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Ranking Intersecting Lorenz Curves

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Author Info
Rolf Aaberge () (Statistics Norway)

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Abstract

This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations two alternative sequences of nested dominance criteria between Lorenz curves are introduced. At the limit the systems of dominance criteria appear to depend solely on the income share of either the worst-off or the bestoff income recipient. This result suggests two alternative strategies for increasing the number of Lorenz curves that can be strictly ordered; one that places more emphasis on changes that occur in the lower part of the income distribution and the other that places more emphasis on changes that occur in the upper part of the income distribution. Both strategies turn out to depart from the Gini coefficient; one requires higher degree of downside and the other higher degree of upside inequality aversion than what is exhibited by the Gini coefficient. Furthermore, it is demonstrated that the sequences of dominance criteria characterize two separate systems of nested subfamilies of inequality measures and thus provide a method for identifying the least restrictive social preferences required to reach an unambiguous ranking of a given set of Lorenz curves. Moreover, it is demonstrated that the introduction of successively more general transfer principles than the Pigou-Dalton principle of transfers and more restrictive transformations than the mean-preserving spread (contractions) forms a helpful basis for judging the normative significance of higher degrees of Lorenz dominance.

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Paper provided by Tor Vergata University, CEIS in its series CEIS Research Paper with number 45.

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Length: 52
Date of creation: 19 Jan 2004
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Handle: RePEc:rtv:ceisrp:45

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Postal: CEIS - Centre for Economic and International Studies - Faculty of Economics - University of Rome "Tor Vergata" - Via Columbia, 2 00133 Roma
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Related research
Keywords: The Lorenz curve; partial orderings; the Gini coefficient; rank-dependent measures;

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Find related papers by JEL classification:
D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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References listed on IDEAS
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Rolf Aaberge, 2006. "Gini’s Nuclear Family," Discussion Papers 491, Research Department of Statistics Norway. [Downloadable!]
    Other versions:
  2. Jean-Yves Duclos & Paul Makdissi & Quentin Wodon, 2004. "Socially-Improving Tax Reforms," Cahiers de recherche 0401, CIRPEE. [Downloadable!]
    Other versions:
  3. Rolf Aaberge, 2005. "Asymptotic Distribution Theory of Empirical Rank-dependent Measures of Inequality," Discussion Papers 402, Research Department of Statistics Norway. [Downloadable!]
    Other versions:
  4. Mario Fortin & Andre Leclerc & Jean-Baptiste Nesmy, 2006. "L’impact des opérations transactionnelles sur la croissance de la productivité dans le secteur bancaire," Cahiers de recherche 06-01, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke. [Downloadable!]
  5. 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. [Downloadable!]
  6. Paul Makdissi & Jean-Yves Duclos, 2001. "Restricted Inequality and Relative Poverty," Cahiers de recherche 01-06, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke. [Downloadable!]
    Other versions:
  7. Rolf Aaberge, . "Mean-Spread-Preserving Transformations," Discussion Papers 360, Research Department of Statistics Norway. [Downloadable!]
  8. Juan Prieto Rodríguez & Juan Gabriel Rodríguez & Rafael Salas, 2004. "Is an inequality-neutral flat tax reform really neutral?," Economic Working Papers at Centro de Estudios Andaluces E2004/43, Centro de Estudios Andaluces. [Downloadable!]
    Other versions:
  9. Paul Makdissi & Stéphane Mussard, 2006. "Decomposition of s - Concentration Curves," Cahiers de recherche 0641, CIRPEE. [Downloadable!]
    Other versions:
  10. Paul Makdissi & Stéphane Mussard, 2006. "Analyzing the Impact of Indirect Tax Reforms on Rank Dependant Social Welfare Functions: A Positional Dominance Approach," Cahiers de recherche 06-02, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke. [Downloadable!]
    Other versions:
  11. Santiago Álvarez-García & Juan Prieto-Rodríguez & Rafael Salas, 2004. "The evolution of income inequality in the European Union during the period 1993-1996," Applied Economics, Taylor and Francis Journals, vol. 36(13), pages 1399-1408, July. [Downloadable!] (restricted)
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