Inequality Measurement with Subgroup Decomposability and Level-Sensitivity

Subgroup decomposability is a very useful property in an inequality measure, and level-sensitivity, which requires a given level of inequality to acquire a greater significance the poorer a population is, is a distributionally appealing axiom for an inequality index to satisfy. In this paper, which is largely in the nature of a recollection of important results on the characterization of subgroup decomposable inequality measures, the mutual compatibility of subgroup decomposability and level-sensitivity is examined, with specific reference to a classification of inequality measures into relative, absolute, centrist, and unit-consistent types. Arguably, the most appealing combination of properties for a symmetric, continuous, normalized, transfer-preferring and replication-invariant (S-C-N-T-R) inequality measure to satisfy is that of subgroup decomposability, centrism, unit-consistency and level-sensitivity. The existence of such an inequality index is (as far as this author is aware) yet to be established. However, it can be shown, as is done in this paper, that there does exist an S-C-N-T-R measure satisfying the (plausibly) next-best combination of properties - those of decomposability, centrism, unit-consistency and level-neutrality

New unit-consistent intermediate inequality indices

Income distribution, Intermediate inequality indices, Unit-consistency, Ray-invariance, D63,

A note on progressive taxation and inequality equivalence

We investigate the relationship between the notion of progressive taxation and inequality reduction under a general version of the concept of inequality equivalence. We consider a two parameter formalization of the concept of inequality equivalence that both includes as special cases the intermediate inequality equivalence and the unit-consistent inequality equivalence. Both criteria could range from relative to absolute inequality views as the parameters in the formulation change. For the unit-consistent inequality equivalence the condition of non-decreasing average tax rate is necessary and sufficient to guarantee the post-tax inequality reduction for all the inequality views in between the relative and the absolute

A Note on Progressive Taxation and Inequality Equivalence

We investigate the relationship between the notion of progressive taxation and inequality reduction under a general version of the concept of inequality equivalence. We consider a two-parameter formalization of the concept of inequality equivalence that both includes, as special cases, the intermediate inequality equivalence and the path-independent/unit-consistent inequality equivalence. Both criteria could range from relative to absolute inequality views as the parameters in the formulation change. For the path-independent/unit-consistent inequality equivalence the condition of nondecreasing average tax rate is necessary and sufficient to guarantee the inequality-reducing effect of taxation for all the inequality views in between the relative and the absolute