This file is part of IDEAS, which uses RePEc data


[ Papers | Articles | Software | Books | Chapters | Authors | Institutions | JEL Classification | NEP reports | Search | New papers by email | Author registration | Rankings | Volunteers | FAQ | Blog | Help! ]

Mean-Spread-Preserving Transformations

Author info | Abstract | Publisher info | Download info | Related research | Statistics
Author Info
Rolf Aaberge () (Statistics Norway)

Additional information is available for the following registered author(s):

Abstract

The purpose of this paper is to define various mean-spread-preserving transformations, which can be considered as generalized versions of the mean-Gini-preserving transformation. The mean-Gini-preserving transformation, which was introduced independently by Zoli (1997, 2002) and Aaberge (2000b), is a combination of progressive and regressive transfers that leaves the Gini coefficient unchanged. It will be demonstrated that the various mean-spread-preserving transformations form a useful basis for judging the normative significance of two alternative sequences of nested Lorenz dominance criteria that can be used to rank Lorenz curves in situations where the Lorenz curves intersect. The two alternative sequences of Lorenz dominance criteria suggest 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. 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. Scaling up the introduced Lorenz dominance relations of this paper by the mean income ì and replacing the rank-dependent measures of inequality JP with the rank-dependent social welfare functions WP = m(1- JP), it can be demonstrated that the present results also apply to the generalized Lorenz curve and moreover provide convenient characterizations of the corresponding social welfare orderings.

Download Info
To download:

If you experience problems downloading a file, check if you have the proper application to view it first. Information about this may be contained in the File-Format links below. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.ssb.no/publikasjoner/DP/pdf/dp360.pdf
File Format: application/pdf
File Function:
Download Restriction: no

Publisher Info
Paper provided by Research Department of Statistics Norway in its series Discussion Papers with number 360.

Download reference. The following formats are available: HTML (with abstract), plain text (with abstract), BibTeX, RIS (EndNote, RefMan, ProCite), ReDIF
Length:
Date of creation:
Date of revision:
Handle: RePEc:ssb:dispap:360

Contact details of provider:
Postal: P.O.Box 8131 Dep, N-0033 Oslo, Norway
Phone: (+47) 21 09 00 00
Fax: (+47) 21 09 49 73
Email:
Web page: http://www.ssb.no
More information through EDIRC

For technical questions regarding this item, or to correct its listing, contact: (B Mellemstrand).

Related research
Keywords: The Lorenz curve; the Gini coefficient; rank-dependent measures of inequality; generalized Gini families of inequality measures; mean-spread-preserving transformations.;

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

This paper has been announced in the following NEP Reports:

References listed on IDEAS
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. Hadar, Josef & Russell, William R, 1969. "Rules for Ordering Uncertain Prospects," American Economic Review, American Economic Association, vol. 59(1), pages 25-34, March. [Downloadable!] (restricted)
  2. Rolf Aaberge, 2000. "Ranking Intersecting Lorenz Curves," Discussion Papers 271, Research Department of Statistics Norway. [Downloadable!]
    Other versions:
  3. Kolm, Serge-Christophe, 1976. "Unequal inequalities. II," Journal of Economic Theory, Elsevier, vol. 13(1), pages 82-111, August. [Downloadable!] (restricted)
  4. Claudio Zoli, 1999. "Intersecting generalized Lorenz curves and the Gini index," Social Choice and Welfare, Springer, vol. 16(2), pages 183-196. [Downloadable!] (restricted)
  5. Yitzhaki, Shlomo, 1983. "On an Extension of the Gini Inequality Index," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 24(3), pages 617-28, October. [Downloadable!] (restricted)
  6. Fields, Gary S & Fei, John C H, 1978. "On Inequality Comparisons," Econometrica, Econometric Society, vol. 46(2), pages 303-16, March. [Downloadable!] (restricted)
  7. Mehran, Farhad, 1976. "Linear Measures of Income Inequality," Econometrica, Econometric Society, vol. 44(4), pages 805-09, July. [Downloadable!] (restricted)
  8. Kolm, Serge-Christophe, 1976. "Unequal inequalities. I," Journal of Economic Theory, Elsevier, vol. 12(3), pages 416-442, June. [Downloadable!] (restricted)
  9. Rothschild, Michael & Stiglitz, Joseph E., 1973. "Some further results on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 188-204, April. [Downloadable!] (restricted)
    Other versions:
  10. Rolf Aaberge, 2000. "Characterizations of Lorenz curves and income distributions," Social Choice and Welfare, Springer, vol. 17(4), pages 639-653. [Downloadable!] (restricted)
  11. 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. [Downloadable!] (restricted)
  12. 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. [Downloadable!] (restricted)
  13. Fishburn, Peter C. & Willig, Robert D., 1984. "Transfer principles in income redistribution," Journal of Public Economics, Elsevier, vol. 25(3), pages 323-328, December. [Downloadable!] (restricted)
  14. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January. [Downloadable!] (restricted)
  15. Menezes, C & Geiss, C & Tressler, J, 1980. "Increasing Downside Risk," American Economic Review, American Economic Association, vol. 70(5), pages 921-32, December. [Downloadable!] (restricted)
  16. Aaberge, Rolf, 2001. "Axiomatic Characterization of the Gini Coefficient and Lorenz Curve Orderings," Journal of Economic Theory, Elsevier, vol. 101(1), pages 115-132, November. [Downloadable!] (restricted)
  17. 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. [Downloadable!] (restricted)
  18. Gajdos, Thibault, 2002. "Measuring Inequalities without Linearity in Envy: Choquet Integrals for Symmetric Capacities," Journal of Economic Theory, Elsevier, vol. 106(1), pages 190-200, September. [Downloadable!] (restricted)
  19. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-92, July. [Downloadable!] (restricted)
  20. Wang, Shaun S. & Young, Virginia R., 1998. "Ordering risks: Expected utility theory versus Yaari's dual theory of risk," Insurance: Mathematics and Economics, Elsevier, vol. 22(2), pages 145-161, June. [Downloadable!] (restricted)
  21. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September. [Downloadable!] (restricted)
  22. 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. [Downloadable!] (restricted)
    Other versions:
  23. Sen, Amartya K, 1976. "Poverty: An Ordinal Approach to Measurement," Econometrica, Econometric Society, vol. 44(2), pages 219-31, March. [Downloadable!] (restricted)
  24. Donaldson, David & Weymark, John A., 1983. "Ethically flexible gini indices for income distributions in the continuum," Journal of Economic Theory, Elsevier, vol. 29(2), pages 353-358, April. [Downloadable!] (restricted)
  25. Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February. [Downloadable!] (restricted)
  26. Yaari, Menahem E., 1988. "A controversial proposal concerning inequality measurement," Journal of Economic Theory, Elsevier, vol. 44(2), pages 381-397, April. [Downloadable!] (restricted)
Full references

Statistics
Access and download statistics

Did you know? You too can volunteer for RePEc, for example by encouraging others to register as authors.

This page was last updated on 2009-12-10.


This information is provided to you by IDEAS at the Department of Economics, College of Liberal Arts and Sciences, University of Connecticut using RePEc data on a server sponsored by the Society for Economic Dynamics.