IDEAS home Printed from https://ideas.repec.org/a/spr/metron/v75y2017i2d10.1007_s40300-017-0117-z.html
   My bibliography  Save this article

On the asymptotic distribution of (generalized) Lorenz transvariation measures

Author

Listed:
  • Teng Wah Leo

    (St. Francis Xavier University)

Abstract

A common problem associated with evaluating dominance relationships between distribution functions and their moments is the lack of resolution regarding the direction of dominance as a result of the functions crossing, prevalent in empirical applications. This paper proposes a method of examining the difference between (Generalized) Lorenz curves over the entire support of the variables, an idea first proposed by Anderson and Leo (On providing a complete ordering of non-combinable alternative prospects. University of Toronto Discussion Paper, 2017) and formalized by Anderson et al. (Somewhere between utopia and dystopia: choosing from multiple incomparable prospect. University of Toronto Discussion Paper, 2017) for the case of stochastic dominance. The method provides a way of ordering all the (Generalized) Lorenz curves under consideration. The paper also provides the exact limit distribution of these associated measures, which in consequence of the results due to Politis and Romano (Ann Stat 22(4):2031–2050, 1994), permits inference via subsampling, in lieu of the crossing of empirical (Generalized) Lorenz curves. We show that due to the relationship between the Lorenz curve and the Gini coefficient, the same can be said of the latter. An example is provided to demonstrate its application.

Suggested Citation

  • Teng Wah Leo, 2017. "On the asymptotic distribution of (generalized) Lorenz transvariation measures," METRON, Springer;Sapienza Università di Roma, vol. 75(2), pages 195-213, August.
  • Handle: RePEc:spr:metron:v:75:y:2017:i:2:d:10.1007_s40300-017-0117-z
    DOI: 10.1007/s40300-017-0117-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s40300-017-0117-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s40300-017-0117-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Suman Seth & Gaston Yalonetzky, 2016. "Has the world converged? A robust analysis of non-monetary bounded indicators," Working Papers 398, ECINEQ, Society for the Study of Economic Inequality.
    2. Oliver Linton & Thierry Post & Yoon‐Jae Whang, 2014. "Testing for the stochastic dominance efficiency of a given portfolio," Econometrics Journal, Royal Economic Society, vol. 17(2), pages 59-74, June.
    3. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
    4. Moshe Leshno & Haim Levy, 2002. "Preferred by "All" and Preferred by "Most" Decision Makers: Almost Stochastic Dominance," Management Science, INFORMS, vol. 48(8), pages 1074-1085, August.
    5. Atkinson, Anthony B., 1970. "On the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 2(3), pages 244-263, September.
    6. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," Review of Economic Studies, Oxford University Press, vol. 50(4), pages 723-735.
    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. Gordon Anderson & Jasmin Thomas, 2019. "Measuring Multi-group Polarization, Segmentation and Ambiguity: Increasingly Unequal Yet Similar Constituent Canadian Income Distributions," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 145(3), pages 1001-1032, October.

    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. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
    2. David Lander & David Gunawan & William Griffiths & Duangkamon Chotikapanich, 2020. "Bayesian assessment of Lorenz and stochastic dominance," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(2), pages 767-799, May.
    3. Enrico Bolzani & Ramses H. Abul Naga, 2002. "La Distribution des Salaires en Suisse: Quelques Observations sur la Récession des Années 90," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 138(II), pages 115-136, June.
    4. Gravel, Nicolas & Moyes, Patrick, 2012. "Ethically robust comparisons of bidimensional distributions with an ordinal attribute," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1384-1426.
    5. Sangeeta Arora & Kanchan Jain, 2006. "Testing for Generalized Lorenz Dominance," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(1), pages 75-88, May.
    6. Sangeeta Arora & Kanchan Jain, 2006. "Testing for Generalized Lorenz Dominance," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(1), pages 75-88, May.
    7. ANDREOLI Francesco & HAVNES Tarjei & LEFRANC Arnaud, 2014. "Equalization of opportunity: Definitions, implementable conditions and application to early-childhood policy evaluation," LISER Working Paper Series 2014-12, LISER.
    8. Arnaud Lefranc & Nicolas Pistolesi & Alain Trannoy, 2008. "Inequality Of Opportunities Vs. Inequality Of Outcomes: Are Western Societies All Alike?," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 54(4), pages 513-546, December.
    9. Francesco Andreoli & Arnaud Lefranc, 2013. "Equalization of opportunity: Definitions and implementable conditions," Working Papers 310, ECINEQ, Society for the Study of Economic Inequality.
    10. Gordon Anderson & Jasmin Thomas, 2019. "Measuring Multi-group Polarization, Segmentation and Ambiguity: Increasingly Unequal Yet Similar Constituent Canadian Income Distributions," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 145(3), pages 1001-1032, October.
    11. Francesco Andreoli & Tarjei Havnes & Arnaud Lefranc, 2019. "Robust Inequality of Opportunity Comparisons: Theory and Application to Early Childhood Policy Evaluation," The Review of Economics and Statistics, MIT Press, vol. 101(2), pages 355-369, May.
    12. Francesco Andreoli, 2018. "Robust Inference for Inverse Stochastic Dominance," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 146-159, January.
    13. Daniel Sotelsek-Salem & Ismael Ahamdanech-Zarco & John Bishop, 2012. "Dominance testing for ‘pro-poor’ growth with an application to European growth," Empirical Economics, Springer, vol. 43(2), pages 723-739, October.
    14. Chiou, Jong-Rong, 1996. "A dominance evaluation of Taiwan's official income distribution statistics, 1976-1992," China Economic Review, Elsevier, vol. 7(1), pages 57-75.
    15. Jo Thori Lind & Karl Moene, 2011. "Miserly Developments," Journal of Development Studies, Taylor & Francis Journals, vol. 47(9), pages 1332-1352, June.
    16. Allanson, Paul & Hubbard, Lionel, 1999. "On the Comparative Evaluation of Agricultural Income Distributions in the European Union," European Review of Agricultural Economics, Foundation for the European Review of Agricultural Economics, vol. 26(1), pages 1-17, March.
    17. Chotikapanich, Duangkamon & Griffiths, William E, 2002. "Estimating Lorenz Curves Using a Dirichlet Distribution," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 290-295, April.
    18. Francois, Joseph & Rojas-Romagosa, Hugo, 2005. "The Construction and Interpretation of Combined Cross-Section and Time-Series Inequality Datasets," CEPR Discussion Papers 5214, C.E.P.R. Discussion Papers.
    19. Karsu, Özlem & Morton, Alec, 2015. "Inequity averse optimization in operational research," European Journal of Operational Research, Elsevier, vol. 245(2), pages 343-359.
    20. Peragine, Vito & Serlenga, Laura, 2007. "Higher Education and Equality of Opportunity in Italy," IZA Discussion Papers 3163, Institute of Labor Economics (IZA).

    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:spr:metron:v:75:y:2017:i:2:d:10.1007_s40300-017-0117-z. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: http://www.springer.com .

    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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.