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A Cautionary Note on Estimating the Standard Error of the Gini Index of Inequality: Comment

Document Cited in Related
Vincent
DOIhttp://doi.org/10.1111/j.1468-0084.2006.00169.x
Published date01 June 2006
Date01 June 2006
PRACTITIONERS’ CORNER
A Cautionary Note on Estimating the Standard
Error of the Gini Index of Inequality:
Comment
David E. A. Giles
Department of Economics, University of Victoria, Victoria, BC, Canada
(e-mail: dgiles@uvic.ca)
Abstract
We observe that care must be taken when using a regression-based approach
to construct a standard error for the Gini coefficient.
Comment
Modarres and Gastwirth (Oxford Bulletin of Economics and Statistics, 2006,
Vol. 68, pp. 385–390) provide some helpful results that show how careful one
must be when constructing a standard error for the Gini index. Their note, and
the associated Monte Carlo evidence reinforce the point that the properties of
any statistical procedure depend crucially on the underlying conditions (or
assumptions). The regression-based approach to constructing a standard error
that was proposed by Giles (2004) assumes a particular form of heteroske-
dasticity, and independence of the errors. The latter condition is clearly
problematic. As Modarres and Gastwirth remind us, even if we have an
independent sample, the order statistics formed from this sample are not
independent. If one wished to retain the regression-based approach, one
response to this problem could be to take the dependency into account in the
construction of the covariance estimator, and hence the standard errors.
JEL Classification numbers: C3, C43, D31, I31.
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 68, 3 (2006) 0305-9049
395
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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