Welfare, inequality and the transformation of incomes the case of weighted income distributions (original) (raw)

Measuring income redistribution: beyond the proportionality standard

2017

Traditional analyses of redistributive effects of the tax-benefit system are rooted in the concepts of relative income inequality and proportionality. This observation also applies to decompositions proposed by Kakwani (1977, 1984) and Lambert (1985) that reveal the vertical and horizontal effects of tax-benefit instruments. This paper generalises those decompositions within the frameworks of the alternative inequality concepts suggested by Ebert (2004) and Bosmans et al. (2014). As expected, the results of the empirical analysis indicate that for different views of inequality, different taxes and benefits play significantly different roles in reducing inequality.

Measuring income inequality based on unequally distributed income

Journal of Economic Interaction and Coordination

This paper proposes a new framework for measuring income inequality. The framework is based on the unequally distributed (UD) incomes that are obtained by removing the equally distributed parts from incomes. We then derive the normalized norm indexes from the cumulative distribution function and the unscaled Lorenz curve of the UD incomes. The relation between the normalized norm indexes and the popular Gini coefficient and coefficient of variation (CV) shows that the Gini coefficient and CV represent only parts of income inequality. We analyze example income distributions and the Luxembourg Income Study datasets to show that the normalized norm indexes evaluate income inequality appropriately and solve the negative income problem.

Measuring income inequality via percentile relativities

The rich are getting richer" implies that the population income distributions are getting more right-skewed and heavy-tailed. For such distributions, the mean is not the best measure of the center, but the classical indices of income inequality, including the celebrated Gini index, are all mean-based. In view of this, Professor Gastwirth sounded an alarm back in 2014 by suggesting to incorporate the median into the definition of the Gini index, although noted a few shortcomings of his proposed index. In the present paper we make a further step in the modification of classical indices and, to acknowledge the possibility of differing viewpoints, arrive at three median-based indices of inequality. They avoid the shortcomings of the previous indices and can be used even when populations are ultra-heavy tailed, that is, when their first moments are infinite. The new indices are illustrated both analytically and numerically using parametric families of income distributions, and further illustrated using a real data set of capital incomes of fifteen countries. We also discuss the performance of the indices from the perspective of the Pigou-Dalton principle of transfers.

A SOCIAL WELFARE VIEW OF THE MEASUREMENT OF INCOME EQUALITY

Review of Income and Wealth, 1967

Economists' use of the term “equality” in reference to a distribution of incomes has historically been in the sense of a consensus for some statistical characteristic(s) of the distribution rather than a firm concept of equality. Of course such a concept rests on appropriate welfare assumptions about income and its distribution, assumptions which, for the most part, have been left implicit (and unknown) in discussions of income equality in the literature.Our purpose in this paper is dual: first, we wish to discover an unambiguous, welfare-related equality measure. This we accomplish through suitable assumptions on a social welfare function. What is produced is an “index” of equality which describes the performance of a given distribution relative to the maximum welfare derivable from the total income it represents. The measure thus depends functionally on the welfare attributes of income, something which in reality we know little about.This impasse leads us to inquire into the sensitivity of the index over specifications of the welfare function, which is done by comparing equality ranks for the states of the United States for 1960 under various functional forms and among curves within a given form. As an interesting secondary issue, the performance of traditional equality measures is tested relative to the welfare-oriented index to discover implications about their welfare content.It is found that the equality index is, in certain ranges for the welfare function, insensitive to its specification. The findings lead directly to conclusions concerning traditional equality measures, their usefulness in correctly accounting for equality differences among alternative income distributions and, concomitantly, their implicit welfare inputs.

Income Inequality Measures

Theoretical Economics Letters, 2018

Income distributions are commonly unimodal and skew with a heavy right tail. Different skew models, such as the lognormal and the Pareto, have been proposed as suitable descriptions of income distribution and applied in specific empirical situations. More wide-ranging tools have been introduced as measures for general comparisons. In this study, we review the income analysis methods and apply them to specific Lorenz models.

Income Distribution and Inequality

What are the principal issues on which research on income distribution and inequality focus? How might that focus shift in the immediate future? We examine the standard market-based approaches to theorising on the income distribution and the challenges to this analysis posed by the economics of information and various types of market failure. We also consider the problems of representing the income distribution in a way that has economic meaning and of comparing distributions in terms of inequality and social welfare. There is also a snapshot view of some of the remarkable empirical developments concerning the income distribution in advanced countries in the late 20th and early 21st centuries. Prepared for the The Elgar Companion to Social Economics.

Evaluating Distributional Differences in Income Inequality with Sampling Weights

This research note follows up on the article " Evaluating Distributional Differences in Income Inequality " published in this journal (Liao 2016) and extends the methods proposed there by incorporating the functionality of using sampling weights. It also discusses the issue of including zero values in Theil index computation where a common incorrect practice is their exclusion.

Impact of Taxes and Benefits on Inequality among Groups of Income Units

Review of Income and Wealth

This paper analyzes the redistributive impact of the fiscal system and simultaneously explains how each tax and benefit instrument satisfies the principles of vertical and horizontal equity within and across different groups of income units. The decompositions of the redistributive effect are based on new axioms concerning the vertical and horizontal equity of the overall fiscal system, including taxes and benefits. The method is based on pairwise comparisons of income units and the "micro" concepts of income supremacy change, deprivation from reranking, and income distance change. The decomposition results provide more detailed insights into the income redistribution process than is typical in the literature. This is illustrated by an empirical application of the method to the Croatian scheme of personal income taxes and non-pension social benefits, in which households are divided into two groups, those with and those without children.

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