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Efficiency of Pena’s P2 Distance in Construction of Human Development Indices

Nayak, Purusottam and Mishra, SK (2012): Efficiency of Pena’s P2 Distance in Construction of Human Development Indices.

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Abstract

The paper is an attempt to evaluate the efficiency of Pena’s DP-2 method over a host of methods used to make composite indices. To undertake this exercise, variables and data used and methodology adopted in Human Development Report 2011 are employed along with nine other methodologies employed by other scholars. Although there is no agreed principle of judging an index to be best among alternative indices, it may be suggested that the composite index which is most informative among all other indices may be considered as the most acceptable one. The present study reveals that Pena-DP2 index and Penmax index have close similarity. Computationally, Pena’s method of construction of index is much simpler, but the interpretation of Penmax index is more straightforward. On the other hand, Maxmin index is norm-based and has a justification on Wald’s principle of decision-making. The Maxmin index also is the most egalitarian index against the Principal Component based index, which is known to be most elitist. On ‘sum of absolute correlation’ and ‘sum of squared correlation’, too, the Maxmin index is superior to other indices. It appears, therefore, that the Maxmin composite index which is obtained by maximization of minimum of correlation between the composite index and the constituent variables is a better than others. Further, if we go by the argument of Neumann and Morgenstern none of the composite indices is a cardinal measure in the strict sense of measurement.

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