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The Bias of Inequality Measures in Very Small Samples: Some Analytic Results

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Author Info
David E. Giles () (Department of Economics, University of Victoria)

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Abstract

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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File URL: http://web.uvic.ca/econ/research/papers/ewp0514.pdf
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Publisher Info
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
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Postal: PO Box 1700, STN CSC, Victoria, BC, Canada, V8W 2Y2
Phone: (250)721-8540
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Web page: http://web.uvic.ca/econ
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Related research
Keywords: Inequality indices; generalized entropy; bias; small-sigma expansion;

Find related papers by JEL classification:
C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Estimation
C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Econometric and Statistical Methods; Specific Distributions
D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Cowell, Frank A, 1985. "Measures of Distributional Change: An Axiomatic Approach," Review of Economic Studies, Blackwell Publishing, vol. 52(1), pages 135-51, January. [Downloadable!] (restricted)
  2. Aman Ullah & Virendara Srivastava & Nilanjana Roy, 1995. "Moments of the function of non-normal random vector with applications to econometric estimators and test statistics," Econometric Reviews, Taylor and Francis Journals, vol. 14(4), pages 459-471. [Downloadable!] (restricted)
  3. Breunig, Robert, 2001. "An almost unbiased estimator of the coefficient of variation," Economics Letters, Elsevier, vol. 70(1), pages 15-19, January. [Downloadable!] (restricted)
  4. 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, 01. [Downloadable!] (restricted)
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