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

In: Inequality, Redistribution and Mobility

Author

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  • 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
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    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

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