Relative deprivation: a new derivation and application

We derive and express the Yitzhaki index of relative deprivation as a function of mean and median household income within a reference group and one’s income, under the assumption that individual income follows the log-normal distribution or the Pareto distribution. We also suggest a way to calculate annual US regional mean and median household income in each reference group using aggregate income and household size data. Therefore, unlike prior literature that utilizes Decennial Census data due to its big sample size, our suggested methodology allows annual calculation of relative deprivation at different levels of geography (state or county). In an application of the derived index presented to illustrate its feasibility, we analyse the relationship between relative deprivation and mental health, finding suggestive evidence that increases in relative deprivation negatively affect mental health in the United States.