Trend Analysis of Anticipated Lifetime Income Inequality among Post‐war Japanese Youth

This study aims to measure the inequality of anticipated lifetime income and the inequality of annual income among the younger generation (24–29‐year‐old men), and to examine any trends that can be found in terms of inequality between 1955 and 2005 in Japan. Anticipated lifetime income is defined in this study as the present value of the total anticipated annual income that one is likely to earn each year between the ages of 24 and 59 years, assuming that there is no intragenerational class mobility. The anticipated lifetime income for each young male is estimated using the Social Stratification and Social Mobility Survey dataset, which is a Japanese national cross‐sectional survey of social stratification and social mobility. An inequality in the anticipated lifetime income can be regarded as an “inequality of outlook” among the younger generation. As a result of this analysis, it was found that the Gini coefficient, the most general measurement of income inequality, had significantly increased for anticipated lifetime income between 1995 and 2005. At the same time, the gap between the Gini coefficient of anticipated lifetime income and that of annual income had narrowed. It is suggested that “inequality of outlook,” which cannot be easily identified using a superficial index, has increased significantly.     

Spatial approaches to measure subnational inequality: Implications for Sustainable Development Goals

The United Nations expressed an interest in reducing subnational (i.e., province and state level) inequality. We propose using a spatial decomposition of the Gini coefficient (SDGC) to track changes in subnational inequality. Typically, agencies do not track summary measures of subnational clustering of development indicators. Tracking changes in the SDGC can help measure and reduce regional inequality. To illustrate the use of the SDGC, we first present data for 93 nations to obtain cross‐sectional variation. Next, to illustrate how the SDGC trends over time, changes in the Human Development Index in Mongolia are compared to Russia and China. The SDGC can show improvement, decline and persistent clustering of subnational level inequality. The SDGC is a useful measure for the United Nations' Sustainable Development Goals.     

An extended Gini approach to inequality measurement

It is well-known that, when the Lorenz curves do not cross, the ranking of distributions provided by the Gini index is identical to the one implied by the Lorenz criterion. This does not preclude inequality as measured by the Gini index to increase while the Lorenz curves cross. A suitable modification of the Gini coefficient allows the Lorenz quasi-ordering to coincide with the ranking generated by the application of unanimity over the class of extended Gini indices. Recently the Lorenz quasi-ordering and the underlying principle of transfers have come under attack, while new criteria – the differentials, deprivation and satisfaction quasi-orderings – have been proposed for providing unambiguous rankings of distributions. We suggest to weaken the principle of transfers by imposing additional restrictions on the progressive transfers, which take into account the positions on the income scale of the donors and beneficiaries. We identify the subclasses of extended Gini indices that satisfy these weaker versions of the principle of transfers and we show that the application of unanimity among these classes generate rankings of distributions that coincide with those implied by the differentials, deprivation and satisfaction quasi-orderings.      

A general class of inequality elasticities of poverty

Many authors have recently emphasized the crucial role of income inequalities in the design of efficient policies aimed at reducing poverty. However, the link between variations in the degree of inequality and variations in poverty is not well documented. The literature, for instance, does not provide any satisfying tool for predicting how a small relative variation in the Gini index may be associated with a variation in the headcount index. In the present paper, we define a family of Lorenz curve transformations that can directly be interpreted in terms of relative variations of known inequality measures. Then, we extend Kakwani’s (Rev Income Wealth 39(2):121–139, 1993) methodology for the calculation of inequality elasticities of poverty. Improvements are threefold with respect to Kakwani’s work. First, our formulas are not confined to the sole Gini index. Secondly, they embrace the uncertainty and the complexity of the mechanical link between inequality and poverty. Third, using some flexible functional form, one can easily perform an accurate estimation of the point inequality elasticities of poverty corresponding to observed variations of a given income distribution. We also propose a simple measure that may be helpful to assess how “pro-poor” are inequality variations by comparing the observed elasticities with the set of theoretical elasticities that could be obtained from the initial income distribution.     

