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Measuring Directional Mobility: The Bartholomew and Prais-Bibby Indices Reconsidered
... There exists also a definition of a standardized Bartholomew index B standardized (see, Chakravarty et al., 2017) where ...
... For more detailed discussions of the concept of mobility, seeFields and Ok (1999) andFields (2008). For a more recent but short survey of the topic, see the introduction ofChakravarty et al. (2017).© 2022 International Association for Research in Income and Wealth ...
This article proposes a new approach to the measurement of intergenerational mobility in education. Borrowing the concept of inequality‐sensitive and additive achievement measure axiomatically developed by Apouey et al., we derive new indices of upward, downward, and total mobility, using a “movement approach.” It turns out that the Prais‐Bibby and Bartholomew mobility indices are particular cases of the mobility indices we introduce. We then present an empirical illustration based on the 2016 European Social Survey. Particular attention is given to within country differences between fathers to children and mothers to children educational mobility. When comparing two countries, we also make a distinction between gross and net mobility, the latter referring to the case where country differences in the educational structure of parents and children are neutralized.
Despite attention in the literature of intergenerational mobility (IGM) and the welfare state, it remains unclear about how “small” welfare states, South Korea and the United States in particular, play a role in promoting levels of IGM. This article compares levels of IGM using intergenerational elasticity (IGE) of income as well as alternative mobility measures during two study periods (1980‒1995 and 1996‒2015) between Korea and the US. Data come from the Korean Labor and Income Panel Study in Korea and the Panel Study of Income Dynamics in the US. The article found no period effects on IGE in both countries; however, the Korean IGE decreased and the US’s IGE increased. These results confirm that Korea is more mobile than the US. Implications for the observed between‐country differences in IGE levels in relation to sociocultural and institutional contexts of the welfare state are discussed.
We investigate the racial differences in positional and directional earning mobility for blacks and whites using seven 6-year longitudinal samples drawn from the Panel Study of Income Dynamics, extending from 1973 through 2015. Positional mobility comparisons are mixed for the proportion of each sample moving to a higher earnings category but reveal a higher percentage of blacks than whites trapped in the bottom 25% of the distribution of earnings. Directional mobility comparisons show that the mean increase from the initial to final earnings distribution was significantly greater for whites than for blacks throughout 1973–85 and 1997–2009. A breakdown of these findings by gender reveals that they arise primarily from the labor market experience of black men, who face more severe racial disparities in positional and directional earning mobility than black women. Overall, these findings on intragenerational earning mobility are in line with recent research on intergenerational mobility in the US.
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 global matrices, it is equivalent to Spearman's [rho] index.
Income mobility may be seen as arising from two sources: (i) the transfer of income among individuals with total income held constant, and (ii) a change in the total amount of income available. In this paper, we propose several sensible properties defining the concept of income mobility and show that an easily applicable measure of mobility is uniquely implied by these properties. We also show that the resulting measure is additively decomposable into the two sources listed above, namely, mobility due to the transfer of income within a given structure and mobility due to economic growth or contraction. Finally, these results are compared and contrasted with other mobility concepts and measures in the literature.Journal of Economic Literature: Classification Numbers: D31, D63.
A class of anonymous measures of mobility is defined that considers the relationship between the long-run and short-run distributions of income. Several measures of long-run income and inequalityare explored. Michigan panel data are analyzed.
Given a set of longitudinal data pertaining to two populations, a question of interest is the following: Which population has experienced a greater extent of income mobility? The aim of the present paper is to develop a systematic way of answering this question. We first put forth four axioms for income movement-mobility indices, and show that a familiar class of measures is characterized by these axioms. An unambiguous (partial) ordering is then defined as the intersection of the (complete) orderings induced by the mobility measures which belong to the characterized class; a transformation of income distributions is "more mobile" than another if, and only if, the former is ranked higher than the latter for all mobility measures which satisfy our axioms. Unfortunately, our mobility ordering depends on a parameter, and therefore, it is not readily apparent how one can apply it to panel data directly. In the second part of the paper, therefore, we derive several sets of parameter-free necessary and sufficient conditions which allow one to use the proposed mobility ordering in making unambiguous income mobility comparisons in practice.
