Discussion paper

DP12404 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 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, in- cluding 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. Us- ing 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 com- monly 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.

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Citation

Piketty, T and T Blanchet (2017), ‘DP12404 Generalized Pareto Curves: Theory and Applications‘, CEPR Discussion Paper No. 12404. CEPR Press, Paris & London. https://cepr.org/publications/dp12404