Target Shortfall Orderings and Indices

Satya Chakravarty, Conchita D'Ambrosio and Pietro Muliere

No 340, Discussion Papers of DIW Berlin from DIW Berlin, German Institute for Economic Research

Abstract: 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 shortfall ordering is also discussed.

Keywords: Target shortfall orderings; transfer; indices (search for similar items in EconPapers)
JEL-codes: D31 D63 (search for similar items in EconPapers)
Pages: 23 p.
Date: 2003
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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