Variance Estimation for Generalized Entropy and Atkinson Inequality Indices: the Complex Survey Data Case*
| DOI | http://doi.org/10.1111/j.1468-0084.2006.00166.x |
| Published date | 01 June 2006 |
| Author | Stephen P. Jenkins,Martin Biewen |
| Date | 01 June 2006 |
Variance Estimation for Generalized Entropy
and Atkinson Inequality Indices: the Complex
Survey Data Case*
Martin Biewenand Stephen P. Jenkins
Department of Economics, Johann Wolfgang Goethe-University, Frankfurt,
Germany (e-mail: biewen@wiwi.uni-frankfurt.de)
Institute for Social and Economic Research, University of Essex, Colchester, Essex,
UK (e-mail: stephenj@essex.ac.uk)
Abstract
We derive the sampling variances of generalized entropy and Atkinson indices
when estimated from complex survey data, and show how they can be
calculated straightforwardly using widely available software. We also show
that, when the same approach is used to derive variance formulae for the
independent and identically distributed case, it leads to estimators that are
simpler than those proposed before. Both cases are illustrated with a
comparison of income inequality in Britain and Germany.
I. Introduction
Clustering, stratification, and probability weighting are design features
characterizing most of the social surveys that economists and others use, and
it is well known that these features may have a large impact on the sampling
variability of statistics.
1
However, complex survey design is rarely taken into
account in empirical work, and the measurement of inequality is no exception.
In this paper, this deficiency was rectified by deriving the sampling variance of
every member of the two most commonly used families of inequality indices,
*We thank two anonymous referees for their comments and suggestions. Financial support from
the Deutsche Forschungsgesellschaft (DFG) and core funding to ISER from the ESRC and the
University of Essex are gratefully acknowledged.
JEL Classification numbers: C14, D31.
1
See, e.g. Kish and Frankel (1974).
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 68, 3 (2006) 0305-9049
371
Blackwell 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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