16 November 2014

Group Differential Measure

This blog is meant for a lay explanation of the paper Group Differential for Attainment and Failure Indicators (see Enhanced HTMLview) in the Journal of International Development. It develops on the premise that if a society is progressing then it ought to reduce gaps across groups. In other words, as society progresses, it ought to be become increasingly inequity conscious.

For instance, if there exists a society, with equal proportion of female and male population, where literacy rate for females is 40 per cent and that for males is 50 per cent. After a decade, there is not much change in the population composition, but due to public policy interventions and the literacy rate for females increases to 50 per cent and that for males increases to 60 per cent. This increased attainment in literacy rates is commendable, but it is equally worrisome that the gap in literacy rates between the two groups remains the same at 10 percentage points. Thus, we would state that such an increase an attainment of literacy rate has fails a simple difference based level sensitivity. It is in this sense that this higher level of attainment is not commensurate with the society being increasingly inequity conscious.

A group differential measure that takes the simple difference of the measures for the two groups would fail this level sensitivity test.  

To address this, one could suggest, squaring of the literacy rates and then taking the difference and then after manipulation (for a comparable value that lies between 0 and 100) gives us a group differential measure that is {(50^2)-(40^2)}/100=9 percentage points in the first scenario and 11 percentage points in the second scenario. This satisfies level sensitivity, as it gives a lower value at the lower level of attainment. However, it fails to be policy sensitive at the lower level of attainment. In other words, when the actual gap between the literacy rates is 10 percentage points, our measure shows a 9 percentage point difference. Thus, it is possible that while this measure is not a representation of the actual percentage point difference, but it could lead to complacency at lower levels of attainment.

One possible way out is to take a ratio of the simple difference to the simple difference between maximum attainment and half of the attainment for female literacy rate and then manipulate to obtain a comparable value, that is {(50-40)/(100-20)}*100=12.5 percentage points in the first scenario and 13.3 percentage points for the second scenario.

Thus, we come up with a group differential measure that imposes greater inequity consciousness at higher levels of attainment and also is sensitive to policy implications. The discussion in the paper also shows that this approach also satisfies normalisation and montonocity properties. It also proposes an alternative measure that satisfy similar properties for failure indicators. The paper has examples using an attainment and a failure indicator that are relevant for the Millennium Development Goals (MDGs).

Other related papers

Working Paper version of the Current Paper

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