Modelling Lorenz Curves: Robust and Semi-parametric Issues

Abstract

Modelling Lorenz curves (LC) for stochastic dominance comparisons is central to the analysis of income distribution. It is conventional to use non-parametric statistics based on empirical income cumulants which are 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 datagenerating 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.

Wealth inequality: Theory, measurement and decomposition

“…Cowell and Mehta (1982) was an important early contribution. See Bishop, Chakraborti et al (1991); Bishop, Formby et al (1991); Davidson and Duclos (2000); and Victoria-Feser (1996, 2008) for examples of later work.…”

Wealth Inequality: A Survey

“…It is therefore desirable to implement estimators robust to the presence of extreme data. One commonly-used option is the optimal B-robust estimator (OBRE) described by Hampel et al (1986) and applied to income distribution models by Victoria-Feser and Ronchetti (1994), Victoria-Feser (2000) and Cowell and Victoria-Feser (2008). More recent approaches are based on Robust Indirect Inference (Genton and Ronchetti, 2003).…”

Relative Risk Aversion and Power-Law Distribution of Macroeconomic Disasters

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