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Reference distributions and inequality measurement


  • Frank Cowell
  • Emmanuel Flachaire


  • Sanghamitra Bandyopadhyay


We investigate a general problem of comparing pairs of distributions which includes approaches to inequality measurement, the evaluation of “unfair” income inequality, evaluation of inequality relative to norm incomes, and goodness of fit. We show how to represent the generic problem simply using (1) a class of divergence measures derived from a parsimonious set of axioms and (2) alternative types of “reference distributions.” The problems of appropriate statistical implementation are discussed and empirical illustrations of the technique are provided using a variety of reference distributions. Copyright Springer Science+Business Media New York 2013

Suggested Citation

  • Frank Cowell & Emmanuel Flachaire & Sanghamitra Bandyopadhyay, 2013. "Reference distributions and inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 11(4), pages 421-437, December.
  • Handle: RePEc:kap:jecinq:v:11:y:2013:i:4:p:421-437 DOI: 10.1007/s10888-012-9238-z

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    References listed on IDEAS

    1. Jenkins, Stephen P & O'Higgins, Michael, 1989. "Inequality Measurement Using 'Norm Incomes': Were Garvy and Paglin onto Something after All?," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 35(3), pages 265-282, September.
    2. Magdalou, Brice & Nock, Richard, 2011. "Income distributions and decomposable divergence measures," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2440-2454.
    3. Russell Davidson, 2012. "Statistical inference in the presence of heavy tails," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 31-53, February.
    4. Christian Schluter, 2012. "On the problem of inference for inequality measures for heavy‐tailed distributions," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 125-153, February.
    5. Davidson, Russell & Flachaire, Emmanuel, 2007. "Asymptotic and bootstrap inference for inequality and poverty measures," Journal of Econometrics, Elsevier, vol. 141(1), pages 141-166, November.
    6. Paglin, Morton, 1975. "The Measurement and Trend of Inequality: A Basic Revision," American Economic Review, American Economic Association, vol. 65(4), pages 598-609, September.
    7. Cowell, Frank A. & Flachaire, Emmanuel, 2007. "Income distribution and inequality measurement: The problem of extreme values," Journal of Econometrics, Elsevier, vol. 141(2), pages 1044-1072, December.
    8. Cowell, Frank A., 1980. "Generalized entropy and the measurement of distributional change," European Economic Review, Elsevier, vol. 13(1), pages 147-159, January.
    9. Schluter, Christian & van Garderen, Kees Jan, 2009. "Edgeworth expansions and normalizing transforms for inequality measures," Journal of Econometrics, Elsevier, vol. 150(1), pages 16-29, May.
    10. Davidson, Russell & MacKinnon, James G., 2007. "Improving the reliability of bootstrap tests with the fast double bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3259-3281, April.
    11. Almås, Ingvild & Cappelen, Alexander W. & Lind, Jo Thori & Sørensen, Erik Ø. & Tungodden, Bertil, 2011. "Measuring unfair (in)equality," Journal of Public Economics, Elsevier, vol. 95(7), pages 488-499.
    12. Sanghamitra Bandyopadhyay & Frank A. Cowell, 2009. "Goodness-of-Fit: An Economic Approach," Economics Series Working Papers 444, University of Oxford, Department of Economics.
    13. Wertz, Kenneth L, 1979. "The Measurement of Inequality: Comment," American Economic Review, American Economic Association, vol. 69(4), pages 670-672, September.
    14. Kurt Devooght, 2008. "To Each the Same and to Each his Own: A Proposal to Measure Responsibility-Sensitive Income Inequality," Economica, London School of Economics and Political Science, vol. 75(298), pages 280-295, May.
    15. Ebert, Udo, 1984. "Measures of distance between income distributions," Journal of Economic Theory, Elsevier, vol. 32(2), pages 266-274, April.
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    Cited by:

    1. Frank A. Cowell & Emmanuel Flachaire, 2014. "Statistical Methods for Distributional Analysis," Working Papers halshs-01115996, HAL.
    2. Nicholas Rohde, 2016. "J-divergence measurements of economic inequality," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(3), pages 847-870, June.
    3. repec:sgh:annals:i:45:y:2017:p:299-314 is not listed on IDEAS

    More about this item


    Divergence measures; Generalised entropy measures; Income distribution; Inequality measurement; D63; C10;

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General


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