IDEAS home Printed from https://ideas.repec.org/h/eme/reinzz/s1049-258520200000028003.html
   My bibliography  Save this book chapter

Measuring Directional Mobility: The Bartholomew and Prais-Bibby Indices Reconsidered

In: Inequality, Redistribution and Mobility

Author

Listed:
  • Satya R. Chakravarty
  • Nachiketa Chattopadhyay
  • Nora Lustig
  • Rodrigo Aranda

Abstract

This paper attempts to interpret the Bartholomew (1973) index of mobility in terms of a directional mobility index based on the one-step expected states of movement corresponding to a specific state of transition matrix. A partial ordering of directional mobility of a general state of transition matrices, referred to as “upward mobility favoring sequential averaging (UMFSA),” is proposed using the algebraic equivalent of the generalized Lorenz ordering of expected states. When the underlying mobility depends on the initial distribution of the states, using a Bayesian approach, the indices are reexamined for a general class of matrices. This enables us to interpret the Prais (1955) and Bibby (1975) mobility index in this framework.

Suggested Citation

  • Satya R. Chakravarty & Nachiketa Chattopadhyay & Nora Lustig & Rodrigo Aranda, 2020. "Measuring Directional Mobility: The Bartholomew and Prais-Bibby Indices Reconsidered," Research on Economic Inequality, in: Inequality, Redistribution and Mobility, volume 28, pages 75-96, Emerald Group Publishing Limited.
    • Handle: RePEc:eme:reinzz:s1049-258520200000028003
    DOI: 10.1108/S1049-258520200000028003
    as

