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Ranking Inequality: Applications of Multivariate Subset Selection

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Author Info
William C. Horrace () (Center for Policy Research, Maxwell School, Syracuse University)
Joseph T. Marchand
Timothy M. Smeeding

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Abstract

Inequality measures are often presented in the form of a rank ordering to highlight their relative magnitudes. However, a rank ordering may produce misleading inference, because the inequality measures themselves are statistical estimators with different standard errors, and because a rank ordering necessarily implies multiple comparisons across all measures. Wityhin this setting, if differences between several inequality measures are *simultaneously* and statistically insignificant, the interpretation of the ranking is changed. This study uses a multivariate subset selection procedure to make simultaneous distinctions across inequality measures at a pre-specified confidence level. Three applications of this procedure are explored using country-level data from the Luxembourg Income Study. The findings show that simultaneous precision plays an important role in relative inequality comparisons and should not be ignored.

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File URL: http://www-cpr.maxwell.syr.edu/cprwps/pdf/wp70.pdf
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Publisher Info
Paper provided by Center for Policy Research, Maxwell School, Syracuse University in its series Center for Policy Research Working Papers with number 70.

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Length: 47 pages
Date of creation: Oct 2005
Date of revision:
Handle: RePEc:max:cprwps:70

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Related research
Keywords: income distribution; inference; poverty; subset selection;

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Find related papers by JEL classification:
D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Hypothesis Testing

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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. William C. Horrace, 2005. "On the ranking uncertainty of labor market wage gaps," Journal of Population Economics, Springer, vol. 18(1), pages 181-187, 09. [Downloadable!] (restricted)
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  2. Russell Davidson & Emmanuel Flachaire, 2004. "Asymptotic and bootstrap inference for inequality and poverty measures," Cahiers de la Maison des Sciences Economiques v04100, Université Panthéon-Sorbonne (Paris 1). [Downloadable!]
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  3. Biewen, Martin, 2002. "Bootstrap inference for inequality, mobility and poverty measurement," Journal of Econometrics, Elsevier, vol. 108(2), pages 317-342, June. [Downloadable!] (restricted)
  4. Cowell, F.A., 2000. "Measurement of inequality," Handbook of Income Distribution, in: A.B. Atkinson & F. Bourguignon (ed.), Handbook of Income Distribution, edition 1, volume 1, chapter 2, pages 87-166 Elsevier. [Downloadable!] (restricted)
  5. Francesco Farina & Eugenio Peluso & Ernesto Savaglio, 2005. "Ranking opportunity sets in the space of functionings," Journal of Economic Inequality, Springer, vol. 2(2), pages 105-116, January. [Downloadable!] (restricted)
  6. John A. Weymark, 2001. "Generalized Gini Indices of Equality of Opportunity," Working Papers 0114, Department of Economics, Vanderbilt University, revised Jun 2002. [Downloadable!]
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  7. Dean Jolliffe & Bohdan Krushelnytskyy, 2000. "Bootstrap standard errors for indices of inequality," Stata Technical Bulletin, StataCorp LP, vol. 9(51). [Downloadable!]
  8. Jean-Yves Duclos & Paul Makdissi, 2005. "Sequential Stochastic Dominance And The Robustness Of Poverty Orderings," Review of Income and Wealth, Blackwell Publishing, vol. 51(1), pages 63-87, 03. [Downloadable!] (restricted)
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  9. Vito Peragine, 2004. "Ranking Income Distributions According to Equality of Opportunity," Journal of Economic Inequality, Springer, vol. 2(1), pages 11-30, April. [Downloadable!] (restricted)
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  11. Cowell, Frank A., 1989. "Sampling variance and decomposable inequality measures," Journal of Econometrics, Elsevier, vol. 42(1), pages 27-41, September. [Downloadable!] (restricted)
  12. Karl Mosler, 2005. "Restricted Lorenz dominance of economic inequality in one and many dimensions," Journal of Economic Inequality, Springer, vol. 2(2), pages 89-103, January. [Downloadable!] (restricted)
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  13. Sarabia, J. -M. & Castillo, Enrique & Slottje, Daniel J., 1999. "An ordered family of Lorenz curves," Journal of Econometrics, Elsevier, vol. 91(1), pages 43-60, July. [Downloadable!] (restricted)
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  18. repec:kap:jecinq:v:2:y:2004:i:2:p:105-116 is not listed on IDEAS
  19. Mills, Jeffrey A & Zandvakili, Sourushe, 1997. "Statistical Inference via Bootstrapping for Measures of Inequality," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 12(2), pages 133-50, March-Apr. [Downloadable!]
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  21. 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.
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  22. Xu, Kuan, 2000. "Inference for Generalized Gini Indices Using the Iterated-Bootstrap Method," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(2), pages 223-27, April.
  23. Raquel Andres & Samuel Calonge, 2005. "Inference on Income Inequality and Tax Progressivity Indices: U-Statistics and Bootstrap Methods," Working Papers 09, ECINEQ, Society for the Study of Economic Inequality. [Downloadable!]
  24. Kuan Xu & L. Osberg, 1998. "A distribution-free test for deprivation dominance," Econometric Reviews, Taylor and Francis Journals, vol. 17(4), pages 415-429. [Downloadable!] (restricted)
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  25. Frank Cowell & Maria-Pia Victoria-Feser, 2003. "Distribution-Free Inference for Welfare Indices under Complete and Incomplete Information," Journal of Economic Inequality, Springer, vol. 1(3), pages 191-219, December. [Downloadable!] (restricted)
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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. Alfonso Flores-Lagunes & William C. Horrace & Kurt E. Schnier, 2007. "Identifying technically efficient fishing vessels: a non-empty, minimal subset approach," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(4), pages 729-745. [Downloadable!]
    Other versions:
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