## Generalized Pareto Curves: Theory and Applications

**WID.world Working Paper Series**

with Juliette Fournier and Thomas Piketty

### 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 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 flexibly 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.

Full TextPresentation Slides

#### Online Application

We developed a freely accessible online application, 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.

Go to Application

#### R package

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.

Go to Source on GitHub

#### Graphs and Replication Codes

The data and Stata/R programs to replicate all the graphs and the tables of the article are available on GitHub

Go to Source on GitHub

#### Mathematica Notebooks

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.

Go to Source on GitHub