A short note revisiting the concentration index: Does the normalization of the concentration index matter?

The concentration index, including its normalization, is prominently used to assess socioeconomic inequalities in health and health care. Wagstaff's and Erreygers' normalizations or corrections of the standard concentration index are the most suggested approaches when analyzing binary health variables encountered in many health economics and health services research. In empirical applications of the corrected or normalized concentration indices, researchers interpret them similarly to the standard concentration index, which may be problematic as this ignores their underlying behaviors. This paper shows that the empirical bounds of the standard concentration index, including the corrected indices, depend not only on the sample size directly but also on the sampling weight. Notably, the paper highlights critical challenges for assessing and interpreting the popular Wagstaff's and Erreygers' corrected concentration indices with binary health variables. Specifically, it shows that it might be misleading, for example, to assess socioeconomic health inequalities using the magnitude of the "symmetric" Erreygers' corrected concentration index in the face of progressive improvements in the binary health variable. Also, Wagstaff's normalized concentration index may give a spurious "concentration" of the binary health variable among the rich or the poor in certain rare instances.