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This paper examines the notion of intermediate inequality and its measurement. Specifically, we investigate whether the intermediateness of an intermediate measure can be preserved through repeated (affine) inequality-neutral income transformation. For all existent intermediate measures of inequality, we show that the intermediateness cannot be preserved through the transformation; each intermediate measure tends to either a relative measure or an absolute measure. This observation is then generalized to the class of unit-consistent inequality measures. An inequality measure is unit-consistent if inequality rankings by the measure are not affected by the measuring units in which incomes are expressed. We show that the unit-consistent class of intermediate measure of inequality consists of generalizations of an existent intermediate measure and, hence, the intermediateness also cannot be retained in the limit through transformations.
The purpose of this paper is to analyze the advantages and disadvantages of several intermediate inequality measures, paying special attention to the unit-consistency…
The purpose of this paper is to analyze the advantages and disadvantages of several intermediate inequality measures, paying special attention to the unit-consistency axiom proposed by Zheng (2007). First, we demonstrate why one of the most referenced intermediate indices, proposed by Bossert and Pfingsten (1990), is not unit-consistent. Second, we explain why the invariance criterion proposed by Del Río and Ruiz-Castillo (2000), recently generalized by Del Río and Alonso-Villar (2008), leads instead to inequality measures that are unaffected by the currency unit. Third, we show that the intermediate measures proposed by Kolm (1976) may also violate unit-consistency. Finally, we reflect on the concept of intermediateness behind the above notions together with that proposed by Krtscha (1994). Special attention is paid to the geometric interpretations of our results.
When health is measured by a bounded variable, differences in health can be presented as levels of attainment or shortfall. Measurement of heath inequality then usually…
When health is measured by a bounded variable, differences in health can be presented as levels of attainment or shortfall. Measurement of heath inequality then usually involves the choice of either the attainment or the shortfall distribution, and this choice may affect comparisons of inequality across populations. A number of indices have been introduced to overcome this problem. This chapter proposes a framework in which attainment and shortfall distributions can be jointly analyzed. Joint distributions of attainments and shortfalls are defined from points of view consistent with concerns for relative, absolute or intermediate inequality. Inequality measures invariant according to the corresponding ethical criterion are then applied. A dominance criterion that guarantees unanimous rankings of the joint distributions is also proposed.
This paper introduces a unit-consistent Lorenz dominance criterion that allows ranking income distributions according to centrist measures à la Seidl and Pfingsten (1997)…
This paper introduces a unit-consistent Lorenz dominance criterion that allows ranking income distributions according to centrist measures à la Seidl and Pfingsten (1997). In doing so, it defines α-Lorenz curves that generalize the absolute Lorenz curve. These curves allow implementing unanimous rankings for a broad set of centrist inequality notions, whereas they become closer and closer to the absolute curve when α approaches equity. In addition, this paper provides an empirical illustration of these tools using Australian income data. The results suggest that despite the reduction of relative inequality for Australian-born people between 1999 and 2003, their inequality increased for most centrist value judgments.
What change in the distribution of a population’s health preserves the level of inequality? The answer to this analogous question in the context of income inequality lies…
What change in the distribution of a population’s health preserves the level of inequality? The answer to this analogous question in the context of income inequality lies somewhere between a uniform and a proportional change. These polar positions represent the absolute and 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 chapter 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.
Theil's approach to the measurement of inequality 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 decomposable inequality measures. It is thus closely related to a number of other commonly used families of inequality measures.
Research on Economic Inequality Volume 12 is the outgrowth of University of Alabama Poverty and Inequality Conference, May 22–25, 2003. The motivation for the conference was to honor John P. Formby upon his retirement. The conference, funded by the University, was designed to bring together three groups of people; first, some of the most recognized scholars in the field, second, current and former colleagues of John Formby’s working in this field, and third, Dr. Formby’s former Ph.D. and post-doctoral students. Seventeen papers were presented, 11 of which are authored or co-authored by Dr. Formby’s former students. Peter Lambert and Yoram Amiel also participated in the conference. Dan Slottje, John Creedy, Shlomo Yitzhaki and Quentin Wodon did not attend but contributed papers.
“It should also be noted that the objective of convergence and equal distribution, including across under-performing areas, can hinder efforts to generate growth…
“It should also be noted that the objective of convergence and equal distribution, including across under-performing areas, can hinder efforts to generate growth. Contrariwise, the objective of competitiveness can exacerbate regional and social inequalities, by targeting efforts on zones of excellence where projects achieve greater returns (dynamic major cities, higher levels of general education, the most advanced projects, infrastructures with the heaviest traffic, and so on). If cohesion policy and the Lisbon Strategy come into conflict, it must be borne in mind that the former, for the moment, is founded on a rather more solid legal foundation than the latter” European Commission (2005, p. 9)Adaptation of Cohesion Policy to the Enlarged Europe and the Lisbon and Gothenburg Objectives.
Purpose: Most of the characterizations of inequality or poverty indices assume some invariance condition, be that scale, translation, or intermediate, which imposes value…
Purpose: Most of the characterizations of inequality or poverty indices assume some invariance condition, be that scale, translation, or intermediate, which imposes value judgments on the measurement. In the unidimensional approach, Zheng (2007a, 2007b) suggests replacing all these properties with the unit-consistency axiom, which requires that the inequality or poverty rankings, rather than their cardinal values, are not altered when income is measured in different monetary units. The aim of this paper is to introduce a multidimensional generalization of this axiom and characterize classes of multidimensional inequality and poverty measures that are unit consistent.
Design/methodology/approach: Zheng (2007a, 2007b) characterizes families of inequality and poverty measures that fulfil the unit-consistency axiom. Tsui (1999, 2002), in turn, derives families of the multidimensional relative inequality and poverty measures. Both of these contributions are the background taken to achieve our characterization results.
Findings: This paper merges these two generalizations to identify the canonical forms of all the multidimensional subgroup- and unit-consistent inequality and poverty measures. The inequality families we derive are generalizations of both the Zheng and Tsui inequality families. The poverty indices presented are generalizations of Tsui's relative poverty families as well as the families identified by Zheng.
Originality/value: The inequality and poverty families characterized in this paper are unit and subgroup consistent, both of them being appropriate requirements in empirical applications in which inequality or poverty in a population split into groups is measured. Then, in empirical applications, it makes sense to choose measures from the families we derive.