The adjusted generalised entropy curve as a general descriptive and normative measure of income inequality, with a compression and estimation procedure (original) (raw)
Related papers
2015
The Atkinson Index provides a normative measure of income inequality which is identical to welfare losses from inequality under an additive utilitarian SWF where utility is solely based on individual income or consumption, and the inequality aversion parameter is equal to the elasticity of marginal utility of income. However, it is now generally accepted that wellbeing is partially dependent on relative, in addition to absolute income, and therefore the standard Atkinson index is not a very good predictor of utilitarian welfare losses when relative income effects are salient. Furthermore prioritarian concerns may raise inequality aversion somewhat above the utilitarian optimum. This paper introduces a five parameter generalization of the Atkinson index, adding parameters to control the intensity of relative income effects, the weight given to individuals with varying income in determining reference income, and two parameters regulating the effect of inequality on reference income via an indirect pathway. The index is further generalized to a seven parameter case, where prioritarian concerns are modelled via an additive nonlinear SWF. Depending on parameter values, the index is capable of simultaneously being sensitive to both bottom and top tail inequality. In particular, the index may be sensitive to super-heavy power law (Pareto) top tail inequality, for example within a lognormal-Pareto two class distribution, as shown by example. A closed form solution is given for lognormal inequality; the index can be estimated via a simple transformation under the lognormal assumption from various inequality measures, including all generalized entropy (GE) indexes and the variance of logarithms. Under restricted conditions estimates are obtainable without the lognormality assumption, less restrictively estimation of the index may be obtained with some precision simply from a pair of generalized entropy indexes of order 0 and 1.
On the capacity of the Gini index to represent income distributions
Metron-International Journal of Statistics, 2020
Almost all governmental and international agencies use the Gini index to summarize income inequality in a nation or the world. The index has been criticized because it can have the same value for two different distributions. It will be seen that other commonly used summary measures of inequality are subject to the same criticism. The Gini index has the advantage that it is able to distinguish between two distributions that have identical integer valued generalized entropy measures. Because no single measure can fully summarize a distribution, researchers should consider combining the Gini index with another measure appropriate for the topic being studied. Keywords Generalized entropy measures • Gini index • Lorenz curve • Measures of income inequality • Pareto distribution • Moment problem
The estimation of a family of measures of economic inequality
Journal of Econometrics, 1975
This paper shows that a broad class of measures of inequality (including those of Herfindahl and Theil) can be readily (and accurately) estimated from grouped data. The methods are similar to those developed earlier by the author for estimating the Gini index. The results are illustrated by estimating Theil's index from tax data and show that the standard textbook grouping method of assuming that all incomes in any class are at the mid-point can lead to serious error in the resulting estimate of inequality.
Dual-Index Measurement of Income Inequality
Bulletin of Economic Research
This study introduces the concept of unequally distributed income and proposes a dual-index measurement of income inequality that evaluates the magnitude and dispersion of unequally distributed income. We use the Rawlsian index as a magnitude index and employ current income inequality indices as a dispersion index. We describe the properties of the Rawlsian and dispersion indices, and apply these indices to real income data. Further, we show that the Gini dispersion index is a weighted average of Rawlsian indices for the sub-distributions of the unequally distributed income distribution.
