Generalized entropy and the measurement of distributional change

Journal of Public Economics, 1984

Cahiers De Recherche, 1995

We establish the asymptotic sampling distribution of general functions of quantile-based estimators computed from samples that are not necessarily independent. The results provide the statistical framework within which t o assess the progressivity of taxes and bene ts, their horizontal inequity, and the change in the inequality of income which they cause. By the same token, these ndings characterise the sampling distribution of a number of popular indices of progressivity, horizontal inequity, and redistribution. They can also be used to assess welfare and inequality c hanges using panel data, and to assess poverty when it depends on estimated population quantiles. We illustrate these results using micro data on the incidence of taxes and bene ts in Canada.

Documents de Travail du Centre d’Economie de la Sorbonne, 2018

The present paper proposes a theoretical framework to examine the relationship between the functional and personal distribution of income. To this end, it introduces the concept of inequality in income composition. Inequality in income composition is high when two di erent sources of income are separately earned by the top and the bottom of the income distribution. On the contrary, it is low when each individual has the same population share of the two sources. This article designs an indicator to measure income composition inequality, named income- factor concentration index. The sign of the indicator determines the condition of transmission for the rising share of income from any source to increase overall income inequality. This framework is then applied to several European countries on basis of EU-SILC data.

Journal of Development Economics, 2004

Based on certain desirable properties, a subset of entropy decomposition rules is proposed to assign inequality contributions to different components of income. In addition, a method of assessing the impact on inequality of marginal changes in income components originally applied to Gini index by Lerman and Yitzhaki (The Review of Economics and Statistics 67 (1985) 151) is extended to other measures of inequality. An empirical exercise based on Australian income distribution data illustrates the usefulness of the proposed analytical framework.

RePEc: Research Papers in Economics, 2003

Theil's information-theoretic approach to the measurement of inequality (Theil 1967) is set in the context of subsequent developments over recent decades. It is shown that Theil's initial insight leads naturally to a very general class of inequality measures. It is thus closely related to a number of other commonly used families of inequality measures.

Journal of Economic Theory, 2011

Inequality indices (i) evaluate the divergence between the income distribution and the hypothetical situation where all individuals have the mean income and (ii) are unambiguously reduced by a Pigou-Dalton progressive transfer. This paper proposes a new approach to evaluate the divergence between any two income distributions, where the second one can be a reference distribution for the first. In the case where the reference distribution is perfectly egalitarian -and uniquely in this case -we assume (i) that any progressive transfer reduces the divergence and (ii) that the divergence can be additively separated between inequality and efficiency loss. We characterize the unique class of decomposable divergence measures consistent with these views, and we derive the associated relative (resp. absolute) subclasses, which express constant relative (resp. absolute) inequality aversion. This approach extends the generalized entropy studied in inequality measurement.

2018

The paper aims at assessing and comparing the level of income inequalities in the Visegrad Group countries and at analysing how different social and demographic factors are associated with the extent of income inequality. The contribution of our article consists in the decomposition of income inequality by subgroups of household classified by characteristics such as the type and size of the household, the socio-economic group of the household, the educational level of the household head and the place of residence. The analysis on income inequality is based on microdata obtained from the Eurostat (EU-SILC). To assess the overall income inequality the measures of Generalized Entropy were used. The study shows that in the V4 group the lowest level of income inequality is observed in Slovakia and Czech Republic. Our findings suggest that education and prevailing source of income are among the main determinants of income inequality. In all V4 countries, the difference in the level of edu...

Mathematical Social Sciences, 1992

Exploiting the intermediate view of progressivity and inequality developed by Pfingsten (1988), we examine the effect on post-tax inequality of shifts in pre-tax distribution which preserve or reduce pre-tax inequality. It is shown that, although progressive taxation is unambiguously redistributive in the within-time context, this is no longer the case when modifications in pre-tax incomes are allowed for. In particular, progressive schemes may well reverse the inequality ranking of distributions, something which violates an intuitive conception of tax justice. We prove that the only schemes that preserve after tax the inequality ranking of distributions are atline.

The Journal of Economic Inequality, 2007

The Luxembourg Income Study data is used to explore the impact of taxes and transfer payments on the distribution of income across thirteen countries for different years. The five-parameter generalized beta distribution and ten of its special cases are considered as models for the size distribution of income. Maximum likelihood methods are used to estimate the model with corresponding measures of goodness of fit and inequality reported. These results identify the best-fitting two, three, and four-parameter models as well as describe the inter-temporal patterns of inequality corresponding to earnings, total income, and disposable income. A general pattern of increasing inequality is observed for almost all countries considered along with significantly different distributional impacts of taxes and transfer payments across countries.