Premium
An Axiomatic Foundation of the Multiplicative Human Development Index
Author(s) -
Kawada Yoko,
Nakamura Yuta,
Otani Shuhei
Publication year - 2019
Publication title -
review of income and wealth
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.024
H-Index - 57
eISSN - 1475-4991
pISSN - 0034-6586
DOI - 10.1111/roiw.12370
Subject(s) - multiplicative function , axiom , mathematics , normalization (sociology) , geometric mean , human development index , homogeneity (statistics) , mathematical economics , power index , human development (humanity) , statistics , economics , mathematical analysis , geometry , sociology , anthropology , economic growth
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).
Accelerating Research
Robert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom
Address
John Eccles HouseRobert Robinson Avenue,
Oxford Science Park, Oxford
OX4 4GP, United Kingdom