An Axiomatic Foundation of the Multiplicative Human Development Index10:56 2018/08/0210:56 2018/08/02

Yoko Kawada, Yuta Nakamura and Shuhei Otani
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Yoko Kawada: Graduate School of Economics, Keio University
Yuta Nakamura: Graduate School of Economics, Keio University
Shuhei Otani: Department of Economics, University of Wisconsin-Madison

No DP2018-18, Discussion Paper Series from Research Institute for Economics & Business Administration, Kobe University

Abstract: The aggregation formula in the Human Development Index (HDI) was changed to 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, Martinez, and Villar (2010).

Keywords: Human Development Index; Aggregation theory; Geometric mean; Quasi-geometric means; Power means (search for similar items in EconPapers)
JEL-codes: D63 I32 (search for similar items in EconPapers)
Pages: 25 pages
Date: 2018-08
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