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.
For comments and suggestions, the authors thank an anonymous referee. They also thank Jacques Silber for his comments on an earlier draft. All errors and omissions remain the authors’ sole responsibility.
Chakravarty, S.R., Chattopadhyay, N., Lustig, N. and Aranda, R. (2020), "Measuring Directional Mobility: The Bartholomew and Prais-Bibby Indices Reconsidered", Rodríguez, J.G. and Bishop, J.A. (Ed.) Inequality, Redistribution and Mobility (Research on Economic Inequality, Vol. 28), Emerald Publishing Limited, pp. 75-96. https://doi.org/10.1108/S1049-258520200000028003Download as .RIS
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