Generalized Pareto Curves : Theory and Applications

Thomas Blanchet (1, 2, 3) , Juliette Fournier (4) , Thomas Piketty (1, 2, 3)

1 PSE - Paris School of Economics
2 PJSE - Paris Jourdan Sciences Economiques
3 WIL - World Inequality Lab
4 MIT - Massachusetts Institute of Technology

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) = E[X|X > Q(p)]/Q(p)). We use them to characterize entire distributions, including places like the top where power laws are a good description, and places further down where they are not. 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 distributions by random growth models.

Mots clés: Pareto Curves; income data; wealth data; inequality; income; wealth; Pareto; power law; interpolation World Inequality Lab

Domaines: Economies et finances

Thomas Blanchet, Juliette Fournier, Thomas Piketty. Generalized Pareto Curves : Theory and Applications. 2017. ⟨halshs-02658851⟩