IDEAS home Printed from https://ideas.repec.org/a/kap/jeczfn/v77y2002i1p91-117.html
   My bibliography  Save this article

Approximating unanimity orderings: An application to Lorenz dominance

Author

Listed:
  • Anthony Shorrocks
  • Daniel Slottje

Abstract

Stochastic dominance and Lorenz dominance are examples of orderings which require unanimous agreement among an infinite set of indices. This paper considers various subsets of inequality measures that respect Lorenz dominance, and assesses the extent to which a small number of indices can reproduce the Lorenz ordering. Using income data for 80 countries, our results suggest that Lorenz dominance can be predicted with 99% accuracy using just 3 or 4 inequality measures, as long as two of them focus on the extreme upper and lower tails of the distribution. In contrast, confining attention to the index families and parameter ranges normally considered may fail to detect the majority of occasions when Lorenz curves intersect. These results lead us to question the faith placed in procedures based on a finite set of inequality indices, and to suggest that similar lessons will apply to other types of unanimity orderings. Copyright Springer-Verlag 2002

Suggested Citation

  • Anthony Shorrocks & Daniel Slottje, 2002. "Approximating unanimity orderings: An application to Lorenz dominance," Journal of Economics, Springer, vol. 77(1), pages 91-117, December.
    • Handle: RePEc:kap:jeczfn:v:77:y:2002:i:1:p:91-117
    DOI: 10.1007/BF03052501
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/BF03052501
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/BF03052501?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Cowell, Frank A. & Kuga, Kiyoshi, 1981. "Additivity and the entropy concept: An axiomatic approach to inequality measurement," Journal of Economic Theory, Elsevier, vol. 25(1), pages 131-143, August.
    2. Shorrocks, A F, 1980. "The Class of Additively Decomposable Inequality Measures," Econometrica, Econometric Society, vol. 48(3), pages 613-625, April.
    3. Atkinson, A B, 1987. "On the Measurement of Poverty," Econometrica, Econometric Society, vol. 55(4), pages 749-764, July.
    4. Bishop, John A. & Formby, John P. & Thistle, Paul D., 1991. "Rank dominance and international comparisons of income distributions," European Economic Review, Elsevier, vol. 35(7), pages 1399-1409, October.
    5. 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.
    6. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-809, July.
    7. Shorrocks, Anthony F, 1984. "Inequality Decomposition by Population Subgroups," Econometrica, Econometric Society, vol. 52(6), pages 1369-1385, November.
    8. Donaldson, David & Weymark, John A., 1980. "A single-parameter generalization of the Gini indices of inequality," Journal of Economic Theory, Elsevier, vol. 22(1), pages 67-86, February.
    9. A. B. Atkinson & F. Bourguignon, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(2), pages 183-201.
    10. repec:bla:econom:v:50:y:1983:i:197:p:3-17 is not listed on IDEAS
    11. Sen, Amartya, 1973. "On Economic Inequality," OUP Catalogue, Oxford University Press, number 9780198281931.
    12. Foster, James E & Shorrocks, Anthony F, 1988. "Poverty Orderings," Econometrica, Econometric Society, vol. 56(1), pages 173-177, January.
    13. Bossert, Walter, 1990. "An axiomatization of the single-series Ginis," Journal of Economic Theory, Elsevier, vol. 50(1), pages 82-92, February.
    14. Jenkins,Stephen P. & Kapteyn,Arie & Praag,Bernard M. S. van (ed.), 1998. "The Distribution of Welfare and Household Production," Cambridge Books, Cambridge University Press, number 9780521623025, September.
    15. Coulter, Fiona A E & Cowell, Frank A & Jenkins, Stephen P, 1992. "Equivalence Scale Relativities and the Extent of Inequality and Poverty," Economic Journal, Royal Economic Society, vol. 102(414), pages 1067-1082, September.
    16. Jenkins, Stephen P & Lambert, Peter J, 1997. "Three 'I's of Poverty Curves, with an Analysis of UK Poverty Trends," Oxford Economic Papers, Oxford University Press, vol. 49(3), pages 317-327, July.
    17. Shorrocks, Anthony F, 1995. "Revisiting the Sen Poverty Index," Econometrica, Econometric Society, vol. 63(5), pages 1225-1230, September.
    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. Guanghua Wan & Ming Lu & Zhao Chen, 2004. "Globalization and Regional Income Inequality: Evidence from within China," WIDER Working Paper Series DP2004-10, World Institute for Development Economic Research (UNU-WIDER).
    2. Buhong Zheng, 2018. "Almost Lorenz dominance," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 51-63, June.
    3. Buhong Zheng, 2021. "Stochastic dominance and decomposable measures of inequality and poverty," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(2), pages 228-247, April.
    4. Zheng, Buhong, 2017. "A class of generalized Sen poverty indices," Economics Letters, Elsevier, vol. 159(C), pages 100-103.
    5. Guanghua Wan & Ming Lu & Zhao Chen, 2007. "Globalization And Regional Income Inequality: Empirical Evidence From Within China," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 53(1), pages 35-59, March.
    6. Greselin Francesca, 2014. "More Equal and Poorer, or Richer but More Unequal?," Stochastics and Quality Control, De Gruyter, vol. 29(2), pages 99-117, December.
    7. 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.
    8. John Creedy & S. Subramanian, 2023. "Exploring A New Class of Inequality Measures and Associated Value Judgements: Gini and Fibonacci-Type Sequences," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 110-131, May.
    9. Guanghua Wan, 2002. "Regression-based Inequality Decomposition: Pitfalls and a Solution Procedure," WIDER Working Paper Series DP2002-101, World Institute for Development Economic Research (UNU-WIDER).

