On the axiomatization of the weakly decomposable inequality indices |
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| Affiliation: | 1. Physics Department, Faculty of Science, Tanta University, 31527 Tanta, Egypt;2. Reactor and Neutron Physics Department, Nuclear Research Center, Atomic Energy Authority, Cairo, Egypt;1. INSEAD, France;2. University of Torino, Italy;3. EDHEC Business School, France;4. Frankfurt School of Finance & Management, Germany;5. NBER, United States;6. CEPR, United Kingdom;7. SAFE, Germany;1. Center for Crystal Research and Development, Key Laboratory of Functional Crystals and Laser Technology, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, PR China;2. Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, PR China;3. State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, PR China;4. Institute of Functional Crystal Materials, Tianjin University of Technology, Tianjin 300384, PR China |
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| Abstract: | In this paper, we focus on a decomposition property recently introduced in the inequality literature and known as the weak decomposition. Such a property provides interesting analyses by allowing one to separate the within-group contribution to total inequality from the between-group contribution. A limitation of the current method of decomposition is that, depending on the structure–absolute, relative, compromise–of the inequality index, specific weights have to be used. To avoid such a problem, we propose a unique decomposition property where the weighting functions depend on the size of the population and the mean income. This allows us to characterize a large family of weakly decomposable inequality indices without any recourse to implicit invariance value judgments. |
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