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A Large Deviation Approach to the Measurement of Mobility

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  • Robert Aebi
  • Klaus Neusser
  • Peter Steiner

Abstract

We propose an approach to measure the mobility immanent in Markov processes. For this purpose, we distinguish between mobility in equilibrium and mobility associated with convergence towards equilibrium. The former aspect is measured as the expectation of a functional, defined on the Cartesian square product of the state space, with respect to the invariant distribution. Based on large deviations techniques, we show how the two aspects of mobility are related and how the second one can be characterized by a certain relative entropy. Finally, we show that some prominent mobility indices can be considered as special cases.

Suggested Citation

  • Robert Aebi & Klaus Neusser & Peter Steiner, 2002. "A Large Deviation Approach to the Measurement of Mobility," Diskussionsschriften dp0220, Universitaet Bern, Departement Volkswirtschaft.
    • Handle: RePEc:ube:dpvwib:dp0220
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    References listed on IDEAS

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    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. Fields, Gary S. & Leary, Jesse B. & Ok, Efe A., 2002. "Stochastic dominance in mobility analysis," Economics Letters, Elsevier, vol. 75(3), pages 333-339, May.
    3. Martin Browning & Mette Ejrnæs & Javier Alvarez, 2010. "Modelling Income Processes with Lots of Heterogeneity," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 77(4), pages 1353-1381.
    4. Maasoumi, Esfandiar & Zandvakili, Sourushe, 1990. "Generalized entropy measures of mobility for different sexes and income levels," Journal of Econometrics, Elsevier, vol. 43(1-2), pages 121-133.
    5. 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.
    6. Dardanoni Valentino, 1993. "Measuring Social Mobility," Journal of Economic Theory, Elsevier, vol. 61(2), pages 372-394, December.
    7. Chakravarty, Satya R., 1995. "A note on the measurement of mobility," Economics Letters, Elsevier, vol. 48(1), pages 33-36, April.
    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. Robert Aebi & Klaus Neusser & Peter Steiner, 2006. "A Large Deviation Approach to the Measurement of Mobility," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 142(II), pages 195-222, June.
    10. 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.
    11. Geweke, John & Marshall, Robert C & Zarkin, Gary A, 1986. "Mobility Indices in Continuous Time Markov Chains," Econometrica, Econometric Society, vol. 54(6), pages 1407-1423, November.
    12. Shorrocks, A F, 1978. "The Measurement of Mobility," Econometrica, Econometric Society, vol. 46(5), pages 1013-1024, September.
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    Cited by:

    1. Robert Aebi & Klaus Neusser & Peter Steiner, 2006. "A Large Deviation Approach to the Measurement of Mobility," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 142(II), pages 195-222, June.
    2. Robert Aebi & Klaus Neusser & Peter Steiner, 2004. "Equilibrium Mobility," Diskussionsschriften dp0408, Universitaet Bern, Departement Volkswirtschaft.
    3. Christopher Spencer, 2005. "Consensus Formation in Monetary Policy Committees," School of Economics Discussion Papers 1505, School of Economics, University of Surrey.
    4. Robert Aebi & Klaus Neusser & Peter Steiner, 2008. "Improving Models of Income Dynamics using Cross-Section-Information," Swiss Journal of Economics and Statistics (SJES), Swiss Society of Economics and Statistics (SSES), vol. 144(II), pages 117-151, June.

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    More about this item

    Keywords

    mobility index; large deviations; relative entropy;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • J62 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Job, Occupational and Intergenerational Mobility; Promotion

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