Assessing the Between-Group Inequality Through Alternative Measures of Grouping: An Indian Evidence

Abstract

Conventionally the ratio of observed between-group inequality to the overall inequality is used to examine the contribution of between-group inequality to total inequality. It is also widely used for defining the relative importance of alternative types of grouping. This conventional statistic is criticized by some scholars on the ground of comparability and extreme benchmark. They have proposed an alternative measure and suggest using this measure as a complementary instrument to the former for examining the relative importance of different types of grouping in any country setting. However, they have not suggested any specific method to use these measures. The major objectives of this study are—to review the conventional and alternative measures for assessing the relative importance of alternative ways of grouping, and to specify the method of the use of these measures for this purpose. Furthermore, we apply these measures on Indian data and analyze the state of between-group inequality for some meaningful ways of grouping in India, and develop a discussion on the relative importance of these ways of groupings. This will enable planners and policymakers to design effective policies for reducing between-group inequality.

Appendix I: Proposed modification of the alternative measure

An important limitation of the alternative statistic (${\hat{\text{R}}}_{{\text{B}}}$) lies in its mathematical form, as after complete segregation of the actual distributions of the groups the value of this measure fails to display any divergence of the distributions of the groups. For this reason, some modification in the mathematical form of the alternative statistic is essential to assess the divergence of the groups in a completely segregated society. The modified form of the alternative estimate is given below,

$$ {\hat{\text{R}}}_{{{\text{B}}0}} = \frac{{{\text{I}}_{{\text{B}}} }}{{{\text{I}}_{{\text{B}}}^{{\text{M}}} }} {\text{x}} {\upalpha } $$

The term ${\upalpha }$ may take the following functional forms:

${\upalpha } = {\text{e}}^{{{\text{ln}}\left( {\frac{{{\upmu }_{{\text{R}}} }}{{{\upmu }_{{\text{P}}} }}} \right)}}$, or, ${\upalpha } = {\text{e}}^{{{\text{ln}}\sqrt {\frac{{{\upmu }_{{\text{R}}} }}{{{\upmu }_{{\text{P}}} }}} }}$.Where ${\upmu }_{{\text{R}}}$ and ${\upmu }_{{\text{P}}}$ are the mean values of the attribute of the richest and poorest groups. The minimum and maximum values of ${\hat{\text{R}}}_{{{\text{B}}0}}$ are different from ${\hat{\text{R}}}_{{\text{B}}}$. After this modification, the value of ${\hat{\text{R}}}_{{\text{B}}}$ lies between 0 and $\infty$. If there is no between-group inequality, then the value of ${\hat{\text{R}}}_{{{\text{B}}0}}$ is 0, and its value rises with the reduction in the overlapping spectrum of the distributions of the groups.