A demarcation of the Gini coefficient - Oded Stark; Grzegorz Kosiorowski (ZBW - Leibniz Information Centre for Economics, 2025)
We specify the domain in the income distribution that includes the people to whom income transfers will not increase inequality in that income distribution. Inspired by Sen's (1973, 1997) characterization of the Gini coefficient as a ratio between a measure of aggregate income-based “depression” (stress) and aggregate income, we inquire as to whether in the wake of an increase of an income or of incomes in a given income distribution, the Gini coefficient does not increase. To this end, we identify the corresponding “safe” domain and show that the pivotal value that demarcates this domain can be elicited from a simple linear function of the Gini coefficient itself. Our rule of demarcation provides for policy interventions that seek to increase a particular income or particular incomes while not exacerbating inequality in the income distribution as measured by the Gini coefficient.
Keywords: C43; D31; D63; H11; H53; I31; I38; P46; 330; Aggregate income; Aggregate income-based stress; Gini coefficient; Rank-preserving increase of an income or incomes; Sufficient condition for the Gini coefficient not to increase; Pivotal value