We propose and characterize a new measure of rank mobility. The index is given by the head count of those whose positions change in the move from one period to the next divided by population size. The interpretation of this head-count ratio is straightforward and intuitive. In addition, we illustrate how the measure can be decomposed into an index of upwards mobility and an index of downwards mobility. The axioms used in our characterization results are appealing and easy to justify. We conclude with an application to the Human Development Index, a summary measure of average achievement in key dimensions of human development: a long and healthy life, being knowledgeable and having a decent standard of living.
The concepts of exchange and structural mobility are introduced and their relationship with the notion of Equality of Opportunity discussed. It is then shown that exchange mobility can have an impact on social welfare when the utility of any one generation is dependent on the consumption levels of overlapping generations. Whether such consumption interrelationships imply a preference for mobility or the reverse depends on whether the marginal utility of current consumption is raised or lowered by an increase in the consumption level of the associated generation. The rest of this paper examines these two cases in the context of a simple two-class family model. The analysis is concerned with the description of the optimal intergenerational behaviour within this framework. In order to be able to say anything substantial, however, it is necessary to impose some restrictions on the structure of the utility function. One restriction which has some appeal and which yields plausible patterns of optimal policy is that intergenerational links through the utility function be not too strong, in a sense that is made specific in the paper. Imposing this condition, one can show how intra-generational equity is affected both by intergenerational considerations and by the inherited past. Where intragenerational transfers involve efficiency losses, a simple tax model is examined. The circumstances under which, starting with no taxes, the tax rates converge are worked out in both the cases where the utility function has a pro as well as an anti-mobility bias.
Finally a specific utility function is taken, in which the fathers utility depends not only on his own consumption but also on the average consumption of his son and himself. In this case the utility function has a pro mobility bias and one can evaluate the response of the long-run tax rate to parameters that measure mobility and equality. Using a similation model, one can also assess the speed of convergence and the sensitivity of the tax rates to the parameters.
The welfare analysis of tax reforms most often consists of comparing the post‐reform distribution of individual welfare with the pre‐reform distribution or possibly that obtained from another reform as if they were completely independent. Such an “anonymous” approach does not take into account “changes” in individual situations, generally the main source of contention in any tax reform debate. This paper proposes a welfare criterion that allows comparison of reforms while taking into account individual status quo - i.e. pre‐reform - situations. This is done by extending standard utilitarian social welfare criteria to the case where individual utilities depend on initial income and income change.
Ethical indices of income mobility measure the change in welfare resulting from mobility. The concept of mobility we explore consists of a welfare comparison between the actual time path of the income distribution with a hypothetical time path obtained by supposing that starting from the actual first-period distribution, the remaining income receipts exhibit complete immobility.
This paper introduces a new approach to rank and measure socioeconomic inequality in health. A novel feature of the approach
is the use of an income-health matrix that relates socioeconomic class with health status; each row of the matrix corresponds
to a socioeconomic class and contains the respective probability distribution of health. By invoking a monotone assumption
on the income-health matrix, which is a direct translation of the well-known hypothesis of social gradients in health outcomes,
we derive a set of welfare-dominance and inequality-dominance conditions for ranking health distributions. Unlike other existing
health inequality measures, our conditions require no cardinal specification of ordinal heath data and, hence, are robust.
We then apply the dominance conditions to compare socioeconomic health inequality in the US and Canada using the newly released
JCUSH data.
KeywordsHealth inequality–Lorenz dominance–Income-health matrix–Super-Lorenz dominance–Income mobility
In this paper, characterizations of the single-series Gini social evaluation functions and their illfare-ranked counterparts, functions introduced and discussed by Donaldson and Weymark [10] and Weymark [19], are provided. It is shown that the single-series Ginis (resp. illfare-ranked single-series Ginis) are the only sequences of social evaluation functions allowing for the derivation of both relative and absolute ethical inequality measures which satisfy a high income (resp. low income) group aggregation property. In the case of the illfare-ranked single-series Ginis, the aggregation condition is important for the construction of ethical indices of poverty.
In most developing countries, income inequality tends to worsen during initial stages of growth, especially in urban areas. The People’s Republic of China (PRC) provides a sharp contrast where income inequality among urban households is lower than that among rural households. In terms of inclusive growth, the existence of income mobility over a longer period of time may mitigate the impacts of widening income inequality measured using crosssectional data. We explore several ways of measuring income mobility and found considerable income mobility in the PRC, with income mobility lower among rural households than among urban households. When incomes are averaged over 3 years and when adjustments are made for the size and composition of households, income inequality decreases. Social welfare functions are posited that allow for a trade-off between increases in income and increases in income inequality. These suggest strong increases in well-being for urban households in the PRC. In comparison, the corresponding changes in rural households are much smaller.
