On Measuring Group Differential – Some Further Results

We impose a value judgment that a decrease in failure should be accompanied by a
decrease in gap (difference or ratio) between sub-groups. In other words, the same gap at
lower levels of failure is to be considered worse off. This, in line with transfer sensitivity
axiom of poverty indices, is formalized by Mishra and Subramanian (2006) through two
level-sensitive axioms in group differential measures. In addition, Mishra (2007) imposes
an axiom of normalization. At a basic level it means that the group differential measure
lies between zero and unity. However, at a fundamental level it should also mean that
zero indicates no differential between the two sub-groups whereas unity indicates
maximum differential between the two sub-groups. A group differential measure
discussed in the above-mentioned two papers satisfied the level-sensitivity axioms but
failed the normalization axiom at a fundamental level. Further, the comparison between
two situations under this measure also happened to be dependent on the choice of some
parameters. Both these problems are done away with in the measure proposed in this
paper. Empirical illustration with infant mortality rate data for selected Indian states has
also been given.