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The Measurement of Rank Mobility

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  • Valentino Dardanoni

    () (Università di Palermo)

  • Marcello D’Agostino

    (Università di Ferrara)

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 two global matrices, it is equivalent to Spearman’s index.

Suggested Citation

  • Valentino Dardanoni & Marcello D’Agostino, 2007. "The Measurement of Rank Mobility," Working Papers 80, ECINEQ, Society for the Study of Economic Inequality.
    • Handle: RePEc:inq:inqwps:ecineq2007-80
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    References listed on IDEAS

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    Cited by:

    1. Markus Jäntti & Stephen P. Jenkins, 2013. "Income Mobility," SOEPpapers on Multidisciplinary Panel Data Research 607, DIW Berlin, The German Socio-Economic Panel (SOEP).
    2. Katharina Jenderny, 2016. "Mobility of Top Incomes in Germany," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 62(2), pages 245-265, June.
    3. Sergio Rey, 2014. "Fast algorithms for a space-time concordance measure," Computational Statistics, Springer, vol. 29(3), pages 799-811, June.
    4. Walter Bossert & Burak Can & Conchita D’Ambrosio, 2016. "Measuring rank mobility with variable population size," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 917-931, April.
    5. Van Kerm, Philippe, 2006. "Comparisons of income mobility profiles," IRISS Working Paper Series 2006-03, IRISS at CEPS/INSTEAD.
    6. 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.
    7. Frank A. Cowell & Emmanuel Flachaire, 2011. "Measuring mobility," Working Papers 199, ECINEQ, Society for the Study of Economic Inequality.
    8. Decancq, Koen, 2012. "Elementary multivariate rearrangements and stochastic dominance on a Fréchet class," Journal of Economic Theory, Elsevier, vol. 147(4), pages 1450-1459.
    9. Kai-yuen Tsui, 2009. "Measurement of income mobility: a re-examination," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(4), pages 629-645, November.
    10. 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. 67(2), pages 139-153, April-Jun.
    11. repec:eme:reinzz:s1049-258520150000023004 is not listed on IDEAS
    12. Yoram Amiel & Michele Bernasconi & Frank Cowell & Valentino Dardanoni, 2015. "Do we value mobility?," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 44(2), pages 231-255, February.
    13. Satya R. Chakravarty & Nachiketa Chattopadhyay & Nora Lustig & Rodrigo Aranda Balcazar, 2017. "Measuring Directional Mobility: The Bartholomew and Prais-Bibby Indices Reconsidered," Working Papers 1720, Tulane University, Department of Economics.
    14. Rolf Aaberge & Magne Mogstad, 2009. "On the Measurement of Long-Term Income Inequality and Income Mobility," ICER Working Papers 09-2009, ICER - International Centre for Economic Research.
    15. Aristei, David & Perugini, Cristiano, 2015. "The drivers of income mobility in Europe," Economic Systems, Elsevier, vol. 39(2), pages 197-224.
    16. Walter Bossert & Burak Can & Conchita D'Ambrosio, 2016. "A head-count measure of rank mobility and its directional decomposition," Working Papers 424, ECINEQ, Society for the Study of Economic Inequality.
    17. Louis Chauvel & Anne Hartung & Flaviana Palmisano, 2017. "Dynamics of Income Rank Volatility: Evidence from Germany and the US," SOEPpapers on Multidisciplinary Panel Data Research 926, DIW Berlin, The German Socio-Economic Panel (SOEP).
    18. Chiara Gigliarano & Francesco Maria Chelli, 2016. "Measuring inter-temporal intragenerational mobility: an application to the Italian labour market," Quality & Quantity: International Journal of Methodology, Springer, vol. 50(1), pages 89-102, January.
    19. Joachim Jarreau, 2015. "The Impact of Naturalizations on Job Mobility and Wages: Evidence from France," Working Papers halshs-01117449, HAL.
    20. Chiara Gigliarano & Francesco Chelli, 2016. "Measuring inter-temporal intragenerational mobility: an application to the Italian labour market," Quality & Quantity: International Journal of Methodology, Springer, vol. 50(1), pages 89-102, January.
    21. Olga Cantó & David O. Ruiz, 2015. "The Contribution of Income Mobility to Economic Insecurity in the US and Spain during the Great Recession," Research on Economic Inequality,in: Measurement of Poverty, Deprivation, and Economic Mobility, volume 23, pages 109-152 Emerald Publishing Ltd.
    22. Rolf Aaberge & Magne Mogstad, 2014. "Income mobility as an equalizer of permanent income," Discussion Papers 769, Statistics Norway, Research Department.
    23. Jean HINDRIKS & Mattéo GODIN, 2016. "Equité et efficacité des écoles : une comparaison internationale basée sur la mobilité sociale à l'école," CORE Discussion Papers 2016049, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    More about this item

    Keywords

    Mobility measurement; Concordance; Partial matrices; Sperman's index.;

    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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