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.

csranks: An R Package for Estimation and Inference Involving Ranks

This article introduces the R package csranks for estimation and inference involving ranks. First, we review methods for the construction of confidence sets for ranks, namely marginal and simultaneous confidence sets as well as confidence sets for the identities of the tau-best. Second, we review methods for estimation and inference in regressions involving ranks. Third, we describe the implementation of these methods in csranks and illustrate their usefulness in two examples: one about the quantification of uncertainty in the PISA ranking of countries and one about the measurement of intergenerational mobility using rank-rank regressions

Decomposing the Dynamics of Regional Earnings Disparities in Israel

The literature on regional growth convergence and economic disparities has tended to confound four interwoven measurement phenomena. i) mean reversion (so-called beta convergence) where richer regions move towards the average from above and poorer regions from below. ii) diminishing inequality (so called sigma convergence) where the horizontal or spatial distribution of income becomes more equal. iii) mobility, where the rank of a region in the overall distribution of income changes either upwards or downwards. iv) leveling, where the richer regions become poorer (leveling-down) or the poorer regions become richer (leveling-up). We use a new statistical methodology, which treats these four phenomena on an integrated basis. The methodology is applied to Israeli regional earnings and house price data. We find that whereas earnings are strongly sigma divergent during the 1990s, this trend is offset when regional cost of living differences are taken into consideration. In this event, regional housing markets induce convergence in similar measure to the divergence induced by regional labor earnings.

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

The Economic Mobility in Money Transfer

In this paper, we investigate the economic mobility in some money transfer models which have been applied into the research on wealth distribution. We demonstrate the mobility by recording the time series of agents' ranks and observing their volatility. We also compare the mobility quantitatively by employing an index, "the per capita aggregate change in log-income", raised by economists. Like the shape of distribution, the character of mobility is also decided by the trading rule in these transfer models. It is worth noting that even though different models have the same type of distribution, their mobility characters may be quite different.Comment: 17 pages, 4 figures, 2nd versio

Vertical occupational mobility and its measurement

This paper describes a number of alternative approaches to devising a vertical occupational scale and compares the outcomes of different scales on calculations of occupational mobility. The paper describes the conceptual issues relevant to calculating occupational mobility and documents the measurement error embedded in the choice of measure, as applied to different data sets. The ranking schemes used include SOC (9) major codes ranked by mean occupational hourly earnings, Hope-Goldthorpe collapsed 36-point scores, a 15-category SOC ranking based on educational qualifications, and a 77 category ranking based on 2-digit SOC90 occupations, wage rates, educational qualifications, training and job tenure. These ranking schemes are applied to data from the 1958 NCDS cohort between the ages of 23 to 33 and 33 to 42, and to 1.25 year transitions in the Quarterly Labour Force Survey panel data. The calculations carried out show that variations in the extent of vertical occupational mobility, both upward and downward, had systematic elements. The extent of mobility was found to vary by the composition of the individuals´ data particularly in terms of lifecourse stages and gender, the number of categories in the ranking scheme, attrition in the data and flows out of employment over the mobility period, and changes in labour market conditions over time. However, the sizes of these effects were very variable

Dundee Discussion Papers in Economics 214:Longitudinal analysis of income-related health inequality

This paper considers the characterisation and measurement of income-related health inequality using longitudinal data. The paper elucidates the nature of the Jones and Lopez Nicholas (2004) index of “health-related income mobility” and explains the negative values of the index that have been reported in all the empirical applications to date. The paper further questions the value of their index to health policymakers and proposes an alternative index of “income-related health mobility” that measures whether the pattern of health changes is biased in favour of those with initially high or low incomes. We illustrate our work by investigating mobility in the General Health Questionnaire measure of psychological well-being over the first nine waves of the British Household Panel Survey from 1991 to 1999