Comparing indices of relative deprivation using behavioural evidence

What measure of relative deprivation best predicts health? While numerous indices of relative deprivation exist, few studies have compared how well different measures account for empirical data. Hounkpatin et al. (2016) demonstrated that the relative ranked position of an individual i's income within a comparison group (their relative rank) was a better predictor of i's health than i's relative deprivation as assessed by the widely-used Yitzhaki index. In their commentary, Stark and Jakubek (2020) argue that both relative rank and relative deprivation may matter, and they develop a composite index. Here we identify some issues with their composite index, develop an alternative based on behavioural evidence, and test the various indices against data. Although almost all existing indices assume that the significance of an income y_j to an individual with income y_i (y_j>y_i) will be some increasing function of the difference between y_j and y_i, we find that the influence of j's income on i's health is actually a reducing function of (y_j-y_i). This finding - that less significance is assigned to distant higher incomes than to near higher incomes - is consistent with the well-established idea that we compare ourselves primarily to similar others.