On the standard achievement and well-being indexes and their relation to the Hicks–Moorsteen productivity index

In a recent paper Ramos and Silber (2005) used techniques developed in efficiency analysis to obtain estimates of human development obtained on the basis of Sen (1985) and Narayan et al. (2000) capability approach. In particular they propose to measure standard achievement and well being indexes using a distance function approach. In this paper, it is shown that the ratio based of well-being and standard achievement indexes form the Hicks–Moorsteen index introduced by Bjurek (1996). Along this line, an additive form of the standard achievement and well-being indexes is proposed. In particular, the paper focusses on the case of social inputs. Axiomatic and dual properties are established and some parametric and nonparametric models are proposed.