Misery for the same GINI

Martin Wolf of the FT, an economist I really do enjoy listening to, in his big “global economic outlook” talk on Intelligence Squared in 2024 made a comment on the stationarity of Gini coefficients in the western world that irked me somewhat. He claimed that actually, the Gini coefficient only rose in the 80s and has stayed stable since, contradicting Piketty.

He neglects that the Gini coefficient is not unique. It’s not one-to-one (injective) to the Lorenz curve. You can deform a given Lorenz curve such that more money moves to the top of the distribution at the expense of the middle class while leaving the coefficient unchanged. Therefore, a previously moderately egalitarian society can move to one with a top-heavy upper class and an immiserated middle class without any change to the Gini coefficient. And the economists at the IMF and World Bank would be none the wiser, unless they measured the changes to the entropy of the underlying distribution, or the fractal dimension, or total curvature of the Lorenz curve (arc length might also tell you that things have gotten worse).