ON THE ASSIGNMENT OF INDIVIDUALS TO LATENT CLASSES

Consider an m-way cross-classification table (for m = 3, 4, … ) of m dichotomous variables that describes (1) the 2 ^m possible response patterns to a set of m questions (where the response to each question is binary), and (2) the number of individuals whose responses to the m questions can be described by a particular response pattern, for each of the 2 ^m possible response patterns. Consider the situation where the data in the cross-classification table are analyzed using a particular latent class model having T latent classes (for T = 2, 3, …), and where this model fits the data well. With this latent class model, it is possible to estimate, for an individual who has a particular response pattern, what is the conditional probability that this individual is in a particular latent class, for each of the T latent classes. In this article, the following question is considered: For an individual who has a particular response pattern, can we use the corresponding estimated conditional probabilities to assign this individual to one of the T latent classes? Two different assignment procedures are considered here, and for each of these procedures, two different criteria are introduced to help assess when the assignment procedure is satisfactory and when it is not. In addition, we describe here the particular framework and context in which the two assignment procedures, and the two criteria, are considered. For illustrative purposes, the latent class analysis of a classic set of data, a four-way cross-classification of some survey data, obtained in a two-wave panel study, is discussed; and the two different criteria introduced herein are applied in this analysis to each of the two assignment procedures .     

THE DECOMPOSITION OF INEQUALITY BY CLASS AND BY OCCUPATION:

Sociological research on earnings and income has focused on predicting individual income. Analyses most often use occupational status or class, along with other economically relevant variables, to explain earnings or income variations among individuals (income determination). Aggregate inequality (income distribution) has received considerably less attention, except in cross-national research. This especially holds for applying central concepts of stratification to the analysis of inequality. That is, class and occupation differences in economic rewards are rarely used to investigate aggregate earnings or income inequality. This study, using 1976 and 1977 Panel Study of Income Dynamics survey data, estimates the proportion of total earnings/income inequality accounted for by class and by occupation. Theil's index is used to measure earnings and income inequality and thus decompose total inequality into between-and within-group components. Wright's five-category schema is replicated for decomposition of inequality by class and a traditional four-category ordinal typology for decomposition by occupation. The two schemas show similar results: both class and occupation respectively account for between one-fifth and one-fourth of total earnings and income inequality. The results show the relevance of these central stratification typologies for the analysis of aggregate inequality.     

Deprivation,welfare and inequality

We provide a characterization of the generalised satisfaction—in our terminology non-deprivation—quasi-ordering introduced by S.R. Chakravarty (Keio Econ Stud 34:17–32, (1997)) for making welfare comparisons. The non-deprivation quasi-ordering obeys a weaker version of the principle of transfers: welfare improves only for specific combinations of progressive transfers, which impose that the same amount be taken from richer individuals and allocated to one arbitrary poorer individual. We identify the extended Gini social welfare functions that are consistent with this principle and we show that the unanimity of value judgements among this class is identical to the ranking of distributions implied by the non-deprivation quasi-ordering. We extend the approach to the measurement of inequality by considering the corresponding relative and absolute ethical inequality indices. This is a shortened version of Magdalou and Moyes (2008), which contains the details of the proofs as well as an empirical illustration.     

On the generalization and decomposition of the Bonferroni index

A simple algorithm is proposed which defines the Bonferroni as the product of a row vector of individual population shares, a linear mathematical operator called the Bonferroni matrix and a column vector of income shares. This algorithm greatly simplifies the decomposition of the Bonferroni index by income sources or classes and population subgroups. The proposed algorithm links also the Bonferroni index to the concepts of relative deprivation and social welfare and leads to a generalization where the traditional Bonferroni and Gini indices are special cases. The paper ends with an empirical illustration based on EU-SILC data for the year 2008.     

