Discussion Paper

No. 2011-7 | April 11, 2011
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.

Paper submitted to the special issue
The Measurement of Inequality and Well-Being: New Perspectives 

JEL Classification:

D30, D31, D63


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Cite As

Subbu Subramanian (2011). Inequality Measurement with Subgroup Decomposability and Level-Sensitivity. Economics Discussion Papers, No 2011-7, Kiel Institute for the World Economy. http://www.economics-ejournal.org/economics/discussionpapers/2011-7

Comments and Questions

Anonymous - Referee Comment
May 24, 2011 - 09:02

see attached file

Sreenivasan Subramanian - Author's Response to Referee 1
May 27, 2011 - 15:24

S. Subramanian: Response to Referee Report 1

I am grateful to the referee for the time and effort expended in reading and commenting on my paper, as well as for the substantive content of her/his assessment. I take it that the referee finds elements of the paper interesting, although ...[more]

... s/he also sees a case for a greater measure of completeness of analysis, with specific reference to the benefit to be had from providing a characterization result on the class of level-sensitive inequality measures. I readily accept the referee’s point. In addition to the two definite existence and two definite impossibility results I present, the prospect of a fifth definite result (which is presently offered in the spirit of an open, undecided question) would be greatly enhanced if one could obtain a characterization of the class of level-sensitive inequality measures. It is thus unquestionably true that a characterization result is desirable. It is not completely clear if the referee also deems such a result to be an essential part of the paper. If that is the case, then I must admit with humility and honesty – both virtues born, I hasten to add, of necessity! – that I myself do not possess the requisite skills to come up with a characterization theorem. I suspect that some familiarity with functional analysis might be called for in order to address the problem, and I am afraid I just do not have the necessary mathematical equipment for the exercise. On the other hand, if characterization is seen as being desirable but not necessarily essential in the context of the present paper, then it would be my hope that there is something of sufficient motivational interest in the paper to attract the interest of a theorist with the required analytical ability to make good the paper’s shortfall.