Pillai N, Vijayamohanan (2008): CES Function, Generalized Mean and Human Poverty Index: Exploring Some Links.

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Abstract
The Sennian capability approach has facilitated to capture poverty in its multidimensional incidence and thus to raise a new aggregate poverty index – the UNDP’s Human Poverty Index (HPI). The UNDP has found power mean of order α > 1 as possessing some of the most desirable properties in describing the distribution of deprivation dimensions and hence as the most appropriate aggregate index of multidimensional deprivation. The UNDP elevates power mean of order α > 1 (PM) in comparison with arithmetic mean (AM) commonly used for averaging, leaving out others. It would hence be worthwhile to look into the links among the means, both the known and the potential ones, and their strengths and weaknesses in terms of their properties in comparison with each other. The present paper is a preliminary attempt at this. We find that the means we commonly use, the AM, the geometric mean (GM) and the harmonic mean (HM), along with the PM, are special cases of the CES function. We acknowledge the possibility of an inverse CES function, and hence, that of an inverse power mean (IPM) also. Among these means, the AM is an average, typical of all the components, but its infinite elasticity of substitution renders it less desirable. To the extent that we need an average typical of the components, we seek for one that is closer to the AM, so that this second best choice will have the minimum deviations next to the AM. And we find this basic criterion is satisfied by the IPM only. Hence, while the PM captures the multidimensional deprivation, its inverse, the IPM, seems to offer a multidimensional development index.
Item Type:  MPRA Paper 

Original Title:  CES Function, Generalized Mean and Human Poverty Index: Exploring Some Links 
Language:  English 
Keywords:  Generalised mean, CES function, Human Poverty Index, Deprivation, development 
Subjects:  C  Mathematical and Quantitative Methods > C4  Econometric and Statistical Methods: Special Topics > C43  Index Numbers and Aggregation I  Health, Education, and Welfare > I3  Welfare, WellBeing, and Poverty 
Item ID:  6951 
Depositing User:  Vijayamohanan Pillai N 
Date Deposited:  01. Feb 2008 10:36 
Last Modified:  26. Feb 2015 01:23 
References:  1. Abramowitz, M and Stegun, I A (1965) Handbook of Mathematical Functions, New York: Dover. 2. Apostol, T. M. (1967) Calculus, Vol. I, 2nd edition, New York: Wiley. 3. Sen, AK.(1999) Development as Freedom. New York: Alfred A. Knopf, Inc. 4. UNDP (1997) Human Development Report 1997. Oxford: OUP. 5. UNDP (2000) Human Development Report 2000. Oxford: OUP. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/6951 