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 Measurement of Inequality and Compression of Mortality in India for 4 Decades: 1970–2015

2020 ◽  
Vol 4 (Supplement_1) ◽  
pp. 68-68
Author(s):  
Mukesh Parmar
Keyword(s):  
Standard Deviation ◽  
Gini Coefficient ◽  
Age At Death ◽  
Registration System ◽  
Death Rates ◽  
Male And Female ◽  
Inequality Measures ◽  
Sample Registration System ◽  
Dispersion Measures ◽  
Measurement Of Inequality

Abstract The studies relating to measurement of compression of Mortality in India is scarce. Most of the studies relating to mortality in India are focused on either life expectancy, or adult, and child mortality. We have used methods suggested by Kannisto (2000) and Canudos (2008) to measure the compression of mortality phenomenon for India for four decades viz. 1970-2015. Dispersion measures like simple mean, median, modal age at death; and some complicated measures like life disparity, standard deviation above mode, standard deviation in highest quartile, Interquartile range, Gini coefficient, AID and C-family were calculated for India from 1970-2015. We used the age specific death rates from abridged Life tables given by Sample Registration System published by Govt. of India. Our results show that inequality in mortality is decreasing in general but the gap between male and female is increasing. There was an average of three years difference in mean and modal age at death between male females in 2011-15. Overall, mean, median and modal age at death has increased in four decades but other inequality measures like Gini coefficient, AID, Standard deviation (SD) and coefficient of variation has decreased in four decades in India. C50 indicator, which indicates that 50 percent of deaths are happening in that age interval, declined from 26 years to 20 years for males and 27 years to 17 years for females, thus indicating the rate of compression of mortality is higher for females than males in India during 1970-75 till 2011-15.

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.

On the Measurement of Participation Equality

2014 ◽  
Vol 10 (4) ◽  
pp. 32-48 ◽  
Author(s):  
Bruce A. Reinig ◽  
Roberto J. Mejias
Keyword(s):  
Standard Deviation ◽  
Gini Coefficient ◽  
Coefficient Of Variation ◽  
Exploratory Study ◽  
Support Systems ◽  
Collaborative Work ◽  
Group Support Systems ◽  
Group Support ◽  
Work Practices ◽  
Team Members

Participation equality is often a key process construct in research models that examine the effects of group support systems (GSS) technology and e-collaboration. GSS are generally thought to reduce the dispersion of participation among team members and thus make participation more equally distributed. However, research conclusions in the literature regarding participation equality are not always consistent with this finding. Researchers have used a variety of approaches to operationalize participation equality including unit-based measures, such as the standard deviation, and dimensionless measures such as the Gini coefficient and the coefficient of variation. Researchers have also varied in their measurement of participation units with some counting phenomena such as comments, words, or remarks. The authors report on an exploratory study that demonstrates conditions in which research conclusions regarding the participation equality construct are dependent on both the participation unit analyzed and whether a unit-based or dimensionless measure is used to compute participation equality. The authors conclude with recommendations for researchers investigating participation equality and practitioners that seek to measure and track participation equality in their collaborative work practices.

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.

ASPECTS OF INCOME INEQUALITY IN GREECE: 1959-1982

1988 ◽  
Author(s):  
Αλεξάνδρα Λειβαδά
Keyword(s):  
Income Inequality ◽  
Income Distribution ◽  
Survey Data ◽  
Inequality Index ◽  
Lorenz Curves ◽  
Inequality Measures ◽  
Inflation Rates ◽  
Income Data ◽  
Distributional Impact ◽  
Reported Income

THIS THESIS EXAMINES MACROECONOMIC AND MICROECONOMIC ASPECTS OF INCOME INEQUALITY IN GREECE DURING THE PERIOD 1959-1982. THE MACROECONOMIC ASPECTS ARE CONCERNED WITH THE TREND AND CYCLES OF INCOME DISTRIBUTION. THE MICROECONOMIC ASPECTS ARE RELATED TO THE DISTRIBUTIONAL IMPACT OF HOUSEHOLD'S INFLATION RATES. A BROAD SET OF SUMMARY AND DISAGGREGATED INEQUALITY MEASURES IS COMPUTED FOR THE FORMER PURPOSE USING REPORTED INCOME DATA FROM TAX DECLARATIONS. THERE IS A DISCREPANCY IN THE SUGGESTED INEQUALITY TREND DUE TO INTERSECTING LORENZ CURVES AND THE PROPERTIES SATISFIED BY EACH INEQUALITY INDEX. ALSO, THE 1981-82 HOUSEHOLD EXENDITURE SURVEY DATA ARE USED TO CALCULATE THE DISTRIBUTION RATES ACROSS HOUSEHOLDS.

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 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.

Intraregional Income Distribution and Poverty: Some Investigations for the Netherlands, 1960–81

1989 ◽  
Vol 21 (7) ◽  
pp. 881-904 ◽  
Author(s):  
P Rietveld ◽  
H Ouwersloot
Keyword(s):  
The Netherlands ◽  
Income Distribution ◽  
Metropolitan Areas ◽  
Urban Poverty ◽  
Rural Poverty ◽  
Provincial Level ◽  
Income Distributions ◽  
Income Inequalities ◽  
Widespread Phenomenon

This paper is addressed to intraregional income inequalities in the Netherlands. Various concepts are used to measure the degree of regional poverty. In addition, dissimilarity between intraregional income distributions is studied. At the provincial level, relatively small and decreasing dissimilarities are observed. However, at lower spatial levels (especially within metropolitan areas) much larger dissimilarities in mean income and income distribution occur. In the Netherlands, urban poverty has become a more intense and widespread phenomenon than rural poverty.

scholarly journals The Croatian banking system total assets concentration dynamics: performing a variety of inequality measures

2018 ◽  
Vol 4 (1) ◽  
pp. 14-26 ◽  
Author(s):  
Adela Delalić ◽  
Maja Čurković ◽  
Josipa Antić
Keyword(s):  
Gini Coefficient ◽  
Coefficient Of Variation ◽  
Banking System ◽  
Theoretical Framework ◽  
Entropy Measure ◽  
Inequality Measures ◽  
The Past ◽  
Atkinson Index ◽  
National Bank ◽  
Concentration Indices

Abstract The paper provides an overview of the trend in the concentration of the total assets of banks in Croatia for the period from 2007 to 2016 with the aim of analysing and presenting the changes that occurred in the system. Also, the paper shows the theoretical framework of the indicators used in the research as well as the comparison of their obtained values. The data used to calculate the total assets concentration are taken from the Croatian National Bank. The concentration indices used in the study include the entropy measure, the Theil entropy, the Gini coefficient, the Pietra index, the Atkinson index and the coefficient of variation. The results indicate a very slight decrease in concentration over the past several years, while the coefficient of variation points to the heterogeneity of the system, as well as to inequalities among the banks, which are most evident in the size of banks assets.

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