Diminishing returns to GDP and the Human Development Index

This paper investigates the assumption of the human development index (HDI) that per capita GDP has diminishing returns to development. Alternative returns to scale assumptions for per capita GDP are evaluated using correlation and principal components analyses conducted on four separate samples of countries. Specifically, the correlation between various transformations of GDP and the other elements of the HDI are examined, and the principal components method of factor analysis is used to construct HDI-like indexes with the alternative transformations of GDP. Results generally support the diminishing returns assumption employed by the HDI, as a concave transformation of GDP is most highly correlated with the other variables, and the corresponding principal components HDI construction explains the largest amount of the variance of the original variables.