Lost in Translation: Rethinking the Inequality Equivalence Criteria for Bounded Health Variables

Abstract

What change in the distribution of a population's health preserves the level of inequality? The answer to the analogous question in the context of income inequality lies somewhere between a uniform and a proportional change. These polar positions represent the absolute and the relative Inequality Equivalence Criterion (IEC), respectively. A bounded health variable may be presented in terms of both health attainments and shortfalls. As a distributional change cannot simultaneously be proportional to attainments and to shortfalls, relative inequality measures may rank populations differently from the two perspectives. In contrast to the literature that stresses the importance of measuring inequality in attainments and shortfalls consistently using an absolute IEC, this paper formalizes a new compromise concept for a bounded variable by explicitly considering the two relative IECs, defined with respect to attainments and shortfalls, to represent the polar cases of defensible positions.We use a surplus-sharing approach to provide new insights on commonly used inequality indices by evaluating the underpinning IECs in terms of how infinitesimal surpluses of health must be successively distributed to preserve the level of inequality. We derive a one-parameter IEC that, unlike those implicit in commonly used indices, assigns constant weights to the polar cases independent of the health distribution.

Consistent Comparisons of Attainment and Shortfall Inequality: A Critical Examination

“…Kjellsson and Gerdtham () and Allanson and Petrie () demonstrate that Wagstaff's () variant of the concentration index—a non‐absolute inequality measure that satisfies the mirror condition—is a compromise between the relative and super‐absolute categories. The compromise position has been examined further by Kjellsson and Gerdtham ().…”

“…Interestingly, although the literature does not explicitly discuss uniqueness, some recent studies can be interpreted as being critical of the property. Allanson and Petrie () and Kjellsson and Gerdtham () stress that a relative inequality measure defined on the domain of attainment distributions expresses fundamentally different inequality judgments than the same relative inequality measure defined on the domain of shortfall distributions. In other words, to describe one's judgments on how to make inequality comparisons, it does not suffice to state the chosen inequality measure.…”

On a Family of Achievement and Shortfall Inequality Indices

“…That is, the shortfall is expressed as the difference from the highest level of attainment. Because it reduces the allowable class of indices to a great extent, there have been criticisms (see Allanson and Petrie, 2012, 2013, Bosmans, 2013and Kjellsson and Gerdtham, 2013. If we compute shortfalls in a relative sense, then it has been pointed out that consistency rules out any absolute inequality measure.…”

Conindex: Estimation of Concentration Indices

“… 11 For discussion of the issues, particularly in relation to the measurement of health inequality, see Clarke et al, 2002; Wagstaff, 2005; Erreygers, 2009a,b,c; Wagstaff, 2009; Erreygers and Van Ourti, 2011a-b; Wagstaff, 2011a-b; Kjellsson and Gerdtham, 2013a-b. …”