Measuring well-being dispersion on discrete rating scales

Abstract

Average levels of well-being across countries and time periods have been reported widely over the years as one of the measures that go beyond the Gross Domestic Product. It is relevant for policy makers to also have information on well-being dispersion to identify groups that lag behind with respect to their ability to pursue happiness. In addition, there is an inherent moral appeal to not only maximize wellbeing but also equalize well-being among people. In this paper, we try to answer the following research question: which measure(s) should be used to gain insight into wellbeing dispersion? We review sixteen measures and their properties, study their behavior in over 92 thousand simulated distributions, and apply them to 4 years of the Dutch Social Cohesion and Well-Being Survey, using bootstrapping to quantify their precision. Our inventory shows that when applied to a discrete ordinal rating scale, common measures such as the standard deviation and Gini coefficient do not show any advantage over the less restrictive index of ordinal variation (IOV). Only the generalized entropy and Atkinson index adhere to additional principles, most notably of diminishing transfers, at the expense of full scale invariance. The simulation study illustrates that dispersion measures are positively correlated but do not rank distributions the same. The field study shows that only the Atkinson index with high inequality aversion provides additional insight. We recommend using the index of ordinal variation, supplemented if needed with the Atkinson index using a high value for the inequality aversion parameter.