A general class of additively decomposable inequality measures
James E. Foster,Artyom Shneyerov +1 more
TLDR
In this paper, a generalized form of additive decomposability is defined for within-group and between-group inequality terms using a generalized mean in place of the arithmetic mean, which is based on a minimal form of the transfer principle.Abstract:
This paper presents and characterizes a two-parameter class of inequality measures that contains the generalized entropy measures, the variance of logarithms, the path independent measures of Foster and Shneyerov (1999) and several new classes of measures. The key axiom is a generalized form of additive decomposability which defines the within-group and between-group inequality terms using a generalized mean in place of the arithmetic mean. Our characterization result is proved without invoking any regularity assumption (such as continuity) on the functional form of the inequality measure; instead, it relies on a minimal form of the transfer principle – or consistency with the Lorenz criterion – over two-person distributions.read more
Citations
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Path Independent Inequality Measures
James E. Foster,Artyom Shneyerov +1 more
TL;DR: A natural decomposition property motivated by Shorrocks and Anand (1980, Econometrica 48, 613–625) is explored that is derived—a single parameter family containing both the second Theil measure (the mean logarithmic deviation) and the variance oflogarithms.
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Measuring the Distribution of Human Development: methodology and an application to Mexico
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Inequality Decompositions. A Reconciliation
Frank Cowell,Carlo V. Fiorio +1 more
TL;DR: In this article, the authors show how classic source-decomposition and subgroup decomposition methods can be reconciled with regression methodology used in the recent literature, and highlight some pitfalls that arise from uncritical use of the regression approach.
References
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On the Measurement of Inequality
TL;DR: In this paper, the problem of comparing two frequency distributions f(u) of an attribute y which for convenience I shall refer to as income is defined as a risk in the theory of decision-making under uncertainty.
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The class of additively decomposable inequality measures
TL;DR: In this paper, the authors consider a wide class of inequality indices and identify those which are additively decomposable, including the squared coefficient of variation and the two Theil's entropy formulas.
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Decomposable income inequality measures
TL;DR: In this article, it was shown that Theil's coefficient (T) and the logarithm of the arithmetic mean over the geometric mean (L) are the only decomposable inequality measures such that the weight of the "within-components" in the total inequality of a partitioned population sum to a constant.
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Inequality decomposition by population subgroups
TL;DR: In this paper, the implications of imposing a weak aggregation condition on inequality indices, so that the overall inequality value can be computed from information concerning the size, mean, and inequality value of each population subgroup, are examined.