Robust rankings of socioeconomic health inequality using a categorical variable

When assessing socioeconomic health inequalities, researchers often draw upon measures of income inequality that were developed for ratio scale variables. As a result, the use of categorical data (such as self-reported health status) produces rankings that may be arbitrary and contingent to the numerical scale adopted. In this paper, we develop a method that overcomes this issue by providing conditions for which these rankings are invariant to the numerical scale chosen by the researcher. In doing so, we draw on the insight provided by Allison and Foster (2004) and extend their method to the dimension of socioeconomic inequality by exploiting the properties of rank-dependent indices such as Wagstaff (2002) achievement and extended concentration indices. We also provide an empirical illustration using the National Institute of Health Survey 2012.