A Note on Human Development Indices with Income Equalities

Human Development Index (HDI) is a composite index obtained by a weighted aggregation of other three indices, each measuring one aspect, namely life expectancy, education and real per capita income. Intra-country equality in income distribution, however, is very important with regard to quality of life and, thus, human development. This paper is concerned with the question that if the measure of income equality also were included in construction of the HDI, then what would be the relative weights of different indices. One method could be to assign equal weights to all the four, but it is too pragmatic. Alternatively, the principal component analysis (PCA) may be applied to derive weights. But, again, the PCA is an overly elitist method that undermines the poorly correlated set of variables, which might be very important in their own right, in favor of highly correlated set of variables. We propose an alternative method that maximizes the sum of absolute coefficients of correlation of the composite index with the constituent indices. Such an index is inclusive in nature and gives proper representation to weakly correlated variables also. The method has been applied to data of 125 countries and the HDI so constructed has been compared with the PCA HDI and HDR (UNDP) HDI. We find substantial ups and downs in the HDI ranks of different countries.