A bidimensional inequality index: inference and almost Lorenz dominance

A. Baíllo Moreno, J. Cárcamo Urtiaga, C. Mora Corral

Baíllo et al. (2022) propose a bidimensional inequality index to compare two Lorenz curves corresponding to two income distributions. The first component of the index is the difference of the two Gini indices. The second component is proportional to the L1 distance between the Lorenz curves. This bidimensional index enables to identify variables with different distributions yet with similar Gini indices and permits to detect in a simple way the possible Lorenz ordering between two variables.
Based on samples from the populations, we define the plug-in estimator of the bidimensional inequality index, which under suitable assumptions, is asymptotically normal. We explore bootstrap procedures to do inference on the unknown population index. The test of almost Lorenz dominance in the Lorenz ordering can be equivalently stated in terms of the index being or not in a certain subset of the bidimensional index range. We analyze the performance of a bootstrap critical region of the test.

Keywords: bootstrap; income inequality; Lorenz curves; Lorenz order

Scheduled

GT12 Stochastic Orders and their Applications III
June 8, 2022  5:20 PM
A05

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