Some Considerations Relating to the Measurement and Mitigation of Inequality

Amongst the most widely used measures of income or wealth inequality is the Gini coefficient G. In recent times, there has been a rise in popularity of alternative measures such as the Palma Ratio (which is the ratio of the income-share of the top 10 per cent of a distribution to that of the bottom 40 per cent), or simply the income-shares of 'top incomes' (the top 1 per cent, or 0.1 per cent, or even 0.01 per cent), as in the work of Atkinson, Piketty and others. A particularly simple measure which reckons 'top incomes' is R, the proportionate shortfall of the mean income from the richest person's income. Measures such as G, which take stock of the distribution in its entirety, may be called 'across the board' indices, while measures such as R, which focus attention on the tail(s) of the distribution, may be called 'tailender' indices. Rather than see these categories of measures as being in opposition to each other, the present paper suggests that there is a case for combining them in a composite index. One such measure, which combines G and R, is the index D, given (for 'large' populations) by D=R+(1-R)G. The inequality index D is derived in this paper by way of an elementary extension of what is known as the Sen-Shorrocks-Thon poverty index into a well-defined index of inequality. It turns out that for distributions in which income is heavily concentrated at the upper end, the value of D is significantly influenced by the value of R, and that a natural approach to the reduction of inequality would be to cap top incomes. The paper suggests that considerations of both measurement and political morality would espouse the distributional doctrine of 'limitarianism', as proposed by Ingrid Robeyns, as an inevitable concomitant of the mitigation of inequality.