When more does not necessarily mean better: Health-related illfare comparisons with non-monotone welbeing relationship

Most welfare studies are based on the assumption that wellbeing is monotonically related to the variables used for the analysis. While this assumption can be regarded as reasonable for many dimensions of wellbeing like income, education, or empowerment, there are some cases where it is definitively not relevant, in particular with respect to health. For instance, health status is often proxied using the Body Mass Index (BMI). Low BMI values can capture undernutrition or the incidence of severe illness, yet a high BMI is neither desirable as it indicates obesity. Usual illfare indices derived from poverty measurement are then not appropriate. This paper proposes illfare indices that are consistent with some situations of non-monotonic wellbeing relationships and examines the partial orderings of different distributions derived from various classes of illfare indices. An illustration is provided for health-related illfare as proxied by the BMI and weight-for-age indicators using DHS data for Bangladesh during the period 1997-2007. It is shown inter alia that the gains from the decline of undernutrition for Bangladeshi mothers are undermined by the rapid increase of obesity.