IDEAS home Printed from https://ideas.repec.org/p/bai/series/series_wp_03-2017.html
   My bibliography  Save this paper

Ranking income distributions: a rank-dependent and needs-based approach

Author

Listed:
  • Ida Petrillo

    (Università degli Studi di Bari "Aldo Moro”)

Abstract

This paper provides a normative framework to assess social welfare within a rank-dependent and bidimensional setting where individuals are characterized by income and needs. In line with the growing interest in top incomes and inequalities concerning the upper part of the income distribution (see Atkinson and Piketty, 2007; 2010; Aaberge, Havnes and Mogstad, 2013), we propose a complete framework to rank bidimensional distributions, by focussing on inequalities among the poorest as well as the richest individuals, both in the monetary and non-monetary dimension. To this end, we develop third degree inverse stochastic dominance conditions for classes of social welfare functions satisfying: i) downside inequality aversion with respect to income and upside inequality aversion with respect to needs; ii) upside inequality aversion with respect to income and downside inequality aversion with respect to needs; iii) upside inequality aversion both with respect to income and needs. Our results emerge along with the existing one, formulated by Zoli (2000), supporting downside inequality aversion both with respect to income and needs.

Suggested Citation

  • Ida Petrillo, 2017. "Ranking income distributions: a rank-dependent and needs-based approach," SERIES 03-2017, Dipartimento di Economia e Finanza - Università degli Studi di Bari "Aldo Moro", revised Jul 2017.
    • Handle: RePEc:bai:series:series_wp_03-2017
    as

