Unit Consistency and Bipolarization of Income Distributions

C. Lasso de la Vega, A. M. Urrutia, Henar Diez
Review of Income and Wealth, 56 (1), 65-83.

Many polarization measures proposed in the literature assume some invariance condition. Clearly, each invariance condition imposes a specific value judgement on polarization measurement. In inequality and poverty measurement, B. Zheng suggests rejecting these invariance conditions as axioms, and proposes replacing them with the unit-consistency axiom (Economica 2007, Economic Theory 2007 and Social Choice and Welfare 2007). This property demands that the inequality or poverty rankings, rather than their cardinal values, are not altered when income is measured in different monetary units. Following Zheng’s proposal we explore the consequences of the unit-consistency axiom in the bipolarization field. We introduce a new family of Krtscha-type intermediate bipolarization indices, and also propose and characterize a class of intermediate polarization orderings which are unit-consistent. Finally, a short empirical application using data from Spain is also provided to illustrate how the bipolarization orderings proposed may be used in practice.


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