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Decomposition of the Gini index by income source for aggregated data and its applications

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  • Bin Shao

    (City College of San Francisco)

Abstract

The Gini index is well-known for a single measure of inequality. The purpose of this article is to explore a matrix structure of the Gini index in a setting of multiple source income. Using matrices, we analyze the decomposition of the Gini index by income source and derive an explicit formula for the factors in terms of the associated percentile levels based on aggregated data reporting. Each factor is shown to be the sums of the two split off parts of the income within a percentile bracket. Both have unequalizing and equalizing contribution to the total inequality, respectively. We use R code and apply the methodology to several data sets including a sample of European aggregated income reporting in 2014 for illustration. A byproduct from the Gini decomposition provides a matrix approach to the decomposition of the associated Lorenz curve in terms of the density distribution matrix and a Toeplitz matrix.

Suggested Citation

  • Bin Shao, 2021. "Decomposition of the Gini index by income source for aggregated data and its applications," Computational Statistics, Springer, vol. 36(3), pages 2135-2159, September.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:3:d:10.1007_s00180-021-01069-4
    DOI: 10.1007/s00180-021-01069-4
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    References listed on IDEAS

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    1. Heshmati, Almas, 2004. "A Review of Decomposition of Income Inequality," IZA Discussion Papers 1221, Institute of Labor Economics (IZA).
    2. Achille VERNIZZI & Maria Giovanna MONTI & Mauro MUSSINI, 2010. "A Gini and concentration index decomposition with an application to the APK reranking measure," Departmental Working Papers 2010-10, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano, revised 13 Dec 2010.
    3. Graham Pyatt & Chau-nan Chen & John Fei, 1980. "The Distribution of Income by Factor Components," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 95(3), pages 451-473.
    4. Dejian Lai & Jin Huang & Jan Risser & Asha Kapadia, 2008. "Statistical Properties of Generalized Gini Coefficient with Application to Health Inequality Measurement," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 87(2), pages 249-258, June.
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