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Social Indicators Research

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23.04.2021 | Original Research

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

verfasst von: Madhabendra Sinha, Anjan Ray Chaudhury

Erschienen in: Social Indicators Research | Ausgabe 3/2021

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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.

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Percentage contribution of between-group inequality to total inequality is the ratio of the observed between-group inequality to the observed total inequality.

According to this measure, between-group inequality is equal to the total inequality minus population share weighted sum of the Theil’s indices of within-group inequality.

It is considered as a ratio of the computed value of observed between-group inequality for a particular partition to the computed value of between-group inequality by considering that every individual form a group, i.e., it become a tool of comparing the observed between-group inequality against an unrealistic benchmark (Elbers, 2008).

Apart from comparability the conventional statistic is also criticized on the ground of relatively smaller value of the between-group component of inequality (Elbers et al., 2008).

According to Cowel and Jenkins (1995) and Kanbur (2006), a type of grouping is considered as more important than another type of grouping, if the computed value of the conventional statistic of the contribution of between-group inequality for the former partition of the population is greater than that of the latter.

This alternative measure assesses the severity of the existing between-group inequality as it is the proportion of actual between-group inequality and hypothetically non-overlapping distributions of the groups. If the value of this alternative measure rises then the actual distribution is closer to the non-overlapping distributions of the groups or it can be stated that the actual between-group inequality is more severe.

The value of the conventional measure will rise with the rise in the proportion of the poor groups as the value of its numerator will rise. Actually, the value of \({\text{ln}}\left( {{\upmu }/{\upmu }_{{\text{j}}} } \right)\) is positive for the poor groups, and it is negative for the rich groups. So, when \({\uplambda }_{{\text{j}}}\) rises for the poor groups, then the value of \({\text{I}}_{{\text{B }}} \left( {\uppi } \right)\) will rise.

Total inequality in the distribution of an attribute may be considered as the extreme benchmark of between-group inequality in the distribution of an attribute since it is the between-group inequality while every individual constitutes a separate group.

Complete segregation and non-overlapping (or clustering) of the distributions of the groups defined by certain way of partitioning are two distinct notions. Former is associated with the ‘representational inequality’ (RI) and the latter is associated with the ‘sequence inequality’ (SI), as described by Reddy and Jayadev (2011). If there is complete segregation of the distributions of the groups, then at each income level there is only one group. In the case of clustering, groups are concentrated in different parts of the distribution of the attribute. Thus, clustering is possible if and only if groups are completely segregated.

According to the inequality decomposition analysis as described by Eq. (3), total inequality depends on between-group inequality and within-group inequality. So, total inequality may be regressed on these inequality components. Under this circumstance the test statistic Wilk’s Lambda may be invoked as a test statistic for assessing the percentage variation in total inequality not explained by the variation of the between-group inequality. If the distributions of the groups are clustered, then the absolute value of between-group inequality is certainly high, but the percentage of total inequality existing in the distribution of distribution of an attribute explained by between-group disparity may be low if there is considerable within-group heterogeneity. As a result, the value of Wilk’s Lambda is not likely to be low. However, if the groups are clustered along with low within-group heterogeneity, then the value of the Wilk’s Lambda is likely to be significantly low, since under this circumstance the percentage of total inequality explained by the between-group disparity is high.

A possible modification of the alternative statistic for capturing the divergence of the distributions of the groups after complete segregation is proposed and given in the Appendix I.

The value judgments associated with the mathematical forms of these measures are not identical, but they are related as given in (7). Since the value of the term (\(\frac{{\text{I}}}{{{\text{I}}_{{\text{B}}}^{{\text{M}}} }}){ }\) is greater than unity, the computed value of \({\hat{\text{R}}}_{{\text{B}}}\) is always greater than the computed value of \({\text{R}}_{{\text{B}}}\). The values of \({\text{R}}_{{\text{B}}}\) and \({\hat{\text{R}}}_{{\text{B}}}\) are equal if and only if the observation within all groups defined by a type of groupings are equal.

According to the population shares of the largest group in Kerala and Maharashtra reported in Table 3, population shares of SCs and STs in these two states are 9 percent and 21 percent respectively.

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Titel: Assessing the Between-Group Inequality Through Alternative Measures of Grouping: An Indian Evidence
verfasst von: Madhabendra Sinha
Anjan Ray Chaudhury
Publikationsdatum: 23.04.2021
Verlag: Springer Netherlands
Erschienen in: Social Indicators Research / Ausgabe 3/2021
Print ISSN: 0303-8300
Elektronische ISSN: 1573-0921
DOI: https://doi.org/10.1007/s11205-021-02683-x

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