Robust Stochastic Dominance: A Semi-Parametric Approach
The Journal of Economic Inequality, Vol. 5, No. 1, pp. 21-37, 2007
18 Pages Posted: 12 Feb 2011
Date Written: September 14, 2006
Lorenz curves and second-order dominance criteria, the fundamental tools for stochastic dominance, are known to be sensitive to data contamination in the tails of the distribution. We propose two ways of dealing with the problem: (1) Estimate Lorenz curves using parametric models and (2) combine empirical estimation with a parametric (robust) estimation of the upper tail of the distribution using the Pareto model. Approach (2) is preferred because of its flexibility. Using simulations we show the dramatic effect of a few contaminated data on the Lorenz ranking and the performance of the robust semi-parametric approach (2). Since estimation is only a first step for statistical inference and since semi-parametric models are not straightforward to handle, we also derive asymptotic covariance matrices for our semi-parametric estimators.
Keywords: Lorenz curve, M-estimators, Pareto model, welfare dominance
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