A Convenient Method of Decomposing the Gini Index by Population Subgroups

Open access


We propose a convenient method of estimating the within-group, between-group, and interaction components of the overall traditional Gini index from the estimated parameters of underlying “trick regression models” involving known forms of heteroscedasticity related to income. Two illustrative examples involving both real and artificial data are provided. The issue of appropriate standard error of the subgroup decomposition is also discussed.

Bhattacharya, N. and Mahalanobis, B. (1967). Regional Disparities in Household Consumption in India. American Statistical Association Journal, 62, 143-161. DOI: http://www.dx.doi.org/10.1080/01621459.1967.10482896.

Biewen, M. (2002). Bootstrap Inference for Inequality, Mobility and Poverty Measurement. Journal of Econometrics, 108, 317-342. DOI: http://www.dx.doi.org/10.1016/S0304-4076(01)00138-5.

Cowell, F.A. (1989). Sampling Variance and Decomposable Inequality Measures. Journal of Econometrics, 42, 27-41. DOI: http://www.dx.doi.org/10.1016/ 0304-4076(89)90073-0.

Dagum, C. (1997). A New Approach to the Decomposition of the Gini Income Inequality Ratio. Empirical Economics, 22, 515-531. DOI: http://www.dx.doi.org/10.1007/ 978-3-642-51073-1_4.

Davidson, R. (2009). Reliable Inference for the Gini Index. Journal of Econometrics, 150, 30-40.

Dixon, P.M., Weiner, J., Mitchel-Olds, T., and Woodley, R. (1987). Bootstrapping the Gini Coefficient of Inequality. Ecology, 68, 1548-1551. DOI: http://www.dx.doi.org/10.2307/1939238.

Fei, J.C.H., Ranis, G., and Kuo, S.W.Y. (1978). Growth and the Family Distribution of Income by Factor Components. Quarterly Journal of Economics, 92, 17-53. DOI: http://www.dx.doi.org/10.2307/1885997.

Giles, D. (2004). Calculating a Standard Error for the Gini Coefficient: Some Further Results. Oxford Bulletin of Economics and Statistics, 66, 425-433. DOI: http://www. dx.doi.org/10.1111/j.1468-0084.2004.00086.x.

Gray, D., Mills, J.A., and Zandvakili, S. (2003). Statistical Inference of Inequality With Decompositions: the Canadian Experience. Empirical Economics, 28, 291-302. DOI: http://www.dx.doi.org/10.1007/s001810200131.

Kanbur, R. (2006). The Policy Significance of Inequality Decompositions. Journal of Economic Inequality, 4, 367-374. DOI: http://www.dx.doi.org/10.1007/s10888-005-9013-5.

Karoly, L.A. (1992). Changes in the Distribution of Individual Earnings in the United States: 1967-1986. Review of Economics and Statistics, 74, 107-115. Available at: http://www.jstor.org/stable/2109548 (access September 1, 2011).

Langel, M. and Tille´, Y. (2013). Variance Estimation of the Gini Index: Revisiting a Result Several Times Published. Journal of the Royal Statistical Society Series A Statistics in Society, 176, 521-540. DOI: http://www.dx.doi.org/10.1111/j.1467-985X.2012.01048.x.

Maasoumi, E. (1994). Empirical Analysis of Inequality and Welfare. Handbook of Applied Microeconomics, P. Schmidt and H. Peasaran (eds). Oxford: Blackwell.

Mills, J. and Zandvakili, S. (1997). Statistical Inference Via Bootstrapping for Measures of Economic Inequality. Journal of Applied Econometrics, 12, 133-150. DOI: http://www. dx.doi.org/10.1002/(SICI)1099-1255(199703)12:2,133::AID-JAE433.3.0.CO;2-H.

Modarres, R. and Gastwirth, J.L. (2006). A Cautionary Note on Estimating the Standard Error of the Gini Index of Inequality. Oxford Bulletin of Economics and Statistics, 68, 385-390. DOI: http://www.dx.doi.org/10.1111/j.1468-0084.2006.00167.x.

Mussard, S. and Richard, P. (2012). Linking Yitzhaki’s and Dagum’s Gini Decompositions. Applied Economics, 44, 2997-3010. DOI: http://www.dx.doi.org/10.1080/00036846.2011.568410.

Ogwang, T. (2000). A Convenient Method of Computing the Gini Index and its Standard Error. Oxford Bulletin of Economics and Statistics, 62, 123-129. DOI: http://www.dx. doi.org/10.1111/1468-0084.00164.

Ogwang, T. (2004). Calculating a Standard Error for the Gini Coefficient: Some Further Results: Reply. Oxford Bulletin of Economics and Statistics, 66, 435-437. DOI: http:// www.dx.doi.org/10.1111/j.1468-0084.2004.00087.x.

Ogwang, T. (2006). A Cautionary Note on Estimating the Standard Error of the Gini Index of Inequality: Comment. Oxford Bulletin of Economics and Statistics, 68, 391-393. DOI: http://www.dx.doi.org/10.1111/j.1468-0084.2006.00167.x.

Ogwang, T. (2007). Additional Properties of a Linear Pen’s Parade for Individual Data Using the Stochastic Approach to the Gini Index. Economics Letters, 96, 369-374.

Pyatt, G. (1976). On the Interpretation and Disaggregation of Gini Coefficients. Economic Journal, 86, 243-255. Available at: http://www.jstor.org/stable/2230745.

Radaelli, P. (2010). On the Decomposition by Subgroups of the Gini Index and Zenga’s Uniformity and Inequality Indexes. International Statistical Review, 78, 81-101. DOI: http://www.dx.doi.org/10.1111/j.1751-5823.2010.00100.x.

Rao, V.M. (1969). Two Decompositions of Concentration Ratio. Journal of the Royal Statistical Society Series A (General), 132, 418-425. Available at: http://www.jstor. org/stable/2344120.

Sastry, D.V.S. and Kelkar, U.R. (1994). Note on the Decomposition of Gini Inequality. Review of Economics and Statistics, LXXVI, 584-586. Available at: http://www.jstor. org/stable/2109984.

Shao, J. and Tu, D. (1995). Jackknife and Bootstrap. New York: Springer.

Shorrocks, A.F. (1982). Inequality Decomposition by Factor Components. Econometrica, 50, 193-211. Available at: http://www.jstor.org/stable/1912537.

Silber, J. (1989). Factor Components, Population Subgroups and the Computation of the Gini Index of Inequality. Review of Economics and Statistics, 71, 107-115. Available at: http://www.jstor.org/stable/1928057.

Yao, S. and Liu, J. (1996). Decomposition of the Gini Coefficient by Class: A New Approach. Applied Economics Letters, 3, 115-119.

Yao, S. (1999). On the Decomposition of Gini Coefficients by Population Class and Income Source: A Spreadsheet Approach and Application. Applied Economics, 31, 1249-1264. DOI: http://www.dx.doi.org/10.1080/000368499323463.

Yitzhaki, S. (1991). Calculating Jackknife Variance Estimators for Parameters of the Gini Method. Journal of Business and Economic Statistics, 9, 235-239. DOI: http://www.dx.doi.org/10.1080/07350015.1991.10509849.

Journal of Official Statistics

The Journal of Statistics Sweden

Journal Information

IMPACT FACTOR 2017: 0.662
5-year IMPACT FACTOR: 1.113

CiteScore 2017: 0.74

SCImago Journal Rank (SJR) 2017: 1.158
Source Normalized Impact per Paper (SNIP) 2017: 0.860

Cited By


All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 221 221 33
PDF Downloads 68 68 12