Distributive Analysis and Negative Incomes By: Abdelkrim Araar & JeanYves Duclos 20080621

In much of distributive analysis, it is supposed that wellbeing indicators are positive. In the presence of negative indicators, some of the usual distributive indices and curves cannot be used. This short note suggests how one can choose indices and curves to do distributive distributive analysis in these contexts.
Negative incomes and inequality
1.1 Negative incomes and inequality indices Two main classes of inequality indices exist: relative and absolute ones. Relative indices use the dispersion of incomes around the mean and normalised it by the mean. One virtue of this normalisation is making relative inequality indices scale invariant. This poses a problem however in the presence of negative incomes when average income is zero or negative.
When relative indices fall to assess inequality, absolute inequality indices can still be used since they continue to preserve their useful properties. Moreover, when wellbeing indicators are expressed in real terms, these indices may be found acceptable and easily interpretable as capturing absolute differences in wellbeing.

Recommended references:  Absolute and relative inequality indices and some useful properties for inequality. 

 The CTR_Gini index in the presence of some negative incomes and positive average income 

1.2  The Absolute Gini Index (AGI) Among absolute inequality indices, there is the absolute Gini Index of inequality. The following references recall the definition of the basic inequality axioms and decompose the AGI index across groups and income sources.
Recommended references:
1.3 Decomposing the AGI index across groups or income sources. Recommended references:
1.4 Negative incomes and inequality dominance
Negative incomes and Poverty
2.1 Negative incomes and poverty indices 2.2 Negative incomes and poverty dominance 2.3 Negative incomes, FGT index and Shapley decomposition by income sources
For 2.1, 2.2 and 2.3, see the following mimeo. Araar Abdelkrim & Duclos JeanYves (2006), Poverty and Negative Incomes, CIRPÉE, Université Laval, mimeo.
