Estimating the parameter of inequality aversion on the basis of a parametric distribution of incomes

Stanislaw Maciej Kot

doi:10.24136/eq.2020.018

Abstract

Research background: In applied welfare economics, the constant relative inequality aversion function is routinely used as the model of a social decisionmaker?s or a society?s preferences over income distributions. This function is entirely determined by the parameter, ?, of inequality aversion. However, there is no authoritative answer to the question of what the range of ? an analyst should select for empirical work. Purpose of the article: The aim of this paper is elaborating the method of deriving ? from a parametric distribution of disposable incomes. Methods: We assume that households? disposable incomes obey the generalised beta distribution of the second kind GB2(a,b,p,q). We have proved that, under this assumption, the social welfare function exists if and only if ? belongs to (0,ap+1) interval. The midpoint ?mid of this interval specifies the inequality aversion of the median social-decisionmaker. Findings & Value added: The maximum likelihood estimator of ?mid 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. The ?augmented? inequality?development relationship reveals new phenomena; for instance, the stage of economic development might matter when assessing the impact of inequality aversion on income inequality.

Highlights

We propose a new method of estimating the parameter, ε, of the constant relative inequality aversion function (CRIA) (Atkinson, 1970)
We propose a parametric method, PM, of estimating a society’s inequality aversion, ε, assuming that disposable income distribution, DDP, obeys the GB2(x;a,b,p,q) distribution
We argue that DDP embodies societal aversion to inequality

Summary

Introduction

We propose a new method of estimating the parameter, ε, of the constant relative inequality aversion function (CRIA) (Atkinson, 1970). The parameter ε measures inequality aversion, i.e. the rate at which a society trades-off economic efficiency for income equality.. Suppose m competitive redistributive policies which guaranty the same maximum SWF, but they differ concerning the level of inequality aversion, ε1,...,εm say. To assess the usefulness of our method to retrieve unobservable inequality aversion, we estimate the parameter ε and related normative characteristics for Poland for the years 2000–2015.

Literature review

Findings

Conclusions