Economics and Information Theory

The analysis of inequality is placed in the context of recent developments in economics and statistics.

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Measurement of inequality

The Gini coefficient has long been thought unsuitable for inequality decomposition analysis because of a troublesome and little-understood residual term that occurs when subgroup income ranges overlap after the between-groups and within-groups contributions to inequality have been separated out. In this paper, graphical analysis is used to provide a solid understanding of the residual term as a subarea of the Lorenz diagram. Implications for inequality decomposition analysis are considered. Copyright 1993 by Royal Economic Society.

https://www.jstor.org/stable/pdfplus/2234247.pdf

Inequality decomposition analysis and the Gini coefficient revisited

The purpose of this research is to introduce a new approach to the decomposition of the Gini ratio into three components, supporting them with economic and statistical rigorous interpretations. The three components are: (i) the Gini inequality within subpopulations; (ii) the net contribution of the extended Gini inequality between subpopulations; and (iii) the contribution of the intensity of transvariation between subpopulations. These components are weighted by the product of the population shares times the income shares of the corresponding subpopulations where the weights add to one.

A New Approach to the Decomposition of the Gini Income Inequality Ratio

A simple technique based on matrix algebra is proposed to compute the Gini Index of Inequality; to obtain its decomposition by factor components when detailed data on income sources are available; to derive a breakdown of the inequality into, within, and between classes inequality when the income units are grouped by income range; and to compute the contribution of the within and between groups inequality, as well as that of some interaction term, when the data are classified by population subgroups. Copyright 1989 by MIT Press.

Factor Components, Population Subgroups and the Computation of the Gini Index of Inequality

The main objectives of the paper are to decompose Atkinson's measure into within-group and between-group inequality and to compare it with decompositions of inequality measures, like the Gini coefficient, variance of logarithms, Theil's entropy index and the square of the coefficient of variation. Atkinson's inequality index is given an interpretation of mean order β and then it is decomposed for population subgroups. Various other measures are considered for decompositions and a variety of decomposition schemes for Gini coefficient and other measures in the literature is reviewed and commented upon. Empirical analysis using U.S.A. and U.K. data are performed on the basis of income distribution data classified by family size. For various decomposition schemes, contribution to between size-group and within size-group inequalities are compared in percentage terms. Comparisons are also made over time for the years 1964 and 1974 both for U.S.A. and U.K. and the result indicates that within size-group income inequality has declined while between size group and total income inequality shows an increase. Three important properties of Atkinson's inequality index are proved in the appendix.

Decomposition of inequality measures and a comparative analysis

The paper contains a statistical interpretation and an interesting decomposition of the inequality index due to Atkinson.

T. Das

Papers

Decomposition of inequality measures and a comparative analysis

Statistical interpretation, decomposition and properties of Atkinson's inequality index