The Measurement of Non-economic Inequality in Well-Being Indices

This paper is a critical review of composite well-being indices that account for inequality. Many well-being indices build upon the idea that while income and wealth are important, they do not constitute a person’s actual quality of life. However, first of all, the analysis finds that while well-being indices aim to go “beyond GDP” and other primarily economic indicators, many of them, unfortunately, do not focus on inequality at all. Secondly, most indices which include inequality in their measurement, only account for economic inequality. Thirdly, the article finds that the most comprehensive wellbeing index in terms of inequality is the Inequality-adjusted Human Development Index which adjusts for economic, health and education inequality. This article finds that well-being indices should make further strides to ensure the capture of non-economic inequality in terms of education and health.     

Building Weighted-Domain Composite Indices of Life Satisfaction with Data Envelopment Analysis

The specialised literature has frequently addressed the relationship between life domains and people’s satisfaction with life. Some researchers have posed questions regarding the importance of domains, therefore interpreting them as weightings and creating domain satisfaction indices. This paper illustrates how Data Envelopment Analysis (DEA) and Multi-Criteria-Decision-Making (MCDM) techniques can be employed to compute domain-based composite indices of life satisfaction and weightings for life domains. Furthermore, an empirical application is performed on a sample of 178 people living in a rural community in Yucatan (Mexico). One of the main features of the aforementioned techniques is that weightings might differ from one individual to another. Accordingly, several weighting schemes are used to compute different life satisfaction indices, in addition to a constant equally-weighted index. Based on the goodness-of-fit criteria commonly used in this literature, our main result is that DEA-MCDM indicators of life satisfaction do not improve the relationship with self-reported life satisfaction in comparison to the equally-weighted index.     

Income Inequality Indices Interpreted as Measures of Relative Deprivation/Satisfaction

This paper considers different ways of making comparisons between individuals in terms of deprivation and/or satisfaction. This allows the Gini index, the Bonferroni index and the De Vergottini index to be interpreted as social deprivation measures as well as social satisfaction measures. The inequality measures that belong to the ?? family, or linear combinations of them, are obtained when using different weighting schemes to average the deprivation and satisfaction associated with each income level. Particularly, the generalised Gini indices (Yitzhaki, Int Econ Rev 24:617?C628 in 1983), the indices proposed by Aaberge (J Econ Inequal 5(3):305?C322, 2007) or those proposed by Imedio-Olmedo et al. (J Public Econ Theory 13(1):97?C124, 2011) can be used to evaluate social deprivation or social satisfaction in an income distribution.     

An Overview and Evaluation of Composite Indices of Development

The search for alternative indicators of development has witnessedthe development of a variety of composite indices of development. Theseindices integrate various social, political and economic aspects ofdevelopment in measurement. This paper presents an overview andevaluation of composite indices of development in terms of certain broaddimensions of measurement. In terms of method and technique, compositeindices are generally additive ones with equally weighted componentsconsisting of variables selected in an ad hoc manner. Numerouscriticisms have been leveled at these methods employed in compositeindexing. Composite indices are mainly quantitative insofar as theindices are all presented in numerical format. Composite indices aresubject to subjectivity despite the relative objectivity of the methodsemployed in composite indexing. Composite indices are of a cardinalnature, but remain ordinal insofar as differences in index values cannotbe interpreted meaningfully. The multidimensionality of compositeindices represents one of their main advantages. Indices representaggregate measures of a combination of complex development phenomena.The comparative application of composite indices of development overspace and time remains problematic. Composite indices generally combinemeasures of ends and means. In respect of method and technique,composite indexing is relatively complex. Composite indices arerelatively flexible, because changes in selection, scaling, weightingand aggregation can be effected readily, albeit at the cost ofcomparability. Composite indices perform relatively well in terms ofcross-national availability, but few indices perform well in terms ofinter-temporal availability. On the strength of the systematic positiveassociation between income and popular composite indices such as theHDI, many have claimed that these indices represent no real contributionto the literature on indicators research. Composite indices,furthermore, are often considered to be ideological statements ratherthan practically functional indicators. Yet, composite indices representuseful supplements to income-based development indicators. These indicesremain invaluable in terms of their ability to simplify complexmeasurement constructs, to focus attention and to catch the eye, thusenhancing their political appeal.     

