On measuring group-differentials displayed by socio-economic indicators: an extension

Abstract

In a recent paper, Mishra and Subramanian (2006) propose a measure to explain group-differential which is sensitive to levels in the sense that a given hiatus at lower levels of failure (or higher levels of attainment) is considered worse off. This article critically evaluates their method – refines their two axioms, adds an additional axiom of normalization and proposes an alternative which is more general. It proposes to reduce subjectivity when there is lower hiatus at lower levels of failure and also addresses scenarios when rank ordering of sub-groups will be reversed. Empirical illustration with infant mortality rate data for selected Indian states is also provided.

Acknowledgements

The author thanks Udaya S. Mishra, Manoj Panda, S. Subramanian, M. H. Suryanarayana and students of ‘Contemporary Issues in Human Development and Policy’ (January-May 2006) at IGIDR for discussions and comments. Usual disclaimers apply.

Notes

¹ If an indicator has the maximum of n > 1 then it can be reduced to the (0,1) domain, indicators of attainment like literacy rate should be replaced with illiteracy rate. If we are discussing an attainment indicator like income then a maximum may be posited and the actual observations subtracted from this to obtain an indicator of failure.

² Proofs for the axioms to hold for D ₄ will be similar to the proofs for the extension proposed by us in D ₅ and discussed in Section III.