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Relative Inequality, Absolute Inequality, and Welfare: Large Sample Tests for Partial Orders

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  • Bishop, John A
  • Chakraborti, S
  • Thistle, Paul D

Abstract

Two general welfare criteria, mean-relative Lorenz and mean-absolute Lorenz dominance, induce partial orders on income distributions. We propose asymptotically distribution-free inference procedures, based on the union-intersection principle, for these two welfare criteria. Unlike classical tests, our procedures allow one to distinguish among dominance, equality, and noncomparability. We show that union-intersection tests must be used to test for partial orders, and that the statistical ordering is acyclic. The tests are applied to compare the UK distribution of real family income to five other countries. Copyright 1994 by Blackwell Publishing Ltd and the Board of Trustees of the Bulletin of Economic Research

Suggested Citation

  • Bishop, John A & Chakraborti, S & Thistle, Paul D, 1994. "Relative Inequality, Absolute Inequality, and Welfare: Large Sample Tests for Partial Orders," Bulletin of Economic Research, Wiley Blackwell, vol. 46(1), pages 41-59, January.
    • Handle: RePEc:bla:buecrs:v:46:y:1994:i:1:p:41-59
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    References listed on IDEAS

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    1. Bishop, John A. & Chakraborti, S. & Thistle, Paul D., 1988. "Large sample tests for absolute Lorenz dominance," Economics Letters, Elsevier, vol. 26(3), pages 291-294.
    2. Timothy Smeeding & Gunther Schmaus & Brigitte Buhmann & Lee Rainwater, 1988. "Equivalence Scales, Well-Being, Inequality and Poverty: Sensitivity Estimates Across Ten Countries Using the LIS Database," LIS Working papers 17, LIS Cross-National Data Center in Luxembourg.
    3. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August.
    4. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June.
    5. Beach, Charles M & Richmond, James, 1985. "Joint Confidence Intervals for Income Shares and Lorenz Curves," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 439-450, June.
    6. Bishop, John A & Chakraborti, S & Thistle, Paul D, 1989. "Asymptotically Distribution-Free Statistical Inference for Generalized Lorenz Curves," The Review of Economics and Statistics, MIT Press, vol. 71(4), pages 725-727, November.
    7. Gastwirth, Joseph L, 1971. "A General Definition of the Lorenz Curve," Econometrica, Econometric Society, vol. 39(6), pages 1037-1039, November.
    8. Ebert, Udo, 1987. "Size and distribution of incomes as determinants of social welfare," Journal of Economic Theory, Elsevier, vol. 41(1), pages 23-33, February.
    9. Tsakloglou, Panos, 1992. "Inequality and Welfare in EEC Countries," Bulletin of Economic Research, Wiley Blackwell, vol. 44(1), pages 21-37, January.
    10. repec:bla:revinw:v:34:y:1988:i:2:p:115-42 is not listed on IDEAS
    11. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 723-735.
    12. Moyes, Patrick, 1987. "A new concept of Lorenz domination," Economics Letters, Elsevier, vol. 23(2), pages 203-207.
    13. Bishop, John A & Formby, John P & Thistle, Paul D, 1992. "Convergence of the South and Non-South Income Distributions, 1969-1979," American Economic Review, American Economic Association, vol. 82(1), pages 262-272, March.
    14. Fellman, J, 1976. "The Effect of Transformations on Lorenz Curves," Econometrica, Econometric Society, vol. 44(4), pages 823-824, July.
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    16. repec:bla:econom:v:50:y:1983:i:197:p:3-17 is not listed on IDEAS
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    Cited by:

    1. Duclos, Jean-Yves & Jalbert, Vincent & Araar, Abdelkrim, 2000. "Classical Horizontal Inequity and Reranking: an Integrated Approach," Cahiers de recherche 0002, Université Laval - Département d'économique.
    2. Juan Ramón García López, "undated". "El diseño complejo de la encuesta de estructura salarial 1995: Implicaciones sobre la estimación de medidas de desigualdad," Working Papers 2003-24, FEDEA.
    3. 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.
    4. Thesia I. Garner & Javier Ruiz‐Castillo & Mercedes Sastre, 2003. "The Influence of Demographics and Household‐Specific Price Indices on Consumption‐Based Inequality and Welfare: A Comparison of Spain and the United States," Southern Economic Journal, John Wiley & Sons, vol. 70(1), pages 22-48, July.
    5. Coral del Río, 2002. "Desigualdad intermedia paretiana," Investigaciones Economicas, Fundación SEPI, vol. 26(2), pages 299-321, May.
    6. Garner, Thesia I. & Sastre, Mercedes, 1999. "The influence of demographic and household specific price indices on expenditure based inequality and welfare: a comparison of Spain and the United States," UC3M Working papers. Economics 6165, Universidad Carlos III de Madrid. Departamento de Economía.
    7. Matilde Mas Ivars & Francisco José Goerlich Gisbert, 1999. "- Desigualdad Y Convergencia," Working Papers. Serie EC 1999-07, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    8. Juan Ramón García, "undated". "La desigualdad salarial en España. Efectos de un diseño muestral complejo," Working Papers 2003-26, FEDEA.

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