MEASURING AND ANALYZING CLASS INEQUALITY WITH THE GINI INDEX INFORMED BY MODEL-BASED CLUSTERING

The most widely used measure for studying social, economic, and health inequality is the Gini index/ratio. Whereas other measures of inequality possess certain useful characteristics, such as the straightforward decomposability of the generalized entropy measures, the Gini index has remained the most popular, at least in part due to its ease of interpretation. However, the Gini index has a limitation in measuring inequality. It is less sensitive to how the population is stratified than how individual values differ. The twin purposes of this paper are to explain the limitation and to propose a model-based method—latent class/clustering analysis for understanding and measuring inequality. The latent cluster approach has the major advantage of being able to identify potential "classes" of individuals who share similar levels of income or one or more other attributes and to assess the fit of the model-based classes to the empirical data, based on different cluster distributional assumptions and the number of latent classes. This paper distinguishes class inequality from individual inequality, the type that is better captured by the Gini. Once the classes are estimated, the membership of estimated classes obtained from the best fitting model facilitates the decomposition of the Gini index into individual and class inequality. Class inequality is then measured by two relative stratification indices based on either the relative size of the Gini between-class components or the relative number of stratified individuals. Therefore, the Gini index is extended and assisted by model-based clustering to measure class inequality, thereby realizing its great potential for studying inequality. Income data from France and Hungary are used to illustrate the application of the method.     

Multidimensional inequality and multidimensional generalized entropy measures: An axiomatic derivation

This paper generalizes the axiomatic approach to the design of income inequality measures to the multiattribute context. While the extension of most axioms considered desirable for inequality indices is straightforward, it is not entirely clear when a situation is more unequal than another when each person is characterised by a vector of attributes of well-being. We explore two majorization criteria which are partial orders ranking distributions of attributes by their degree of inequality. The two criteria are motivated by the Pigou-Dalton Transfer Principle in the unidimensional context and its equivalent formulation. These criteria gauge inequality loosely speaking with respect to the dispersion of the multidimensional distribution of the attributes. They, however, fail to address a different dimension of multivariate inequality pertaining to an increase in the correlation of the attributes. In this connection, this paper introduces a correlation-increasing majorization criterion proposed by Boland and Proschan (1988). Finally, in conjunction with other axioms commonly invoked in the literature on inequality, the majorization criteria lead inexorably to the class of multidimensional generalized entropy measures. Received: 15 June 1995 / Accepted: 30 September 1997     

Geographic decomposition of inequality in health and wealth: evidence from Cambodia

Applying the small-area estimation methods to Cambodia data, we decompose the total inequality in wealth (consumption) and health (child undernutrition) indicators into within-location and between-location components. Because the knowledge of the pattern of spatial disparity in poverty and undernutrition is important for the geographic targeting of resources, we conduct a geographic decomposition of the variance of the Foster-Greere-Thorbecke index in addition to the standard decomposition exercise based on the generalized entropy measures. We find that a sizable proportion of wealth inequality is due to between-location inequality, whereas health inequality is mainly due to within-location inequality.     

Information theoretic approaches to income density estimation with an application to the U.S. income data

The size distribution of income is the basis of income inequality measures which in turn are needed for evaluation of social welfare. Therefore, proper specification of the income density function is of special importance. In this paper, using information theoretic approach, first, we provide a maximum entropy (ME) characterization of some well-known income distributions. Then, we suggest a class of flexible parametric densities which satisfy certain economic constraints and stylized facts of personal income data such as the weak Pareto law and a decline of the income-share elasticities. Our empirical results using the U.S. family income data show that the ME principle provides economically meaningful and a very parsimonious and, at the same time, flexible specification of the income density function.     

The Ecological-Evolutionary Typology of Human Societies and the Evolution of Social Inequality

Gerhard Lenski's ecological-evolutionary typology of human societies, based on the level of technology of a society and the nature of its physical environment, is a powerful predictor of various dimensions of social inequality. Analysis of comparative data shows that while some dimensions of the stratification system (such as measures of social complexity) exhibit a monotonic trend of increasing inequality with level of technology from the hunting-and-gathering to the agrarian type, others (such as measures of freedom and sexual inequality among males) exhibit a pattern of "agrarian reversal" in which inequality increases from the hunting‐and‐gathering to the advanced horticultural type but then declines with the agrarian type. Theoretical and empirical implications of the agrarian reversal pattern for the study of social inequality are discussed.     

Measuring inequality of opportunity with imperfect data: the case of Turkey

The measurement of inequality of opportunity has hitherto not been attempted in a number of countries because of data limitations. This paper proposes two alternative approaches to circumventing the missing data problems in countries where a demographic and health survey (DHS) and an ancillary household expenditure survey are available. One method relies only on the DHS, and constructs a wealth index as a measure of economic advantage. The alternative method imputes consumption from the ancillary survey into the DHS. In both cases, we compute a lower bound estimator of the share of (ex-ante) inequality of opportunity in total inequality. Parametric and non-parametric estimates are calculated for each method, and the parametric approach is shown to yield preferable lower-bound measures. In an application to the sample of ever-married women aged 30–49 in Turkey, inequality of opportunity accounts for at least 26% (31%) of overall inequality in imputed consumption (the wealth index).     

