The Gini index,the dual decomposition of aggregation functions, and the consistent measurement of inequality

In several economic fields, such as those related to health, education or poverty, the individuals’ characteristics are measured by bounded variables. Accordingly, these characteristics may be indistinctly represented by achievements or shortfalls. A difficulty arises when inequality needs to be assessed. One may focus either on achievements or on shortfalls but the respective inequality rankings may lead to contradictory results. Specifically, this paper concentrates on the poverty measure proposed by Sen. According to this measure the inequality among the poor is captured by the Gini index. However, the rankings obtained by the Gini index applied to either the achievements or the shortfalls do not coincide in general. To overcome this drawback, we show that an OWA operator is underlying in the definition of the Sen measure. The dual decomposition of the OWA operators into a self-dual core and anti-self-dual remainder allows us to propose an inequality component which measures consistently the achievement and shortfall inequality among the poor.Aggregation functions, dual decomposition, OWA operators, Gini index, consistent measures of achievement/shortfall inequality, Sen index, poverty measures.

The Gini Index and Measures of Inequality

The Gini index is a summary statistic that measures how fairly a resource is distributed in a population; income is a primary example. In addition to a self-contained presentation of the Gini index, we give two equivalent ways to interpret this summary statistic: first in terms of the percentile level of the person who earns the average dollar, and second in terms of how the lower of two randomly chosen incomes compares, on average, to mean income

Measurement and explanation of socioeconomic inequality in health with longitudinal data

This paper presents a method for the measurement of changes in health inequality and income-related health inequality over time in a population. For pure health inequality (as measured by the Gini coefficient) and income-related health inequality (as measured by the concentration index), we show how measures derived from longitudinal data can be related to cross section Gini and concentration indices that have been typically reported in the literature to date, along with measures of health mobility inspired by the literature on income mobility. We also show how these measures of mobility can be usefully decomposed into the contributions of different covariates. We apply these methods to investigate the degree of income-related mobility in the GHQ measure of psychological well-being in the first nine waves of the British Household Panel Survey (BHPS). This reveals that dynamics increase the absolute value of the concentration index of GHQ on income by 10%.Health inequalities, mobility, Gini and concentration indices, mental health, BHPS

Introduction to measures of inequality and concentration in tourism

There are many statistical measures available in the literature for the analysis of inequality and concentration. The most common measure in this field is the Gini index (Roselló Nadal et al.,2004), which is associated to the Lorenz curve. Both were developed at the beginning of the 20th century: the Lorenz curve in 1905 and the Gini index in 1914 (Giorgi,!1993). A revision of recent applications of these measures in the field of tourism can be found in Cisneros Martín and Fernández Morales (2015)and Duro (2016)

A behaviorally-based approach to measuring inequality

The measurement of inequality is often made using observed population-based distributions, such as the distribution of income or the distribution of members of different groups across neighborhoods. Unfortunately, such distributions confound the behavior of a given year with earlier events that influence the composition of the population. Here, we advocate measuring inequality using current behavioral measures and their compositional implications, and show how such measures may be obtained from frequently available data. The approach is then applied to trends in inequality between men and women in the distribution of ages at death. Observed death distributions indicate that, since 1970, mortality in 4 Western countries experienced increases in inequality that recently leveled off. In contrast, life table death distributions, which solely reflect the implications of a given year’s mortality rates, reveal a peak in inequality followed (in 3 of the 4 countries) by appreciable declines. The results are insensitive to whether inequality is measured by entropy, the Gini Index, or the Index of Dissimilarity. However, the type of distribution analyzed---whether observed or behaviorally derived---can make a significant difference in the results obtained. Because behaviorally derived distributions reflect the inequality implications of actual behavior, they are recommended for greater use in analyses of inequality.behaviorally-based, entropy, Gini Index, index of dissimilarity, inequality, measurement

Decomposition of Gini and the generalized entropy inequality measures

In this article we provide an overview of the Gini decomposition and the generalized entropy inequality measures, a free access to their computation, an application on French wages, and a different way than Dagum to demonstrate that the Gini index is a more convenient measure than those issued from entropy: Theil, Hirschman-Herfindahl and Bourguignon.

Measuring Regional Inequality by Internet Car Price Advertisements: Evidence for Germany

We suggest to use Internet car sale price advertisements for measuring economic inequality between and within German regions. Our estimates of regional income levels and Gini indices based on advertisements are highly, positively correlated with the official figures. This implies that the observed car prices can serve as a reasonably good proxy for income levels. In contrast to the traditional measures, our data can be fast and inexpensively retrieved from the web, and more importantly allow to estimate Gini indices at the NUTS2 level-something that never has been done before. Our approach to measuring regional inequality is a useful alternative source of information that could complement officially available measures.Car price advertisements, economic inequality, German NUTS1 and NUTS regions, Gini index, Internet