To compare income and wealth distributions and to assess the effects of policy that affect those distributions require reliable inequality-measurement tools. However, commonly used inequality measures such as the Gini coefficient have an apparently counter-intuitive property: income growth among the rich may actually reduce measured inequality. We show that there are just two inequality measures that both avoid this anomalous behavior and satisfy the principle of transfers. We further show that the recent increases in US income inequality are understated by the conventional Gini coefficient and explain why a simple alternative inequality measure should be preferred in practice.

Despite their high predictive performance, random forest and gradient boosting are often considered as black boxes which has raised concerns from practitioners and regulators. As an alternative, we suggest using partial linear models that are inherently interpretable. Specifically, we propose to combine parametric and non-parametric functions to accurately capture linearities and non-linearities prevailing between dependent and explanatory variables, and a variable selection procedure to control for overfitting issues. Estimation relies on a two-step procedure building upon the double residual method. We illustrate the predictive performance and interpretability of our approach on a regression problem.

Many problems ask a question that can be formulated as a causal question: what would have happened if...? For example, would the person have had surgery if he or she had been Black? To address this kind of questions, calculating an average treatment effect (ATE) is often uninformative, because one would like to know how much impact a variable (such as the skin color) has on a specific individual, characterized by certain covariates. Trying to calculate a conditional ATE (CATE) seems more appropriate. In causal inference, the propensity score approach assumes that the treatment is influenced by $$\boldsymbol{x}$$x, a collection of covariates. Here, we will have the dual view: doing an intervention, or changing the treatment (even just hypothetically, in a thought experiment, for example by asking what would have happened if a person had been Black) can have an impact on the values of $$\boldsymbol{x}$$x. We will see here that optimal transport allows us to change certain characteristics that are influenced by the variable whose effect we are trying to quantify. We propose here a mutatis mutandis version of the CATE, which will be done simply in dimension one by saying that the CATE must be computed relative to a level of probability, associated to the proportion of x (a single covariate) in the control population, and by looking for the equivalent quantile in the test population. In higher dimension, it will be necessary to go through transport, and an application will be proposed on the impact of some variables on the probability of having an unnatural birth (the fact that the mother smokes, or that the mother is Black).

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 interesting properties, that can be easily linked to economic theory. In this paper, we first show that modeling top incomes with Pareto Type I distribution can lead to biased 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 can 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.