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Reference distributions and inequality measurement

Author

Listed:
  • Frank A. Cowell

    (STICERD - LSE - London School of Economics and Political Science)

  • Emmanuel Flachaire

    (GREQAM - Groupement de Recherche en Économie Quantitative d'Aix-Marseille - ECM - Ecole Centrale de Marseille - CNRS - Centre National de la Recherche Scientifique - AMU - Aix Marseille Université - EHESS - École des hautes études en sciences sociales)

  • Sanghamitra Bandyopadhyay

    (STICERD - LSE - London School of Economics and Political Science)

Abstract

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.

Suggested Citation

  • Frank A. Cowell & Emmanuel Flachaire & Sanghamitra Bandyopadhyay, 2013. "Reference distributions and inequality measurement," Post-Print hal-01499629, HAL.
  • Handle: RePEc:hal:journl:hal-01499629
    DOI: 10.1007/s10888-012-9238-z
    Note: View the original document on HAL open archive server: https://hal-amu.archives-ouvertes.fr/hal-01499629
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Magdalou, Brice & Nock, Richard, 2011. "Income distributions and decomposable divergence measures," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2440-2454.
    4. Russell Davidson, 2012. "Statistical inference in the presence of heavy tails," Econometrics Journal, Royal Economic Society, vol. 15(1), pages 31-53, February.
    5. 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(7-8), pages 488-499, August.
    6. 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.
    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 & Flachaire, Emmanuel & Bandyopadhyay, Sanghamitra, 2009. "Goodness-of-fit: an economic approach," LSE Research Online Documents on Economics 25433, London School of Economics and Political Science, LSE Library.
    9. 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.
    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. Cowell, Frank A., 1980. "Generalized entropy and the measurement of distributional change," European Economic Review, Elsevier, vol. 13(1), pages 147-159, January.
    12. 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.
    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

    Keywords

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

    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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