This paper develops a new class of measures of mobility as an equalizer of longer-term incomes – a concept different from other notions such as mobility as time-independence, positional movement, share movement, income flux, and directional income movement. A number of properties are specified leading to a class of indices, one easily-implementable member of which is applied to data for the United States and France. Using this index, income mobility is found to have equalized longer-term earnings among U.S. men in the 1970s but not in the 1980s or 1990s. In France, though, income mobility was equalizing throughout, and it has attained its maximum in the most recent period.
In most developing countries, income inequality tends to worsen during initial stages of growth, especially in urban areas. The People’s Republic of China (PRC) provides a sharp contrast where income inequality among urban households is lower than that among rural households. In terms of inclusive growth, the existence of income mobility over a longer period of time may mitigate the impacts of widening income inequality measured using crosssectional data. We explore several ways of measuring income mobility and found considerable income mobility in the PRC, with income mobility lower among rural households than among urban households. When incomes are averaged over 3 years and when adjustments are made for the size and composition of households, income inequality decreases. Social welfare functions are posited that allow for a trade-off between increases in income and increases in income inequality. These suggest strong increases in well-being for urban households in the PRC. In comparison, the corresponding changes in rural households are much smaller.
We axiomatize three different motivations for being concerned about intergenerational mobility: mobility as a description of movement, as an indication of equality of opportunity, and as an indication of equality of life chances. These three motivations are shown to be incompatible. None of the existing measures is acceptable as an indicator of equality of opportunity or equality of life chances. We propose two new measures of intergenerational mobility which more adequately reflect these concerns. Copyright 2001 by The London School of Economics and Political Science
An index of Inequality is constructed which decomposes into two components, corresponding to vertical and "horizontal" equity respectively. Horizontal equity Is defined in terms of changes in the ordering of a distribution. The proposed index is a function to two inequality aversion parameters. One empirical application is for comparison of a pre-tax distribution with a post-tax distribution, and an example of this is given for the distribution of incomes in the UK in 1977. There is a trade-off between "horizontal"and vertical equity, and for particular combinations of the inequality aversion parameters the original distribution will be preferred to the final distribution. The paper concludes with an application of the proposed index to a model of optimal taxation.
A sufficient condition is given for one mobility matrix to display more mobility than another in the sense of Kanbur and Stiglitz.
This paper presents a framework for the evaluation and measurement of “reversal” and “origin independence” as separate aspects
of economic mobility. We show that evaluation depends on aversion to multi-period inequality, aversion to inter-temporal fluctuations,
and aversion to future risk. We construct “extended Atkinson indices” that allow us to quantify the relative impact of reversal
and origin independence on welfare. We apply our approach to the comparison of income mobility in Germany and in the U.S..
When aversion to inequality is the only consideration, the U.S. gains more from mobility than Germany. This reflects similar
gains from reversal in the two countries but greater gains in the U.S. from origin independence. The introduction of aversion
to intertemporal fluctuations and aversion to future risk makes the impact of mobility in the two countries more similar.
The paper considers the ranking of mobility matrices in a simple Markov model of social mobility. The approach is the dynamic counterpart ot the "static" inequality ranking of income distributions by the Lorenz curve. The derived partial ordering is motivated by welfare considerations, is shown to be equivalent to same intuitive mobility concepts, and is used to screen some immobility indices. The equivalence of the ranking with the "permanent income" Lorenz ordering gives support to the claim that this approach is the natural extension of Kolm′s [The optimal production of social justice, in "Public Economics (J. Margolis and H. Guitton, Eds.), MacMillan, London, 1969], Atkinson′s [On the measurement of inequality, J. Econ. Theory2 (1970), 244–263], and Dasgupta, Sen, and Starrett′s [Notes on the measurement of inequality, J. Econ. Theory6 (1973), 180–187] approaches. Journal of Economic Literature Classification Numbers: D31, D63, J62.
Mobility, inequality and horizontal equity
The measurement of mobility