Inequality measurement and the time structure of household income in Israel

The aim of this paper is to empirically evaluate the effect of the length of the accounting period on indices of inequality of household income in Israel. There are three main findings: (1) The analysis of the impact of the accounting period on the Gini index of inequality can be done in a way which is identical to analyzing the effect of the accounting period on the coefficient of variation; (2) changing the accounting period from one to three months decreases, on average, the Gini index of inequality by about 1.7%. Furthermore, the Gini index calculated from a three-month accounting period was 3.9%–4.1% higher than the index based on a 12-month period. The change in the accounting period from 12 months to three months accounts for 27% to 37% of the increase in inequality in the last two decades, depending on the type of income considered. (3) The above relationship is stable over the years but is sensitive to the definition of income.     

Decomposition of gini and multivariate gini indices

A new type of decomposition by population subgroup is proposed for the Gini inequality index. The decomposition satisfies the completely identical distribution (CID) condition, whereby the between-group inequality is null if and only if the distribution within each subgroup is identical to all the others. Thus, this decomposition contrasts strikingly with the subgroup decomposition of the generalized entropy measures, which satisfy the condition that the between-group inequality is null if the mean within each subgroup equals those of all the others. The new decomposition can be generalized to the distance-Gini index and the volume-Gini index, two multivariate Gini indices introduced by Koshevoy and Mosler, with some modification of the index definition and a somewhat loosened CID condition in the latter case. The source decomposition is also generalized to these multi-dimensional indices. Interaction terms appear among sources of different attributes in the decomposition for the modified volume–Gini index.

An Ex-Post View of Inequality of Opportunity in France and its Regions

This paper proposes an ex-post measure of inequality of opportunity in France and its regions by assessing the inequality between individuals exerting the same effort. To this end, we define a fair income that fulfils ex-post equality of opportunity requirements. Unfairness is measured by an unfair Gini based on the distance between the actual income and the fair income. Our findings reveal that the measures of ex-post inequality of opportunity largely vary across regions, and that this is due to differences in reward schemes and in the impact of the non responsibility factors of income. We find that most regions have actual incomes closer to fair incomes than to average income, excepted Ile de France where the actual income looks poorly related to effort variables. Finally, we find that income inequality and inequality of opportunity are positively correlated among regions.     

Effects of Neighborhood Inequality on the Relative Distance between Objective Position and Subjective Identification

This article is an exploratory attempt to assess the relationship between an individual's objective class position and their subjective class identification and to understand the effects of neighborhood inequality on individual variations. It tests three theses that the relationship between objective class position and subjective identification: is based on reflection, middle-class consciousness or variation. The degree to which neighborhood-level variables impact on the relative distance between objective class position and subjective identification is examined in assessing the possible contextual effects of the spatial setting individuals in which individuals are located. It utilizes 2015 City Policy Index Survey data administered by the Seoul Metropolitan Government and goes through two steps in analysis. First, a correspondence analysis was performed to calculate the relative distance between individuals’ objective position and subjective identification. The relative distance calculated was used as a dependent variable in a multilevel linear model examining the possible cross-level interaction between neighborhood inequality and individual-level variables. The results indicate that the relationship between an individual's objective class position and subjective identification was captured in the variation thesis. Women, and people who are younger, college educated and who hold non-manual occupations are more likely to identify with a position that is lower than their actual position. Neighborhood inequality was found to exaggerate the gap in relative distance scores by gender and occupation.     

Dynamic Measures of Individual Deprivation

We introduce a one-parameter class of individual deprivation measures. Motivated by a suggestion of Runciman, we modify Yitzhaki’s index by multiplying it by a function that is interpreted as measuring the part of deprivation generated by an agent’s observation that others in his reference group move on to a higher level of income than himself. The parameter reflects the relative weight given to these dynamic considerations, and the standard Yitzhaki index is obtained as a special case. In addition, we characterize more general classes of measures that pay attention to this important dynamic aspect of deprivation.     