Robust inequality comparisons

This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such situations, Aaberge (Soc Choice Welf 33:235–259, 2009) introduced two alternative sequences of nested dominance criteria for Lorenz curves, which proved to characterize two separate systems of nested subfamilies of inequality measures. This paper uses the obtained characterization results to arrange the members of two different generalized Gini families of inequality measures into subfamilies according to their relationship to Lorenz dominance of various degrees. Since the various criteria of higher degree Lorenz dominance provide convenient computational methods, these results can be used to identify the largest subfamily of the generalized Gini families, and thus the least restrictive social preferences, required to reach unambiguous ranking of a set of Lorenz curves. We further show that the weight-functions of the members of the generalized Gini families offer intuitive interpretations of higher degree Lorenz dominance, which generally has been viewed as difficult to interpret because they involve assumptions about third and higher derivatives. To demonstrate the usefulness of these methods for empirical applications, we examine the time trend in income and earnings inequality of Norwegian males during the period 1967–2005.     

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.     

Comparison of indirect and direct approaches to measuring patient satisfaction

One indirect (PSQ) and two direct (CSQ-18B and ERS) measures of patient satisfaction were compared across a series of psychometric, acceptability, and concurrent validity criteria. None of the three measures was significantly related to health status or demographic characteristics. Each measure performed as expected from prior research on their psychometric properties. The scales contrasted, however, in regard to acceptability, with the PSQ being much less acceptable to patients than the other two. The PSQ also produced more missing data. The results on the PSQ reflected patient inconsistency on cross-check items and patients tended to be uncertain in their responses to many items. In multivariate analyses the three measures were used as predictors of patient-rated indices of global service satisfaction. The CSQ-18B and the ERS were significant predictors of patient-rated indices of global service satisfaction, whereas the PSQ was unrelated to these indices. It was concluded that the direct and indirect approaches measure different satisfaction domains. The PSQ likely assesses more generalized attitudes about health services while the CSQ-18B and the ERS efficiently reflect opinions about the specific setting in which they are administered.     

Egocentric and sociocentric measures of network centrality

Egocentric centrality measures (for data on a node’s first-order zone) parallel to Freeman’s [Social Networks 1 (1979) 215] centrality measures for complete (sociocentric) network data are considered. Degree-based centrality is in principle identical for egocentric and sociocentric network data. A closeness measure is uninformative for egocentric data, since all geodesic distances from ego to other nodes in the first-order zone are 1 by definition. The extent to which egocentric and sociocentric versions of Freeman’s betweenness centrality measure correspond is explored empirically. Across seventeen diverse networks, that correspondence is found to be relatively close—though variations in egocentric network composition do lead to some notable differences in egocentric and sociocentric betweennness. The findings suggest that research design has a relatively modest impact on assessing the relative betweenness of nodes, and that a betweenness measure based on egocentric network data could be a reliable substitute for Freeman’s betweenness measure when it is not practical to collect complete network data. However, differences in the research methods used in sociocentric and egocentric studies could lead to additional differences in the respective betweenness centrality measures.     

Source decomposition of changes in income inequality: the integral-based approach and its approximation by the chained Shapley-value approach

This paper proposes source decomposition of the change in income inequality between two time points using the integral-based approach (IBA) and the (chained) Shapley-value approach as its approximation. In comparison to static Shapley-value decompositions and traditional decompositions for the square of the coefficient of variation and the Gini index, the new dynamic Shapley-value approach is intuitively appealing as a decomposition procedure for changes in inequality. It is expected to yield relatively small differences among various inequality measures, essentially maintaining consistency with income source classification. Path dependency, a possible drawback of the new decompositions, is not expected to be a particular problem in the usual cases. The properties are illustrated for application to the increase in US family income inequality during 1979–1996. In this empirical study, the new decompositions showed a tendency that was clearly different from those of the existing decompositions, indicating that the proposed procedures shed new light on analysis of the causes of inequality changes. An extension to incorporate other factors such as family structure is also successful without loss of the desirable properties.     

Perceived Freedom and its Sociological Effects: An Inquiry into the Relationship Between Liberalism and Inequality

Abstract:  Individual freedom has been regarded as one of the most important criteria for a desirable society and life. Recently, the theories of liberalism and distributive justice have received increasing attention as a theoretical basis for tackling problems pertaining to socioeconomic inequality and poverty. However, few quantitative analyses focus on the meaning of freedom in the context of socioeconomic inequality and political order in an existing liberal-democratic society. In this paper, I construct a self-rated measure of freedom—the overall perceived freedom scale—and examine (1) whether socioeconomic inequality is related to inequality of freedom, (2) whether freedom is related to subjective well-being, and (3) whether freedom affects people's political attitude toward inequalities. Analyses using data from a 2005 Japanese national survey ( N  = 1320) reveal the following results: (1) people with higher personal income (not household income), higher education, and better health tend to perceive greater freedom, (2) people with higher perceived freedom are more likely to be satisfied with their life, and (3) individuals with higher perceived freedom are more likely to oppose the government's egalitarian policy, and their opposition is based on the liberal principle of freedom and self-responsibility. On the basis of these findings, the double-edged possibility of individual freedom and liberalism as an "enhancer" and "moderator" of socioeconomic inequalities and political conflicts is suggested.     

