With Emmanuel Flachaire, we uploaded on hal a paper on Pareto Models for Top Incomes,
Top incomes are often related to Pareto distribution. To date, economists have mostly used Pareto Type I distribution to model the upper tail of income and wealth distribution. It is a parametric distribution, with an attractive property, that can be easily linked to economic theory. In this paper, we first show that modelling top incomes with Pareto Type I distribution can lead to severe over-estimation of inequality, even with millions of observations. Then, we show that the Generalized Pareto distribution and, even more, the Extended Pareto distribution, are much less sensitive to the choice of the threshold. Thus, they provide more reliable results. We discuss different types of bias that could be encountered in empirical studies and, we provide some guidance for practice. To illustrate, two applications are investigated, on the distribution of income in South Africa in 2012 and on the distribution of wealth in the United States in 2013.
This paper was presented at and UCSB and in several workshops this spring, and this Summer, Emmanuel will present it at ECINEQ.
Note that a R package is also available on github, TopIncomes.
The second part of the graduate course on inequalities and poverty will be based on the slides below
Tomorrow, we will discuss inequality indices, from a statistical perspective, and also an axiomatic point of view. In order to illustrate, we will use to following dataset,
> income <- read.csv("http://www.vcharite.univ-mrs.fr/pp/lubrano/cours/fes96.csv",sep=";",header=FALSE)$V1
Slides can be found online. Since it is the first year I give this course, all comments are welcome…
As mentioned last week, tomorrow, we will work with datasets, and start the part on the econometrics of inequality. I have uploded some slides, but additional concepts and tools will be mentioned on the black board (or on the computer, while coding). We will use some simulated data (mentioned in the slides), as well as us_income, on binned data.
Our paper Log-transform kernel density estimationof income distribution, written with Emmanuel Flachaire is now available on http://papers.ssrn.com/id=2514882,
Standard kernel density estimation methods are very often used in practice to estimate density function. It works well in numerous cases. However, it is known not to work so well with skewed, multimodal and heavy-tailed distributions. Such features are usual with income distributions, defined over the positive support. We first show that a preliminary logarithmic transformation of the data, combined with standard kernel density estimation methods, can provide a much better fit of the overall density estimation. Then, we show that the fit of the bottom of the distribution may not be satisfactory, even if a better fit of the upper tail can be obtained in general.
A few days ago, Jean-François Mignot published an interesting article entitled Tour de France 2014 : pourquoi le vainqueur gagne 100 fois plus que le 10e. In this article, we have the following graph, with the income of the cyclist, as a function of his final ranking (the data where downloaded from http://sportbuzzbusiness.fr/)
+ sep=";",header=TRUE,dec=" ")
+ xlab="(Final) rank",ylab="Bonus")
As pointed out by Jean-François, if the winner gets a lot of money, the bonus decreases fast, very fast actually. Gini index is very high here
and if we look at Lorenz curve, indeed, the Tour de France is not very equalitarian,
Continue reading Income distribution and Tour de France →