Resource title

Target Shortfall Orderings and Indices

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Resource description

Given any income distribution, to each income we associate a subgroup containing all persons whose incomes are not higher than this income and a person?s target shortfall in a subgroup is the gap between the subgroup highest income and his own income. We then develop an absolute target shortfall ordering, which, under constancy of population size and total income, implies the Lorenz and Cowell-Ebert complaint orderings. Under the same restrictions, one distribution dominates the other by this ordering if and only if the dominated distribution can be obtained from the dominant one by a sequence of rank preserving progressive transfers, where each transfer is shared equally by all persons poorer than the donor of the transfer. The relationship of the ordering with the absolute deprivation and differential orderings, and its consistency with ranking of distributions by absolute target shortfall indices are explored. Well-known inequality indices like the absolute Gini index and the standard deviation are interpreted as absolute target shortfall indices. Finally, the possibility of a relative target shorfall ordering is also discussed.

Resource author

Satya R. Chakravarty, Conchita D'Ambrosio, Pietro Muliere

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Resource publish date

Resource language

eng

Resource content type

text/html

Resource resource URL

http://hdl.handle.net/10419/18076

Resource license

Adapt according to the presented license agreement and reference the original author.