An Individual Relative Deprivation Index and Its Curve Considering Income Scope

Abstract

The purpose of this paper is to build a new relative deprivation index with more properties than existing indices such as Yitzhaki index, Kakwani index and Esposito index. Through detailed analysis of the properties of above indices, we find that a new individual index can be derived through introducing income scope into deprivation between two individuals. The proposed index fills up the shortcomings of existing indices. It satisfies more properties including non-negative decrease, concave, weak focus, dimensionless, normalization, translation invariance, scale invariance, additive decomposability and so on. Moreover, the new index conforms to our subject feeling and better reflects the connotations of relative deprivation. The article finally uses CGSS2008 rural data to draw the relative deprivation curves and analyze its sensitivity to max and min income.