Measuring inequality of opportunity through between-group inequality components

Opportunity egalitarians support rich-to-poor redistribution whenever this allows for the compensation of income disparities due to non-responsible choices (circumstances). In this paper we focus on the measurement of opportunity inequality within Roemer’s (Philos Public Aff 22:146–166, 1993) pragmatic theory where a disjoint and exhaustive partition rule is assumed such that individuals within the same population can be grouped depending on the sole circumstances. Given entropy-based, deprivation-based and welfaristic inequality decomposition procedures, we show that the between-group Gini component from Dagum’s decomposition is the only well known between-group inequality index satisfying the Pigou-Dalton principle of transfer as reformulated for opportunity egalitarianism.     

The impact of unionization,right-to-work laws,and female labor force participation on earnings inequality across states

This study examines the effect of unionization, right-to-work laws, and participation of women in the labor force on income inequality. Two distinct models are developed using 1970 and 1980 census data on the 50 states in the U.S. First, an income inequality model is specified as a beta distribution of the second kind to estimate Gini measures of income inequality. Second, these Gini estimates are used in a simultaneous equations model. The 1970 results indicate that higher unionization rates decreased inequality while right-to-work laws increased inequality. In 1980, the measure of inequality was lower in states with higher female labor force participation. We thank an unknown referee and the editor for comments and criticisms that greatly improved the paper. The usual caveat applies.     

Basil Bernstein 1924-2000

This paper introduces the Tog coefficient, which can be used to measure the level of inequality in a cross-tabulation of two ordinal-level variables. The Gini coefficient is a standard measure of income inequality which has been adapted by other authors for use in different contexts such as the measurement of health inequalities and the quantification of occupational segregation; the Tog coefficient represents a further stage in this process of development. The paper outlines the construction of the Tog coefficient and illustrates this using a social mobility table based on data from the 1972 Oxford Mobility Study. The trend in social mobility-related inequality as measured by the Tog coefficient is compared with the findings of Goldthorpe et al. based on odds ratios. A more elaborate application of the Tog coefficient uses a variety of data relating to the similarity of spouses' class backgrounds to demonstrate the existence of a long-term decline in the level of inequality in British society.     

Entropy Measures of Inequality*

Although sociologists have long been interested in the analysis of inequality, there have been relatively few systematic attempts to measure it. Most measurement has utilized popular existing measures such as the Gini coefficient, which unfortunately is relatively difficult to compute and interpret. This article presents a new measure of inequality (B) that is based upon the concept of entropy. The B measure is used for categorical data and complements Theil's (T) entropy measure for continuous data. The B measure is illustrated for both income and wealth data and successfully meets several criteria for evaluating measures of inequality. These include the criteria of scale invariance, sensitivity to transfers, and adequate upper bounds. A further advantage of sociological entropy measures of inequality is that they facilitate interdisciplinary comparison of work on inequality between sociology and other disciplines (such as economics) which use entropy measures of inequality.     

Regional Well-Being and its Inequality in the OECD Member Countries

This paper analyses the inequality between the regions of the Organization for Economic Co-operation and Development (OECD) member countries by using stochastic multi-objective acceptability analysis and the associated multivariate Gini index. By considering a large number of possible combinations of weights, the distribution of the potential rankings for each region is used to measure multidimensional inequality both within and between countries. Our results show that beyond the expected two clubs of rich and poor countries, a third group of countries emerges that belongs neither to the top nor to the bottom of the ranking, an outcome that can be attributed to the presence of significant economic differences among regions within those countries. Most of the inequality lies between countries, but regional well-being also significantly varies within the same countries and we find an inverse U-shape connection between regional well-being and its inequality within the OECD member countries.

     

Generalized Gini Indices of Equality of Opportunity

This article considers the ranking of profiles of opportunity sets on the basis of their equality. A version of the Pigou–Dalton transfer principle that is appropriate for the measurement of opportunity inequality is introduced and used to axiomatize the class of generalized Gini equality of opportunity orderings. A characterization of the class of generalized Gini social preference orderings for opportunity profiles is also provided.