Modelling Lorenz Curves: Robust and Semi-parametric Issues

Modelling Lorenz curves (LC) for stochastic dominance comparisons is central to the analysis of income distributions. It is conventional to use non-parametric statistics based on empirical income cumulants which are used in the construction of LC and other related second-order dominance criteria. However, although attractive because of its simplicity and its apparent flexibility, this approach suffers from important drawbacks. While no assumptions need to be made regarding the data-generating process (income distribution model), the empirical LC can be very sensitive to data particularities, especially in the upper tail of the distribution. This robustness problem can lead in practice to “wrong” interpretation of dominance orders. A possible remedy for this problem is the use of parametric or semi-parametric models for the data-generating process and robust estimators to obtain parameter estimates. In this paper, we focus on the robust estimation of semi-parametric LC and investigate issues such as sensitivity of LC estimators to data contamination (Cowell and Victoria-Feser, 2002), trimmed LC (Cowell and Victoria-Feser, 2006), and inference for trimmed LC (Cowell and Victoria-Feser, 2003), robust semi-parametric estimation for LC (Cowell and Victoria-Feser, 2007), selection of optimal thresholds for (robust) semi-parametric modelling (Dupuis and Victoria-Feser, 2006), and use both simulations and real data to illustrate these points.