Extraction ratio as a political measure of income inequality (Milanovic et al, 2011)

A Fine Theorem blog (link) points to an interesting new paper on “Pre-Industrial Inequality” by Branko Milanovic, Peter H. Lindert, and Jeffrey G. Williamson forthcoming in The Economic Journal (link). The paper defines a new measure of income inequality called the “extraction ratio.” The extraction ratio is the ratio of the measured Gini coefficient to the “maximum possible Gini coefficient” that would obtain were all available societal surplus to be in the hands of a vanishingly small elite. The motivation for the extraction ratio measure is as follows: Consider a society divided into a poor and rich class, and for illustration suppose that the poor each earn P per year and the rich each earn R (that is, incomes are constant within classes) with P << R. If P is fixed to subsistence level, then the surplus that the rich enjoy relative to the poor (R-P) is a linear function of total income in society. As such, levels of inequality as measured by, say, the Gini coefficient are also a function total income. Two societies may exhibit class stratification that is similarly reprehensible in that in both cases, only the rich enjoy any surplus income over the subsistence level, but they may differ greatly in their Gini measures; or, two societies may have the same Gini coefficient, but differ in whether the poor obtain any surplus over subsistence. The extraction ratio allows one to distinguish these cases. The cases would seem to imply very different political circumstances, with a higher extraction ratio being associated with a more exploitative society, intuitively. The authors find that while the distribution of Gini coefficients does not differ so much between the pre-industrial and post-industrial ages, extraction ratios tended to be quite a bit higher in the pre-industrial age. Many studies attempt to correlate inequality as measured by the Gini coefficient to political outcomes, with very mixed results. It would be interesting to see if this new measure produces different insights.