Thomas Blanchet

Generalized Pareto Curves: Theory and Applications (2017) , 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.

We developed an online application that you can freely access, that doesn’t require any installation or prior technical knowledge. This application lets you use the generalized Pareto interpolation method developed in the paper to recover distributions of income and wealth based on tabulated data, as is typically available from tax authorities or national statistical institutes. The application is hosted on WID.world’s website.
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We developed an R package to use the generalized Pareto interpolation method described in the paper. This package also includes the application mentioned above, which can be run locally on your computer. The source code is freely available on GitHub.
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The data and Stata/R programs to replicate all the graphs and the tables of the article are available on GitHub.
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We provide the Mathematica notebooks used for some of the symbolic computations used in the article. Both the actual notebooks and their output in PDF are available on GitHub.
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