    Download full text from publisher

    File URL: https://www.emerald.com/insight/content/doi/10.1108/S1049-258520200000028003/full/html?utm_source=repec&utm_medium=feed&utm_campaign=repec
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://www.emerald.com/insight/content/doi/10.1108/S1049-258520200000028003/full/epub?utm_source=repec&utm_medium=feed&utm_campaign=repec&title=10.1108/S1049-258520200000028003
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://www.emerald.com/insight/content/doi/10.1108/S1049-258520200000028003/full/pdf?utm_source=repec&utm_medium=feed&utm_campaign=repec
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1108/S1049-258520200000028003?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Peter Gottschalk & Enrico Spolaore, 2002. "On the Evaluation of Economic Mobility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(1), pages 191-208.
    2. Conlisk, John, 1989. "Ranking mobility matrices," Economics Letters, Elsevier, vol. 29(3), pages 231-235.
    3. John Bibby, 1975. "Methods of measuring mobility," Quality & Quantity: International Journal of Methodology, Springer, vol. 9(2), pages 107-136, June.
    4. 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.
    5. repec:bla:econom:v:68:y:2001:i:272:p:519-37 is not listed on IDEAS
    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. 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.
    8. Gary Fields, 2010. "Does income mobility equalize longer-term incomes? New measures of an old concept," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(4), pages 409-427, December.
    9. Buhong Zheng, 2011. "A new approach to measure socioeconomic inequality in health," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 9(4), pages 555-577, December.
    10. Shorrocks, A F, 1978. "The Measurement of Mobility," Econometrica, Econometric Society, vol. 46(5), pages 1013-1024, September.
    11. D'Agostino, Marcello & Dardanoni, Valentino, 2009. "The measurement of rank mobility," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1783-1803, July.
    12. 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.
    13. Chakravarty, S. R., 1984. "Normative indices for measuring social mobility," Economics Letters, Elsevier, vol. 15(1-2), pages 175-180.
    14. repec:bla:econom:v:50:y:1983:i:197:p:3-17 is not listed on IDEAS
    15. Markandya, Anil, 1982. "Intergenerational exchange mobility and economic welfare," European Economic Review, Elsevier, vol. 17(3), pages 307-324.
    16. Tapan Mitra & Efe A. Ok, 1998. "The measurement of income mobility: A partial ordering approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 12(1), pages 77-102.
    17. Maasoumi, Esfandiar & Zandvakili, Sourushe, 1986. "A class of generalized measures of mobility with applications," Economics Letters, Elsevier, vol. 22(1), pages 97-102.
    18. Dirk Van De Gaer & Erik Schokkaert & Michel Martinez, 2001. "Three Meanings of Intergenerational Mobility," Economica, London School of Economics and Political Science, vol. 68(272), pages 519-538, November.
    19. Dardanoni Valentino, 1993. "Measuring Social Mobility," Journal of Economic Theory, Elsevier, vol. 61(2), pages 372-394, December.
    20. Dasgupta, Partha & Sen, Amartya & Starrett, David, 1973. "Notes on the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 6(2), pages 180-187, April.
    21. 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.
    22. Unknown, 1986. "Letters," Choices: The Magazine of Food, Farm, and Resource Issues, Agricultural and Applied Economics Association, vol. 1(4), pages 1-9.
    23. Shorrocks, Anthony, 1978. "Income inequality and income mobility," Journal of Economic Theory, Elsevier, vol. 19(2), pages 376-393, December.
    24. Bossert, Walter, 1990. "An axiomatization of the single-series Ginis," Journal of Economic Theory, Elsevier, vol. 50(1), pages 82-92, February.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Joachim Jarreau, 2015. "The Impact of Naturalizations on Job Mobility and Wages: Evidence from France," AMSE Working Papers 1508, Aix-Marseille School of Economics, France.
    2. Markus Jäntti & Stephen P. Jenkins, 2013. "Income Mobility," SOEPpapers on Multidisciplinary Panel Data Research 607, DIW Berlin, The German Socio-Economic Panel (SOEP).
    3. Thomas Demuynck & Dirk Van de gaer, 2012. "Inequality Adjusted Income Growth," Economica, London School of Economics and Political Science, vol. 79(316), pages 747-765, October.
    4. 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.
    5. C. Schluter & D. Van De Gaer, 2003. "Mobility as distributional difference," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 03/182, Ghent University, Faculty of Economics and Business Administration.
    6. Sanghamitra Bandyopadhyay & Gaston Yalonetzky, 2016. "An individual-based approach to measurement of multiple-period mobility for nominal and ordinal variables," Working Papers 65, Queen Mary, University of London, School of Business and Management, Centre for Globalisation Research.
    7. 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.
    8. VAN KERM Philippe, 2006. "Comparisons of income mobility profiles," IRISS Working Paper Series 2006-03, IRISS at CEPS/INSTEAD.
    9. 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.
    10. Chattopadhyay, Nachiketa & Sengupta, Debasis, 2020. "Individual, Structural and Exchange Mobility: Decomposition and Axiom based measures," SocArXiv 8m46u, Center for Open Science.
    11. Peter Gottschalk & Enrico Spolaore, 2002. "On the Evaluation of Economic Mobility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 69(1), pages 191-208.
    12. D'Agostino, Marcello & Dardanoni, Valentino, 2009. "The measurement of rank mobility," Journal of Economic Theory, Elsevier, vol. 144(4), pages 1783-1803, July.
    13. Yélé Maweki Batana & Jean-Yves Duclos, 2010. "Testing for Mobility Dominance," Cahiers de recherche 1002, CIRPEE.
    14. Mr. Tom Krebs & Mr. Pravin Krishna & Mr. William Maloney, 2013. "Income Mobility and Welfare," IMF Working Papers 2013/024, International Monetary Fund.
    15. C. Schluter & D. Van De Gaer, 2008. "Structural Mobility, Exchange Mobility and Subgroup Consistent Mobility Measurement – US–German Mobility Measurements Revisited," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 08/543, Ghent University, Faculty of Economics and Business Administration.
    16. Roland Benabou & Efe A. Ok, 2000. "Mobility as Progressivity: Ranking Income Processes According to Equality of Opportunity," Working Papers 150, Princeton University, School of Public and International Affairs, Discussion Papers in Economics.
    17. Baochun Peng & Haidong Yuan, 2021. "Dynamic Fairness: Mobility, Inequality, and the Distribution of Prospects," Scandinavian Journal of Economics, Wiley Blackwell, vol. 123(4), pages 1314-1338, October.
    18. repec:cte:werepe:6070 is not listed on IDEAS
    19. Formby, John P. & Smith, W. James & Zheng, Buhong, 2004. "Mobility measurement, transition matrices and statistical inference," Journal of Econometrics, Elsevier, vol. 120(1), pages 181-205, May.
    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. Luis Ayala & Mercedes Sastre, 2004. "Europe vs. the United States: is there a trade-off between mobility and inequality?," Journal of Income Distribution, Ad libros publications inc., vol. 13(1-2), pages 4-4, March-Jun.

    More about this item

    Keywords

    Equality of opportunity; Social mobility; intergenerational mobility; directional mobility; transition probability; monotonicity; Bayesian analysis; C11; D31; D63; J62;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • D31 - Microeconomics - - Distribution - - - Personal Income and Wealth Distribution
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • J62 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Job, Occupational and Intergenerational Mobility; Promotion

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eme:reinzz:s1049-258520200000028003. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Emerald Support (email available below). General contact details of provider: .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.