    Download full text from publisher

    File URL: http://www.seriesworkingpapers.it/RePEc/bai/series/SERIES_WP_03-2017.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Atkinson, A. B. & Piketty, Thomas (ed.), 2010. "Top Incomes: A Global Perspective," OUP Catalogue, Oxford University Press, number 9780199286898, Decembrie.
    2. Duclos, Jean-Yves & Échevin, Damien, 2011. "Health and income: A robust comparison of Canada and the US," Journal of Health Economics, Elsevier, vol. 30(2), pages 293-302, March.
    3. Flaviana Palmisano & Vito Peragine, 2015. "The Distributional Incidence of Growth: A Social Welfare Approach," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 61(3), pages 440-464, September.
    4. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    5. repec:bla:revinw:v:39:y:1993:i:4:p:337-56 is not listed on IDEAS
    6. Rolf Aaberge & Eugenio Peluso, 2011. "A Counting Approach for Measuring Multidimensional Deprivation," Working Papers 07/2011, University of Verona, Department of Economics.
    7. Davies James & Hoy Michael, 1994. "The Normative Significance of Using Third-Degree Stochastic Dominance in Comparing Income Distributions," Journal of Economic Theory, Elsevier, vol. 64(2), pages 520-530, December.
    8. repec:bla:econom:v:50:y:1983:i:197:p:3-17 is not listed on IDEAS
    9. Rolf Aaberge, 2009. "Ranking intersecting Lorenz curves," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 235-259, August.
    10. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    11. Davies, James & Hoy, Michael, 1995. "Making Inequality Comparisons When Lorenz Curves Intersect," American Economic Review, American Economic Association, vol. 85(4), pages 980-986, September.
    12. Claudio Zoli, 1999. "Intersecting generalized Lorenz curves and the Gini index," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(2), pages 183-196.
    13. Rolf Aaberge & Tarjei Havnes & Magne Mogstad, 2013. "A theory for ranking distribution functions," Discussion Papers 763, Statistics Norway, Research Department.
    14. repec:bla:econom:v:69:y:2002:i:276:p:549-62 is not listed on IDEAS
    15. Anthony F. Shorrocks & James E. Foster, 1987. "Transfer Sensitive Inequality Measures," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(3), pages 485-497.
    16. Weymark, John A., 1981. "Generalized gini inequality indices," Mathematical Social Sciences, Elsevier, vol. 1(4), pages 409-430, August.
    17. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-809, July.
    18. Anthony Atkinson & Thomas Piketty, 2010. "Top Incomes : A Global Perspective," PSE-Ecole d'économie de Paris (Postprint) halshs-00754875, HAL.
    19. Christine Chambaz & Eric Maurin, 1998. "Atkinson And Bourguignon'S Dominance Criteria: Extended And Applied To The Measurement Of Poverty In France," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 44(4), pages 497-513, December.
    20. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    21. Muliere, Pietro & Scarsini, Marco, 1989. "A note on stochastic dominance and inequality measures," Journal of Economic Theory, Elsevier, vol. 49(2), pages 314-323, December.
    22. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    23. Anthony Atkinson & Thomas Piketty, 2007. "Top incomes over the twentieth century: A contrast between continental european and english-speaking countries," Post-Print halshs-00754859, HAL.
    24. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 17(4), pages 639-653.
    25. Atkinson, A. B. & Piketty, Thomas (ed.), 2007. "Top Incomes Over the Twentieth Century: A Contrast Between Continental European and English-Speaking Countries," OUP Catalogue, Oxford University Press, number 9780199286881, Decembrie.
    26. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
    27. Yaari, Menahem E., 1988. "A controversial proposal concerning inequality measurement," Journal of Economic Theory, Elsevier, vol. 44(2), pages 381-397, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Thi Kim Thanh Bui & Guido Erreygers, 2020. "Multidimensional Inequality in Vietnam, 2002–2012," Economies, MDPI, vol. 8(2), pages 1-31, April.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Flaviana Palmisano & Ida Petrillo, 2022. "A general rank‐dependent approach for distributional comparisons," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 24(2), pages 380-409, April.
    2. Rolf Aaberge & Magne Mogstad, 2011. "Robust inequality comparisons," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(3), pages 353-371, September.
    3. Flaviana Palmisano & Ida Petrillo, 2021. "A general rank-dependent approach for distributional comparisons," Working Papers 567, ECINEQ, Society for the Study of Economic Inequality.
    4. Rolf Aaberge & Tarjei Havnes & Magne Mogstad, 2021. "Ranking intersecting distribution functions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(6), pages 639-662, September.
    5. Claudio Zoli, 2002. "Inverse stochastic dominance, inequality measurement and Gini indices," Journal of Economics, Springer, vol. 9(1), pages 119-161, December.
    6. Rolf Aaberge, 2009. "Ranking intersecting Lorenz curves," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(2), pages 235-259, August.
    7. Francesco Andreoli & Claudio Zoli, 2020. "From unidimensional to multidimensional inequality: a review," METRON, Springer;Sapienza Università di Roma, vol. 78(1), pages 5-42, April.
    8. Rolf Aaberge, 2003. "Mean-Spread-Preserving Transformations," Discussion Papers 360, Statistics Norway, Research Department.
    9. Rolf Aaberge & Tarjei Havnes & Magne Mogstad, 2013. "A theory for ranking distribution functions," Discussion Papers 763, Statistics Norway, Research Department.
    10. Luis José Imedio Olmedo & Elena Bárcena Martín, 2007. "Dos familias numerables de medidas de desigualdad," Investigaciones Economicas, Fundación SEPI, vol. 31(1), pages 191-217, January.
    11. Rolf Aaberge, 2007. "Gini’s nuclear family," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 305-322, December.
    12. Aaberge, Rolf & Peluso, Eugenio & Sigstad, Henrik, 2019. "The dual approach for measuring multidimensional deprivation: Theory and empirical evidence," Journal of Public Economics, Elsevier, vol. 177(C), pages 1-1.
    13. Michel Le Breton & Eugenio Peluso, 2009. "Third-degree stochastic dominance and inequality measurement," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 7(3), pages 249-268, September.
    14. Rolf Aaberge & Magne Mogstad, 2009. "On the Measurement of Long-Term Income Inequality and Income Mobility," ICER Working Papers 09-2009, ICER - International Centre for Economic Research.
    15. Chateauneuf, Alain & Gajdos, Thibault & Wilthien, Pierre-Henry, 2002. "The Principle of Strong Diminishing Transfer," Journal of Economic Theory, Elsevier, vol. 103(2), pages 311-333, April.
    16. W. Henry Chiu, 2021. "Intersecting Lorenz curves and aversion to inverse downside inequality," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(3), pages 487-508, April.
    17. Fabio Maccheroni & Pietro Muliere & Claudio Zoli, 2005. "Inverse stochastic orders and generalized Gini functionals," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 529-559.
    18. Rolf Aaberge & François Bourguignon & Andrea Brandolini & Francisco H. G. Ferreira & Janet C. Gornick & John Hills & Markus Jäntti & Stephen P. Jenkins & Eric Marlier & John Micklewright & Brian Nolan, 2017. "Tony Atkinson and his Legacy," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 63(3), pages 411-444, September.
    19. Satya Chakravarty, 2007. "A deprivation-based axiomatic characterization of the absolute Bonferroni index of inequality," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(3), pages 339-351, December.
    20. Rolf Aaberge, 2005. "Asymptotic Distribution Theory of Empirical Rank-dependent Measures of Inequality," Discussion Papers 402, Statistics Norway, Research Department.

    More about this item

    Keywords

    sequential stochastic dominance; social welfare; inequality;
    All these keywords.

    JEL classification:

    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • I31 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - General Welfare, Well-Being

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:bai:series:series_wp_03-2017. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Annalisa Vinella (email available below). General contact details of provider: https://edirc.repec.org/data/debarit.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.