A note on the orness classification of the rank-dependent welfare functions and rank-dependent poverty measures

Abstract

This note focuses on ordering two families of rank-dependent poverty measures in terms of their distribution-sensitivity. It has been proved that a real value, between 1/2 and 1, called orness, which is assigned to every rank-dependent poverty measure, can be interpreted as a distribution-sensitivity indicator. Therefore, the rank-dependent poverty measures can be classified in terms of their distribution-sensitivity using the orness value assigned to them. This ranking has already been carried out for numerous poverty measures. However, two families of poverty measures, the Kakwani and the S-Gini families, which are defined for every real parameter larger than one, have only been ranked for natural values of their parameters. This note broadens the classification of these families for every real parameter larger than one, that is, for every member of these two families. It also provides a ranking between the two families for the same parameter. It concludes that for higher values of the parameter, the families will be more sensitive to the bottom part of the distribution. Furthermore, for the same value of the parameter, the Kakwani index will be more sensitive to poor incomes than the S-Gini index. In addition, we will see that the proposed ranking for the two families in terms of the orness value will be analogous to other distribution-sensitivity criteria existing in the literature.