income Share ◽  
Lorenz Curves ◽  
Growth Outcomes ◽  
The Gini Coefficient ◽  
Household Disposable Income ◽  
The Mean ◽  
Per Capita

The Gini coefficient is widely used in academia to discuss how income inequality affects development and growth. However, different Lorenz curves may provide different development and growth outcomes while still leading to the same Gini coefficient. This paper studies the development effects of ?mean division shares?, i.e., the share of income (mean income share) held by people whose household disposable income per capita is below the mean income and the share of the population (mean population share) with this income, using panel data. Our analysis explores how this income share and population share impact development and growth. It shows that the income and population shares affect growth in significantly different ways and that an analysis of these metrics provides substantial value compared to that of the Gini coefficient.

scholarly journals Why We Should Use the Gini Coefficient to Assess Punctuated Equilibrium Theory

2021 ◽  
pp. 1-6
Author(s):  
Constantin Kaplaner ◽  
Yves Steinebach
Keyword(s):  
Policy Change ◽  
Gini Coefficient ◽  
Policy Making ◽  
Punctuated Equilibrium ◽  
Equilibrium Theory ◽  
Punctuated Equilibrium Theory ◽  
The Gini Coefficient ◽  
Precise Measure

Abstract Punctuated Equilibrium Theory posits that policy-making is generally characterized by long periods of stability that are interrupted by short periods of fundamental policy change. The literature converged on the measure of kurtosis and L-kurtosis to assess these change patterns. In this letter, we critically discuss these measures and propose the Gini coefficient as a (1) comparable, but (2) more intuitive, and (3) more precise measure of “punctuated” change patterns.

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