The Welfare Approach to Measuring Inequality
Sociological Methodology, 1980
and reviewers for their useful comments and suggestions. Any errors, however, are the responsibility of the authors, who contributed equally to the chapter. 1 JOSEPH SCHWARTZ AND CHRISTOPHER WINSHIP Recently, sociologists have expressed a renewed interest in the theoretical and empirical study of inequality, its determinants, and its effects. Recent studies include Gartrell (1977), Rubinson and Quinlan (1977), Blau (1977), Jencks and others (1972), and Chase-Dunn (1975).1 In such studies the analysts usually choose a single index to measure inequality, such as the coefficient of variation or the Gini coefficient, and then use it to analyze their data. With the exception of Blau, few have made an explicit attempt to define the concept of inequality or to justify the chosen index as an appropriate measure of inequality. However, choosing a single index from the available ones implies that inequality is a unidimensional concept and that the chosen index is a valid measure of it. But it is not necessarily the case that different measures of inequality will correlate highly with the concept and with each other and that they will therefore rank distributions in the same order. Different measures may yield different results, and the differences may be considerable. We demonstrate this by analyzing the Kuznets data (1963) on the distribution of individual income for 12 countries in about 1950. Table 1 presents rank-order correlations (Kendall's tau) among four commonly used measures of inequality applied to data (Tables 2 to 4): the coefficient of variation (CV), the Gini coefficient (GC), the standard deviation of the logarithm (SDL), and the mean relative deviation (MRD). Formulas for these measures are given in the appendix. The first three measures are commonly used to measure income inequality; the mean relative deviation is used for this purpose and for measuring degree of segregation.2 The correlations 1 The recent paper by Allison (1978) discusses, with a different emphasis, some of the issues explored in this chapter. Except for this note, we make no reference to it, mainly because we have had too little time to consider its content critically. 2 In this context the mean relative deviation is known as the index of dissimilarity. Duncan and Duncan (1955) show that measuring segregation is structurally similar to measuring economic inequality. (See also Winship, 1978.) Our comments about measures of inequality therefore pertain also to measures of segregation. Although measures of inequality have been applied to many problems outside economics (for example, education; see Blau, 1977), we limit our discussion to the problem of measuring economic inequality. See Agresti and Agresti (1977) for a discussion related to measuring inequality in the distribution of a nominal variable. 2 WELFARE APPROACH TO MEASURING INEQUALITY TABLE 1 Kendall Rank-Order Correlations (Tau) Between Different Measures of Inequality Measure CV MRD GC SDL Coefficient of variation 1.000 0.727 0.697 0.152 Mean relative deviation 1.000 0.909 0.424 Gini coefficient 1.000 0.454 Standard deviation of logarithm 1.000 of the standard deviation of the logarithm of income with each of the other measures are the lowest-0.152, 0.424, and 0.454. The correlations between the coefficient of variation and the mean relative deviation and Gini coefficient are moderately large. Even the correlation of the mean relative deviation and Gini coefficient is not as high as one might expect from the similarity of their definitions. For an example of the point that different measures may yield inconsistent rankings, consider India and Sweden: India is ranked ninth, eleventh, eleventh, and third by the CV, the MRD, the GC, and the SDL, respectively. Sweden is ranked sixth, fourth, fourth, and eleventh by each of these respective measures. TABLE 2 Percentage of Total Income Received by Ranked Cohorts of Population Country Year 0-20
Evaluation of Income Distribution in OECD Countries with Income Inequality Indexes
2016
Income inequality is an indicator of how material resources are distributed across society. Some people consider high levels of income inequality are morally undesirable. Others focus on income inequality as bad for economic progress of country (OECD Report; 2015). Chile, Mexcio and Turkey had the highest income inequality. OECD Anglophone countries had levels of inequality around or above the OECD average. From this point of view, this study aims to analyze the income inequality for OECD countries. For this aim, we use some indexes to analyze inequality. These indexes are GINI Index, GNI, Atkinson Index and Decile Ratio. * Bu çalışma 24-26 Ağustos 2016 tarihinde İstanbul/Türkiye'de düzenlenmiş olan Politik, Ekonomik ve Sosyal Araştırmalar Kongresinde (ICPESS-2016) özet bildiri olarak sunulmuştur. OECD Ülkelerinde Gelir Dağılımının Gelir Eşitsizliği İndeksleri İle Değerlendirilmesi 154 Research Journal of Politics, Economics and Management, 2016, Year:4, Volume:4, Issue:4 We use...
2012
We establish the conditions under which a close functional relationship between objective and subjective inequality measures can be derived. These conditions are satisfied by many of the most important models for the distribution of income that have been proposed in the literature. We illustrate this result looking at the relationship between the Atkinson indices and the Gini coefficient for the lognormal, the Singh-Maddala, and the second kind beta distributions. While in the first case a positive functional relationship exists regardless of the level of inequality aversion, in the other two cases this relationship is observed when the inequality aversion parameter is smaller and greater than one, respectively. Importantly for the natural rate of subjective inequality (NRSI) hypothesis proposed by Lambert et al. (2003), the proportion of countries with aversion to inequality above the unity in the sample used by these authors is above 50 percent for almost every value of the NRSI c...
Income inequality of households in Poland: A subgroup decomposition of generalized entropy measures
Econometrics
A formula of measures applied to assess the level of income inequality results from the intellectual basis on which this approach is founded. Our paper focuses on Generalized Entropy measures. The aim of our paper is twofold. Firstly, it aims at presenting GE measures and discussing their properties, especially the property of additive decomposition. Secondly, the empirical aim is to assess the level of income inequality in Poland and to indicate its main determinants. In the study we use microdata obtained from EU-SILC that cover information about incomes received by individual household members in 2016. Five factors are chosen as the possible drivers of income inequality. The study proves the characteristics related to human capital are the most influential factors of income variability between households. The characteristics describing the composition of the household contribute to the overall level of inequality to a smaller extent.