Generalized Pareto Curves: Theory and Applications (2017) with Juliette Fournier and Thomas Piketty, WID.world Working Paper Series

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## Abstract

We define *generalized Pareto curves* as the curve of inverted Pareto coefficients \(b(p)\), where \(b(p)\) is the ratio between average income or wealth above rank \(p\) and the \(p\)-th quantile \(Q(p)\) (i.e. \(b(p)=\mathbb{E}[X|X>Q(p)]/Q(p)\)). We use them to characterize and visualize power laws. We develop a method to nonparametrically recover the entire distribution based on tabulated income or wealth 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 demonstrate the precision of our method both empirically and analytically. It gives better results than the most commonly used interpolation techniques. Finally, we use Pareto curves to identify recurring distributional patterns, and connect those findings to the existing literature that explains observed distribution by random growth models.