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The measurement of rank mobility

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  • D'Agostino, Marcello
  • Dardanoni, Valentino

Abstract

In this paper we investigate the problem of measuring social mobility when the social status of individuals is given by their rank. In order to sensibly represent the rank mobility of subgroups within a given society, we address the problem in terms of partial permutation matrices which include standard ("global") matrices as a special case. We first provide a characterization of a partial ordering on partial matrices which, in the standard case of global matrices, coincides with the well-known "concordance" ordering. We then provide a characterization of an index of rank mobility based on partial matrices and show that, in the standard case of comparing global matrices, it is equivalent to Spearman's [rho] index.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 144 (2009)
Issue (Month): 4 (July)
Pages: 1783-1803

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Handle: RePEc:eee:jetheo:v:144:y:2009:i:4:p:1783-1803

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Web page: http://www.elsevier.com/locate/inca/622869

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Keywords: Rank mobility Mobility measurement Concordance Partial matrices Spearman's index;

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References

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  1. Peter T. Gottschalk & Enrico Spolaore, 2000. "On the Evaluation of Economic Mobility," JCPR Working Papers 185, Northwestern University/University of Chicago Joint Center for Poverty Research.
  2. Maasoumi, Esfandiar & Zandvakili, Sourushe, 1986. "A class of generalized measures of mobility with applications," Economics Letters, Elsevier, vol. 22(1), pages 97-102.
  3. Dubra, Juan & Maccheroni, Fabio & Ok, Efe A., 2004. "Expected utility theory without the completeness axiom," Journal of Economic Theory, Elsevier, vol. 115(1), pages 118-133, March.
  4. Gary S. Fields, 2002. "Distribution and Development: A New Look at the Developing World," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262561530.
  5. Larry G. Epstein & Stephen M. Tanny, 1980. "Increasing Generalized Correlation: A Definition and Some Economic Consequences," Canadian Journal of Economics, Canadian Economics Association, vol. 13(1), pages 16-34, February.
  6. King, Mervyn A, 1983. "An Index of Inequality: With Applications to Horizontal Equity and Social Mobility," Econometrica, Econometric Society, vol. 51(1), pages 99-115, January.
  7. Javier Ruiz-Castillo, 2004. "The measurement of structural and exchange income mobility," Journal of Economic Inequality, Springer, vol. 2(3), pages 219-228, September.
  8. Fields, Gary S. & Ok, Efe A., 1996. "The Meaning and Measurement of Income Mobility," Journal of Economic Theory, Elsevier, vol. 71(2), pages 349-377, November.
  9. Dardanoni Valentino, 1993. "Measuring Social Mobility," Journal of Economic Theory, Elsevier, vol. 61(2), pages 372-394, December.
  10. Tapan Mitra & Efe A. Ok, 1998. "The measurement of income mobility: A partial ordering approach," Economic Theory, Springer, vol. 12(1), pages 77-102.
  11. Mervyn A. King, 1983. "An Index of Inequality: With Applications to Horizontal Equity and Social Mobility," NBER Working Papers 0468, National Bureau of Economic Research, Inc.
  12. Cowell, Frank A, 1985. "Measures of Distributional Change: An Axiomatic Approach," Review of Economic Studies, Wiley Blackwell, vol. 52(1), pages 135-51, January.
  13. Foster, James E & Shorrocks, Anthony F, 1991. "Subgroup Consistent Poverty Indices," Econometrica, Econometric Society, vol. 59(3), pages 687-709, May.
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Citations

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Cited by:
  1. repec:ese:iserwp:2013-23 is not listed on IDEAS
  2. Rolf Aaberge & Magne Mogstad, 2010. "On the measurement of long-term income inequality and income mobility," Discussion Papers 622, Research Department of Statistics Norway.
  3. Frank A. Cowell & Emmanuel Flachaire, 2011. "Measuring Mobility," Working Papers halshs-00586269, HAL.
  4. Markus Jantti & Stephen P. Jenkins, 2014. "Income Mobility," Working Papers 319, ECINEQ, Society for the Study of Economic Inequality.
  5. Jenderny, Katharina, 2013. "Mobility of top incomes in Germany," Discussion Papers 2013/7, Free University Berlin, School of Business & Economics.
  6. Decancq, Koen, 2012. "Elementary multivariate rearrangements and stochastic dominance on a Fréchet class," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1450-1459.
  7. repec:ese:iserwp:2006-36 is not listed on IDEAS
  8. Kai-yuen Tsui, 2009. "Measurement of income mobility: a re-examination," Social Choice and Welfare, Springer, vol. 33(4), pages 629-645, November.
  9. Chiara Gigliarano, 2013. "Measuring Labour Market Inter-Temporal Mobility In Italy: Theory And Evidence," RIEDS - Rivista Italiana di Economia, Demografia e Statistica - Italian Review of Economics, Demography and Statistics, SIEDS Societa' Italiana di Economia Demografia e Statistica, vol. 0(2), pages 139-153, April-Jun.
  10. Van Kerm, Philippe, 2006. "Comparisons of income mobility profiles," IRISS Working Paper Series 2006-03, IRISS at CEPS/INSTEAD.
  11. Rolf Aaberge & Magne Mogstad, 2014. "Income mobility as an equalizer of permanent income," Discussion Papers 769, Research Department of Statistics Norway.
  12. Yoram Amiel & Michele Bernasconi & Michele Bernasconi & Frank A Cowell & Valentino Dardanoni & Valentino Dardanoni, 2013. "Do We Value Mobility?," STICERD - Public Economics Programme Discussion Papers 17, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  13. T. Demuynck & D. Van De Gaer, 2010. "Rank Dependent Relative Mobility Measures," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 10/628, Ghent University, Faculty of Economics and Business Administration.

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