An Axiomatic Foundation of the Multiplicative Human Development Index

Yoko Kawada, Yuta Nakamura and Shuhei Otani

Review of Income and Wealth, 2019, vol. 65, issue 4, 771-784

Abstract: The aggregation formula in the Human Development Index (HDI) was changed to a geometric mean in 2010. In this paper, we search for a theoretical justification for employing this new HDI formula. First, we find a maximal class of index functions, what we call quasi‐geometric means, that satisfy symmetry for the characteristics, normalization, and separability. Second, we show that power means are the only quasi‐geometric means satisfying homogeneity. Finally, the new HDI is the only power mean satisfying minimal lower boundedness, which is a local complementability axiom proposed by Herrero et al. (2010).

Date: 2019
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