The Measurement of Rank Mobility

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

Measuring mobility

Our new approach to mobility measurement involves separating out the valuation of positions in terms of individual status (using income, social rank, or other criteria) from the issue of movement between positions. The quantification of movement is addressed using a general concept of distance between positions and a parsimonious set of axioms that characterize the distance concept and yield a class of aggregative indices. This class of indices induces a superclass of mobility measures over the different status concepts consistent with the same underlying data. We investigate the statistical inference of mobility indices using two well‐known status concepts, related to income mobility and rank mobility. We also show how our superclass provides a more consistent and intuitive approach to mobility, in contrast to other measures in the literature, and illustrate its performance using recent data from China