To what extent fuzzy set theory and structural equation modelling can measure functionings ? An application to child well being

This paper explores the possibilities of using fuzzy inference system and structural equation modelling to measure capabilities both at a theoretical and empirical level. Fuzzy set theory has been already used to measure functionings (Chiappero Martinetti 1996, 2000, Lelli 2001) while structural equation modelling has not been used till now (apart from some preliminary results on children well being in India presented by Di Tommaso 2003). In this paper we outline the major advantages and disadvantages of both the approaches both in terms of the statistical assumptions implied and in terms of their ability to measure functionings. Are the statistical assumptions implied by these approaches compatible with the capability approach? What limitations the statistical assumptions impose to the capability approach? In order to assess to what extent these two statistical techniques work, we will apply them to measure child well being with a capabilities approach. The aim is also how to propose a list of capabilities with reference to children well being in Italy. The applied part of the paper will use a data set based on a ISTAT (Italian National Statistical Office) multipurpose survey on family and on children condition in Italy to recover information on children's education, the socio-demographic structure of their families, child care provided by relatives and parents according to the type of activities in which the children are involved. In the conclusion of the paper, we outline if and to what extent these statistical and fuzzy techniques can be used to measure functionings with special reference to child well being.