On the importance of the upside down test in absolute socioeconomic health inequality comparisons

This paper shows that it is impossible to obtain a robust ranking of absolute socioeconomic health inequality if one only imposes Bleichrodt and van Doorslaer's (2006) principle of income-related health transfer. This means that for any comparison, some indices obeying this ethical principle will always contradict the ranking produced by other indices obeying the same ethical principle. This results points to the need to impose more ethical structure on indices when one wants to identify robust rankings of absolute socioeconomic health inequality. We show that imposing Erreygers, Clarke and Van Ourti's (2012) upside down test allows for the identification of robust orderings of absolute health inequality. We also show that alternatively one can increase inequality aversion and impose higher order pro-poor principles of income-related health transfer sensitivity. In order to make the identification of all robust orderings implementable using survey data, the paper also discusses statistical inference for these positional dominance tests. To illustrate the empirical relevance of the proposed approach, we compare joint distributions of income and a health-related behavior in the United States in 1997 and 2014.