Permutation Tests for Comparing Inequality Measures |
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| Authors: | Jean-Marie Dufour Emmanuel Flachaire Lynda Khalaf |
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| Affiliation: | 1. Department of Economics, McGill University, Montréal, Québec H3A 2T7, Canada;2. Centre Interuniversitaire de Recherche en Analyse des Organisations (CIRANO) and Centre interuniversitaire de recherche en économie quantitative (CIREQ), Montreal, QC, Canada (jean-marie.dufour@mcgill.ca);3. Aix-Marseille University, AMSE, CNRS, EHESS, Centrale Marseille, 13002, Marseille, France (emmanuel.flachaire@univ-amu.fr);4. Economics Department, Carleton University, Ottawa, Ontario K1S 5B6, Canada;5. Centre Interuniversitaire de Recherche en économie Quantitative (CIREQ), and Groupe de Recherche en économie de l’énergie, de l’environnement et des Ressources Naturelles (GREEN), Université Laval, QC, G1V 0A6, Canada (Lynda_Khalaf@carleton.ca) |
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| Abstract: | ABSTRACTAsymptotic and bootstrap tests for inequality measures are known to perform poorly in finite samples when the underlying distribution is heavy-tailed. We propose Monte Carlo permutation and bootstrap methods for the problem of testing the equality of inequality measures between two samples. Results cover the Generalized Entropy class, which includes Theil’s index, the Atkinson class of indices, and the Gini index. We analyze finite-sample and asymptotic conditions for the validity of the proposed methods, and we introduce a convenient rescaling to improve finite-sample performance. Simulation results show that size correct inference can be obtained with our proposed methods despite heavy tails if the underlying distributions are sufficiently close in the upper tails. Substantial reduction in size distortion is achieved more generally. Studentized rescaled Monte Carlo permutation tests outperform the competing methods we consider in terms of power. |
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| Keywords: | Bootstrap Income distribution Inequality measures Permutation test. |
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