Inequality imbalance and its orderings based on relative and positional transfer sensitivity principles

If inequality in the lower income class is much larger than that in the higher income class in a high-inequality country, i.e., income distribution is highly leftward inequality-imbalanced in the country, policy-makers may prioritize lowering the inequality in the lower class by relevant policies such as an increase of social transfer and enhancement of support to poor households. Conversely, if inequality in the higher class is much larger than that in the lower class, i.e., income distribution is highly rightward inequality-imbalanced, priority may be put on lowering the inequality in the higher class by relevant policies such as raising income tax rates for the top incomes rather than improving policies for poverty reduction. In the existing studies, a specific Lorenz asymmetry measure has been proposed as a measure for inequality imbalance. However, reliance on only specific measures for the evaluation is undesirable to make welfare and redistribution policies widely accepted among stakeholders who may have various views on the inequality measurement. This paper proposes two approaches based on relative and positional transfer sensitivity principles for evaluating the direction and extent of inequality imbalance. Each approach evaluates inequality imbalance coherently with a broad class of inequality indices. Derived criteria for the extent of inequality imbalance create novel stochastic dominance orders. The proposed approaches are applied to income distributions in US and 38 European countries extracted from the World Income Database, which are corrected for underrepresentation of high-income earners in survey data by using tax data and national accounts statistics.