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

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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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  • David E. Giles, 2005. "The Bias of Inequality Measures in Very Small Samples: Some Analytic Results," Econometrics Working Papers 0514, Department of Economics, University of Victoria.
    • Handle: RePEc:vic:vicewp:0514
    Note: ISSN 1485-6441
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    2. 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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    5. 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.
    6. Kadane, Joseph B, 1971. "Comparison of k-Class Estimators when the Disturbances are Small," Econometrica, Econometric Society, vol. 39(5), pages 723-737, September.
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    1. Silvia De Nicol`o & Maria Rosaria Ferrante & Silvia Pacei, 2021. "Mind the Income Gap: Bias Correction of Inequality Estimators in Small-Sized Samples," Papers 2107.08950, arXiv.org, revised May 2023.
    2. Maria Rosaria Ferrante & Silvia Pacei, 2019. "Small Sample Bias Corrections for Entropy Inequality Measures," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 9(3), pages 78-80, April.

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    More about this item

    Keywords

    Inequality indices; generalized entropy; bias; small-sigma expansion;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution

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