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.     

The Individual Deprivation Measure: measuring poverty as if gender and inequality matter

As inequality deepens globally and within countries it is vital that we know how poverty shapes, constrains, and often destroys the lives of women and men. We know from decades of research that poverty is experienced differently by women and men, yet existing mainstream measures of poverty have been blind to gender. This article focuses on the Individual Deprivation Measure (IDM), a multi-dimensional measure of poverty and inequality designed to illuminate rather than obscure gender differences. Developed over the past five years by an inter-disciplinary research team based at the Australian National University, the IDM is grounded in research with women and men across 18 sites in six countries. Unlike most mainstream measures of poverty, the IDM takes the individual, rather than the household, as the unit of analysis. As a result, the IDM is able to capture gendered differences in the ways poverty is experienced, and also differences according to other markers of identity or social status, such as age, ethnicity, or geographic location.     

Improving the measurement of child welfare in the context of intra-household inequality

This study aims to illustrate how to improve the evaluation of child economic well-being and child poverty using the collective approach. International organisations such as the World Bank, OECD and UNICEF have made important efforts in recent years to produce reliable data and to measure poverty according to the most relevant items of household consumption baskets. However, when measuring poverty, it is common practice to assume either that resources are distributed equally within the household or that there are fixed equivalence scales (for example, a child can be counted as 0.5 adults). The methodology based on collective models of consumption overcomes this rigidity by allowing inequality within each household to be taken into account. The method assumes that each household devotes a fraction of resources to children, which can be estimated using the observed expenditure on child-exclusive goods. An example of how child poverty measures can be inaccurately estimated is illustrated through the case of young children in Albania.     

Growth with equity: income inequality in Vietnam, 2002–14

We use the 2002 through 2014 Vietnam Household Living Standards Surveys to construct comparable measures of household income and estimates of income inequality over this high-growth period. We focus on two questions: How have benefits from growth been distributed; and do changes in the structure of the economy map into changes in inequality? We explore dimensions in which inequality may vary, notably urban versus rural, and by ethnic status. We also decompose inequality by income source to highlight key factors underlying the relatively low levels of inequality during this period. We find that agricultural opportunities played an important role in dampening inequality, but more important has been the steady development of wage-labor markets in both urban and rural areas. An important caveat to the generally rosy picture we paint is the deteriorating position of ethnic minorities. Finally, we draw comparisons with China and document key differences in their growth-inequality experiences.     

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.     

Life satisfaction in China and consumption and income inequalities

This research uses nationally representative data to study how economic resources and inequalities are associated with life satisfaction of Chinese residents. We construct economic resource and inequality measures from expenditure rather than from income, after confirming that expenditure inequality is a better measure in the Chinese context. We find that economic inequalities in general are negatively associated with life satisfaction, and that this association is larger for inequalities in the lower half of the distribution than those in the upper half of the distribution. We further explore the mechanisms under which inequality can be associated with life satisfaction, and find that aspiration is potentially one important channel.     

INEQUALITY AND GROWTH IN THE UNITED STATES: WHY PHYSICAL AND HUMAN CAPITAL MATTER

We investigate the relationship between economic growth and top income inequality under the influence of human and physical capital accumulation, using an annual panel of U.S. state‐level data. Our analysis is based upon the “unified” framework offered by Galor and Moav (2004) while the empirics account for cross‐section dependence, parameter heterogeneity, and endogeneity, in nonstationary series. We conclude that changes in inequality do not influence growth, neither in the short run nor in the long run in the United States as a whole in the 1929–2013 period. Our findings are robust to the inclusion of overall income inequality measures. These findings provide support for the theoretical prediction of the unified theory of inequality and growth, according to which the growth effect of inequality becomes insignificant in the latest stages of economic development that the United States experiences during our period of investigation. Therefore, future policies aiming at moderating the concentration at the upper end of income distribution are not likely to have adverse growth consequences in developed countries such as the United States. (JEL I21, O47, C23)     

Baby booming inequality? Demographic change and earnings inequality in Norway, 1967�C2000

In this paper, we demonstrate how age-adjusted inequality measures can be used to evaluate whether changes in inequality over time are due to changes in the age-structure. To this end, we use administrative data on earnings for every male Norwegian over the period 1967–2000. We find that the substantial rise in earnings inequality over the 1980s and into the early 1990s, is to some extent driven by the fact that the large baby boom cohorts are approaching the peak of the age–earnings profile. We further demonstrate that the impact of age-adjustments on the trend in inequality during the period 1993–2000 is highly sensitive to the method used: While the most widely used age-adjusted inequality measure indicates little change in inequality over this period, a new and improved age-adjusted measure suggests a decline in inequality.