Generalized Pareto Curves: Theory and Applications

We define generalized Pareto curves as the curve of inverted Pareto coefficients b(p), where b(p) is the ratio between average income above rank p and the p‐th quantile Q(p) (i.e., b(p)=E[X|X>Q(p)]/Q(p)). We use them to characterize income distributions. We develop a method to flexibly recover a continuous distribution based on tabulated income data as is generally available from tax authorities, which produces smooth and realistic shapes of generalized Pareto curves. Using detailed tabulations from quasi‐exhaustive tax data, we show the precision of our method. It gives better results than the most commonly used interpolation techniques for the top half of the distribution.