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Estimating Inequality Measures from Quantile Data

Enora Belz
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Enora Belz: CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR1 - Université de Rennes 1 - UNIV-RENNES - Université de Rennes - CNRS - Centre National de la Recherche Scientifique

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Abstract: This article focuses on the problem of dealing with aggregate data. It proposes an innovative method for modelling Lorenz curves and estimating inequality indices on small populations, when (only) quantiles are available. When dealing with small population areas and due to privacy restrictions, individual or income share data are often not available and only quantiles are reported. The method is based on conditional expectation in order to find the different income shares and thus model a Lorenz curve with the functional forms already proposed in the literature. From this Lorenz curve, inequality indices (Gini, Pietra, Theil indices) can be derived. A simulation study is performed to evaluate this method and compare it with the other methods used. An example based on real Parisian data is presented to illustrate the method. A R package was written with all functions used in this article.

Keywords: Inequalities; Income; Distribution; Aggregated data; Lorenz Curve; Gini; Pietra; Theil (search for similar items in EconPapers)
Date: 2019-10-18
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-02320110
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