The Bias of Inequality Measures in Very Small Samples: Some Analytic Results
We consider the class of generalized entropy (GE) measures that are commonly used to measure inequality. When used in the context of very small samples, as is frequently the case in studies of industrial concentration, these measures are significantly biased. We derive the analytic expression for this bias for an arbitrary member of the GE family, using a small-sigma expansion. This expression is valid regardless of the sample size, is increasingly accurate as the sampling error decreases, and provides the basis for constructing ‘bias-corrected’ inequality measures. We illustrate the application of these results to data for the Canadian banking sector, and various U.S. industrial sectors.
|Date of creation:||02 Aug 2005|
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- Frank A. Cowell, 1985. "Measures of Distributional Change: An Axiomatic Approach," Review of Economic Studies, Oxford University Press, vol. 52(1), pages 135-151.
- George Deltas, 2003. "The Small-Sample Bias of the Gini Coefficient: Results and Implications for Empirical Research," The Review of Economics and Statistics, MIT Press, vol. 85(1), pages 226-234, February.
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- Breunig, Robert, 2001. "An almost unbiased estimator of the coefficient of variation," Economics Letters, Elsevier, vol. 70(1), pages 15-19, January.
- Bronwyn H. Hall, 2005. "A Note on the Bias in Herfindahl-Type Measures Based on Count Data," Revue d'Économie Industrielle, Programme National Persée, vol. 110(1), pages 149-156.
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