On a Family of Achievement and Shortfall Inequality Indices

Abstract

This paper identifies a family of absolute consistent inequality indices using a weakly decomposable postulate suggested by Ebert. Because one member employs an Atkinson type aggregation we refer to it as the Atkinson index of consistent inequality. A second member of this family parallels the Kolm index of inequality. Two innovative features of these indices are that no specific structure is imposed on the form of the index at the outset and no transformation of any existing index is considered to ensure consistency. Each of them regards an achievement distribution as equally unequal as the corresponding shortfall distribution. We apply these indices to study inequality in grip strength among 50+ year-old Europeans. Copyright © 2015 John Wiley & Sons, Ltd.

Has the World Converged? A Robust Analysis of Non-Monetary Bounded Indicators

“…The first one is the variance ( ), which is the decomposable version of the standard deviation, and the second is the absolute Gini coefficient ( ). 16 The other two measures ( and ) are from the family of absolute inequality measures proposed by Chakravarty et al (2013). 17 1 ,…”

“…The family of indices that include the variance is ∑ where is strictly convex, twice differentiable and 0; whereas the family of indices that include the absolute Gini coefficient is ∑ , where 2 1 /2 is the rank of and a strictly increasing function such that 1 . 17 The general class of indices proposed by Chakravarty et al (2013) is ; θ ln ∑ ∑ exp ; 0. 18 As discussed in the previous section, the bounded indicators that we analyze in this paper are not directly transferable and therefore the applicability of the regressive transfer should be seen as if there were two observed periodic distributions and , such that, in principle, could be obtained from through a sequence of regressive transfers, and then would be deemed less unequal than .…”

“…In addition toMicklewrite and Stewart (1999), a number of studies in the health economics literature have observed this inconsistency and proposed using a consistent measure of inequality. See, for example,Erreygers (2009), Lambert and Zheng (2011), Aristondo and Lasso de la Vega (2012),Chakravarty et al (2013), Kjellson et al (2015,Silber (2015). For an example applying an absolute measure to assess inequality in the poverty counting framework, seeSeth and Alkire (2014).ECINEQ WP 2016 -398 March 2016 …”

Consistent Comparisons of Attainment and Shortfall Inequality: A Critical Examination

“…Particular absolute inequality measures satisfying perfect complementarity or the mirror condition have been proposed by Erreygers () and Chakravarty et al. ().…”

On the Increasing Convex Order of Relative Spacings of Order Statistics

“…represents their total relative deprivation (see, e.g., Paul [23], Chakravarty and Moyes [24] and Chakravarty et al [25]). Given an income random variable X with distribution function F, the theoretical version of (4) is given by…”