A Cautionary Note on Estimating the Standard Error of the Gini Index of Inequality*
| Author | Joseph L. Gastwirth,Reza Modarres |
| Date | 01 June 2006 |
| DOI | http://doi.org/10.1111/j.1468-0084.2006.00167.x |
| Published date | 01 June 2006 |
PRACTITIONERS’ CORNER
A Cautionary Note on Estimating the Standard
Error of the Gini Index of Inequality*
Reza Modarres and Joseph L. Gastwirth
Department of Statistics, The George Washington University, Washington, DC, USA
(e-mail: reza@gwu.edu; jlgast@gwu.edu)
Abstract
We will show that the regression approach to estimating the standard error of
the Gini index can produce incorrect results as it does not account for the
correlations introduced in the error terms once the data are ordered. To assess
the effect of ignoring the correlation in the error terms we examined two
distributions and show that the regression method overestimates the standard
error of the Gini index. We recommend that the more mathematically complex
or computationally intensive methods be used.
I. Introduction
The Gini index is the most widely used measure of income inequality. Both the
index itself and a variety of its extensions are used in many applications
(Yitzhaki, 1991). In the 1980s several authors, Anand (1983), Lerman and
Yitzhaki (1984) and Shalit (1985) represented the index as a covariance, which
enables one to obtain the numerical value of the index using standard regression
software. Recently, Giles (2004) has proposed a method of estimating the
sampling error of the Gini index from those regression programs that was
questioned by Ogwang (2004). Here, we demonstrate by an example that the
*Research was conducted (Reza Modarres) while on sabbatical at the Department of Statistics,
University of Pennsylvania, USA. Research supported in part by grant SES-0317956 (Joseph L.
Gastwirth) from the National Science Foundation.
JEL Classification numbers: C1, C15.
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 68, 3 (2006) 0305-9049
385
ÓBlackwell Publishing Ltd, 2006. Published by Blackwell Publishing Ltd, 9600 Garsington Road, Oxford OX4 2DQ, UK
and 350 Main Street, Malden, MA 02148, USA.
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