    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. James E. Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster-Greer-Thorbecke (FGT) Poverty Measures: Twenty-Five Years Later," Working Papers 2010-14, The George Washington University, Institute for International Economic Policy.
    2. Bibi, Sami & Duclos, Jean-Yves, 2007. "Equity and policy effectiveness with imperfect targeting," Journal of Development Economics, Elsevier, vol. 83(1), pages 109-140, May.
    3. James Foster & Joel Greer & Erik Thorbecke, 2010. "The Foster–Greer–Thorbecke (FGT) poverty measures: 25 years later," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(4), pages 491-524, December.
    4. P. Jenkins, Stephen & Micklewright, John, 2007. "New directions in the analysis of inequality and poverty," ISER Working Paper Series 2007-11, Institute for Social and Economic Research.
    5. Jean–Yves Duclos & Phillipe Grégoire, 2002. "Absolute and Relative Deprivation and the Measurement of Poverty," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 48(4), pages 471-492, December.
    6. P. Jenkins, Stephen & Micklewright, John, 2007. "New directions in the analysis of inequality and poverty," ISER Working Paper Series 2007-11, Institute for Social and Economic Research.
    7. Naouel Chtioui & Mohamed Ayadi, 2018. "Rank-based poverty measures and poverty ordering with an application to Tunisia," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 17(2), pages 117-139, July.
    8. Buhong Zheng, 2021. "Stochastic dominance and decomposable measures of inequality and poverty," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 23(2), pages 228-247, April.
    9. Satya R. Chakravarty & Pietro Muliere, 2003. "Welfare indicators: A review and new perspectives. 1. Measurement of inequality," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 457-497.
    10. Sorger, Gerhard & Stark, Oded, 2013. "Income redistribution going awry: The reversal power of the concern for relative deprivation," Journal of Economic Behavior & Organization, Elsevier, vol. 86(C), pages 1-9.
    11. Coral del Río & Javier Ruiz-Castillo, 2001. "TIPs for poverty analysis. The case of Spain, 1980-81 to 1990-91," Investigaciones Economicas, Fundación SEPI, vol. 25(1), pages 63-91, January.
    12. Zheng, Buhong, 2000. "Minimum Distribution-Sensitivity, Poverty Aversion, and Poverty Orderings," Journal of Economic Theory, Elsevier, vol. 95(1), pages 116-137, November.
    13. 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.
    14. Francisco J. Goerlich-Gisbert & Casilda Lasso de la Vega & Ana Marta Urrutia, 2009. "The ‘extended’ Atkinson family and changes in the expenditure distribution. Spain 1973/74-2003," Journal of Income Distribution, Ad libros publications inc., vol. 18(1), pages 20-41, March.
    15. Jean‐Yves Duclos & Paul Makdissi, 2004. "Restricted and Unrestricted Dominance for Welfare, Inequality, and Poverty Orderings," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 6(1), pages 145-164, February.
    16. Ottó Hajdu, 2021. "A New Generalized Variance Approach for Measuring Multidimensional Inequality and Poverty," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 158(3), pages 839-861, December.
    17. Gian Maria Tomat, 2014. "Revisiting poverty and welfare dominance," ECONOMIA PUBBLICA, FrancoAngeli Editore, vol. 2014(2), pages 125-149.
    18. 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.
    19. Bosmans, Kristof, 2014. "Distribution-sensitivity of rank-dependent poverty measures," Journal of Mathematical Economics, Elsevier, vol. 51(C), pages 69-76.
    20. I. Josa & A. Aguado, 2020. "Measuring Unidimensional Inequality: Practical Framework for the Choice of an Appropriate Measure," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 149(2), pages 541-570, June.

    More about this item

    Keywords

    Inequality; Lorenz Dominance; D63;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

    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:kap:jeczfn:v:77:y:2002:i:1:p:91-117. 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: 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. RePEc uses bibliographic data supplied by the respective publishers.