An Axiomatic Foundation of the Multiplicative Human Development Index. (21st October 2018)

• Record Type: Journal Article
• Authors: Kawada, Yoko; Nakamura, Yuta; Otani, Shuhei
• Is Part Of: Review of income and wealth. Series 65:Number 4(2019)
• Page Start: 771
• Page End: 784
• Publication Date: 2018-10-21
• Subjects: aggregation theory -- geometric mean -- Human Development Index -- quasi‐geometric mean -- power mean; National income -- Accounting -- Periodicals; 332.05
• DOI: 10.1111/roiw.12370
• Languages: English
• ISSNs: 0034-6586

Abstract

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).