Deriving the parameter of inequality aversion from a parametric distribution of incomes

In this paper, the method of deriving the parameter ε of inequality aversion from a parametric distribution of incomes is proposed. It is assumed that a social decision-maker appraises welfare in income distributions by means of the constant inequality aversion utility function and that incomes obey the generalised beta distribution of the second kind GB2(a,b,p,q). It is proved that, under these assumptions, the social welfare function exists if and only if ε belongs to [0,ap+1) interval. The mid-point εmid of this interval specifies inequality aversion of the median socialdecision maker. The maximum likelihood estimator of εmid has been developed. Inequality aversion for Poland 1998-2015 has been estimated. If inequality is calculated on the basis of disposable incomes, the standard inequality-development relationship might be complemented by inequality aversion. Such an augmented inequality-development relationship discloses new evidences. For instance, the Gini index is not a declining function of ε in general, but only for a high stage of the economic development.