Scale-Invariant Measurement of Inequality and Welfare in Ordinal Achievements: An Application to Subjective Well-Being and Education in OECD Countries

Abstract

Designing well-being policies often requires the use of qualitative data. In fact many dimensions of well-being have to be appraised through the use of an ordered status: that is the case with health, happiness and educational attainments. While it is important to look at the mean levels achieved by society, distributional features are also salient aspects for any evaluation exercises, as it is likely that strong disparities in achievements among the population will prevail in those dimensions. Nonetheless, standards tools for inequality analysis, essentially mean-based and thus scale-dependent, are not applicable in this context, as any choice of scale in an ordinal framework is likely to be arbitrary and subject to change. Relying on the median-based approach developed by Allison and Foster (J Health Econ 23:505–524, 2004) for the measurement of self-reported health status inequality, this paper applies scale-invariant measures to subjective well-being and educational attainments in OECD countries using the 2010 round of the Gallup World Poll. This scale-invariant approach, applied to the case of three-category ordinal variables with identical median states, generates an unambiguous inequality and welfare ordering. This ranking is further completed by the computation of a scale-invariant inequality index. Both these measures aim to provide a robust picture of inequality and welfare in an ordinal context.