Calculating the Extended Gini Coefficient from Grouped Data - a Covariance Presentation

8 Pages Posted: 18 Apr 2006 Last revised: 14 Mar 2014

See all articles by Edna Schechtman

Edna Schechtman

Ben-Gurion University of the Negev - Department of Industrial Engineering and Management

Shlomo Yitzhaki

Hebrew University of Jerusalem - Department of Economics; National Bureau of Economic Research (NBER)

Date Written: December 1, 2005

Abstract

The basic approach to estimating the Gini and extended Gini indices is to approximate the Lorenz curve by a number of linear segments, and then estimate the Gini coefficients as the areas (or weighted areas) between the linear segments and the 45-degree line. We show that the estimator for the extended Gini, obtained from the Lorenz curve (Chotikapanich and Griffiths, 2001) is algebraically identical to a covariance-based estimator. The advantages of the covariance-based estimators are twofold; first, they are easy to compute, using any standard statistical software, and second, the covariance-based estimators allow for the decomposition of the Gini index of a sum of variables (or populations).

Keywords: Gini index, Lorenz curve, Grouped data

JEL Classification: C10

Suggested Citation

Schechtman, Edna and Yitzhaki, Shlomo, Calculating the Extended Gini Coefficient from Grouped Data - a Covariance Presentation (December 1, 2005). Available at SSRN: https://ssrn.com/abstract=890041 or http://dx.doi.org/10.2139/ssrn.890041

Edna Schechtman (Contact Author)

Ben-Gurion University of the Negev - Department of Industrial Engineering and Management ( email )

Beer-Sheva 84105
Israel
+972 8 647 2596 (Phone)
+972 8 647 2958 (Fax)

Shlomo Yitzhaki

Hebrew University of Jerusalem - Department of Economics ( email )

Mount Scopus
Jerusalem, 91905
Israel
+972 2 659 2201 (Phone)
+972 2 652 2319 (Fax)

National Bureau of Economic Research (NBER) ( email )

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

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