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.
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- Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-31, March.
- Srijit Mishra, 2008.
"On measuring group-differentials displayed by socio-economic indicators: an extension,"
Applied Economics Letters,
Taylor & Francis Journals, vol. 15(12), pages 935-938.
- Srijit Mishra, 2006. "On measuring group-differentials displayed by socio-economic indicators: An Extension," Indira Gandhi Institute of Development Research, Mumbai Working Papers 2006-005, Indira Gandhi Institute of Development Research, Mumbai, India.
- Srijit Mishra, 2006. "On Measuring Group-differentials Displayed by Socio-economic Indicators - An Extension," Microeconomics Working Papers 22397, East Asian Bureau of Economic Research.
- Kakwani, N., 1993. "Performance in living standards : An international comparison," Journal of Development Economics, Elsevier, vol. 41(2), pages 307-336, August.
- Udaya Mishra & S. Subramanian, 2006. "On measuring group-differentials displayed by socioeconomic indicators," Applied Economics Letters, Taylor & Francis Journals, vol. 13(8), pages 519-521.
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