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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.

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Paper provided by Department of Economics, University of Victoria in its series Econometrics Working Papers with number 0514.

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Length: 16 pages
Date of creation: 02 Aug 2005
Date of revision:
Handle: RePEc:vic:vicewp:0514
Note: ISSN 1485-6441
Contact details of provider: Postal: PO Box 1700, STN CSC, Victoria, BC, Canada, V8W 2Y2
Phone: (250)721-6197
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Web page: http://web.uvic.ca/econ

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  1. Breunig, Robert, 2001. "An almost unbiased estimator of the coefficient of variation," Economics Letters, Elsevier, vol. 70(1), pages 15-19, January.
  2. Ghosh, Arabinda, 1975. "Concentration and Growth of Indian Industries, 1948-68," Journal of Industrial Economics, Wiley Blackwell, vol. 23(3), pages 203-22, March.
  3. Cowell, Frank A, 1985. "Measures of Distributional Change: An Axiomatic Approach," Review of Economic Studies, Wiley Blackwell, vol. 52(1), pages 135-51, January.
  4. 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.
  5. 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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