Attempts have recently been made to assign inequality contributions to various components of income. This paper discusses the issues involved in such assignments and highlights the problems that follow from having a number of possible decomposition rules. U. S. data on the distribution of family incomes are used to examine the relative influence of these income components and to evaluate empirically the performance of different decomposition rules. A wide range of inequality contributions can be obtained, even when restricted to only “naturally†derived decomposition rules. Some of the results are plainly absurd and serve to warn against the indiscriminate use of decomposition formulae without first investigating their properties.

A modification of the official Sen poverty index yields an index which is not only continous in individual incomes and consistent with the transfer axiom, but also admits a geometric interpretation in terms of the area beneath a graph called the inverse generalized Lorenz curve for normalized poverty gaps by Jenkins and Lambert (1993) or the poverty gap profile by Shorrocks (1994).

This paper examines the implications of imposing a weak aggregation condition on inequality indices, so that the overall inequality value can be computed from information concerning the size, mean, and inequality value of each population subgroup. It is shown that such decomposable inequality measures must be monotonic transformations of additively decomposable indices. The general functional form of decomposable indices is derived without assuming that the measures are differentiable. The analysis is suitable for extension to the many other kinds of indices for which a similar relationship between the overall index value and subaggregates is desirable.

Transfer sensitivity has been seen as a means of strengthening the Pigou-Dalton “principle of transfers”, by ensuring that more weight in the inequality assessment is attached to transfers taking place lower down in the distribution. This paper examines the concept of transfer sensitivity in detail and proposes a new definition that can be usefully applied in general contexts. The definition is based on the notion of “favourable composite transfers” which involve a regressive transfer combined with a simultaneous progressive transfer at a lower income level. The paper proceeds to identify when one distribution can be obtained from another using a sequence of progressive transfers and favourable composite transfers, and hence when all transfer sensitive Pigou-Dalton indices agree on their pairwise inequality ranking. Since agreement occurs in some situations when Pigou-Dalton indices are not unanimous, transfer sensitivity adds power to the “unambiguous” inequality judgements based on the Pigou-Dalton condition and, in particular, enables distributions whose Lorenz curves intersect to be conclusively ranked.

It seems desirable that the overall level of poverty should fall whenever poverty decreases within some subgroup of the population and is unchanged outside that group. Yet this simple and attractive property, which we call "subgroup consistency, " is violated by many of the poverty indices suggested in recent years. This paper characterizes the class of subgroup consistent poverty indices, and identifies the special features associated with this property.