The Trade-off Between Poverty Reduction and Carbon Emissions,and the Role of Economic Growth and Inequality: An Empirical Cross-Country Analysis Using a Novel Indicator

Is it possible for countries to eradicate poverty while also meeting environmental goals? Despite the passage of international agreements calling for these issues to be addressed simultaneously, little is known about the direct relationship between them. This study addresses this gap by proposing a new and composite indicator that integrates measures for both poverty and environmental outcomes (carbon emissions) into a single variable, the carbon intensity of poverty reduction (CIPR). This variable defines the trade-off between the proportional changes of emissions per capita and of the share of the population above the poverty line. In parallel an analytic framework is developed to formulate propositions concerning the possible effects of growth and inequality on the CIPR. The propositions are tested empirically using data from 135 countries across a 30-year time period (1981–2012). The findings confirm that the carbon intensity of poverty reduction is heterogeneous across countries. This heterogeneity is partly explained by economic growth, which is found to have a negative effect on the CIPR up to a certain income level, defined here as a “turning point”. Above that turning point, economic growth increases the CIPR. By contrast, inequality reduction is shown to have a significant negative effect on the CIPR. This study contributes to the literature on sustainable development by analytically and quantitatively linking its three dimensions (social, economic and environmental) and by employing a composite indicator that directly measures the trade-off between poverty reduction and emission levels across countries.

     

The Variance as a subgroup decomposable measure of inequality

An inequality index is called subgroup decomposable if it can be expressed as a weighted sum of inequality values calculated for population subgroups plus the contribution arising out of differences among subgroup means. Theil (1967) and Shorrocks (1980) pointed out two important requirements for subgroup decomposable inequality indices. Shorrocks (1980) has shown that Theil's mean logarithmic deviation, for which the weights of subgroup terms are respective population shares, is the only relative inequality index that fulfils these two properties. In this paper we show that the variance is the only absolute inequality index to satisfy the population share weighted subgroup decomposability property, which in turn implies that it also meets the two properties suggested by Theil and Shorrocks. A numerical illustration of several inequality indices in also presented in the paper. JEL classification numbers:D31, D63.     

Who Gets Held Back? An Analysis of Grade Retention Using Stratified Frailty Models

Racial/ethnic disparities in grade retention related to structural inequality are investigated using a quantitative theoretical model from the health literature. Data from the Early Childhood Longitudinal Study-Kindergarten Cohort are linked with segregation indices for dissimilarity and poverty interaction derived from the US Census 2000 data estimate the impact of individual and structural level variables on grade retention. Shared frailty models demonstrate that there are racial/ethnic differences in grade retention, much of which can be explained by structural inequality. Students who are white or African American have lower risk in areas with higher dissimilarity and poverty interaction. Parental involvement mediates the risk of retention.

     

Measuring Well-Being Over Time: The Adjusted Mazziotta–Pareto Index Versus Other Non-compensatory Indices

Most of the socio-economic phenomena such as development, well-being, and quality of life have a multidimensional nature and require the definition of a set of individual indicators to be properly assessed. Often, individual indicators are summarized and a composite index is created. One of the main problems in constructing composite indices is the choice of a method which allows time comparisons. In this paper, we consider the Adjusted Mazziotta–Pareto Index, a non-compensatory composite index used by the Italian National Institute of Statistics for measuring “Equitable and Sustainable Well-being” in Italy. An empirical comparison with some traditional non-compensatory indices is presented and an Influence Analysis is, for the first time, performed in order to assess the robustness of the index.     

A New Generalized Variance Approach for Measuring Multidimensional Inequality and Poverty

The paper suggests a new generalized variance concept for measuring multidimensional inequality of a stratified society, based on multivariate statistical methods, where the members of society form a cloud in the oblique space of dimensions of inequality, such as income, expenditure and property. The cloud presents the multidimensional inequality capsulized in the cloud. The goal is to condense all the inequality information embodied by the cloud into a composite compact metric characterizing both the shape and the inner structure of the cloud. Contrary to the conventional literature that considers multidimensionality as a unidimensional weighted combination of the dimensions, our new composite index measures the inequality of the configuration of the points in the cloud. Our aim is twofold. First, we introduce the Inequality Covariance Matrix (ICM) assigned to the cloud, with elements measuring the correlations among dimensions. Having ICM, we propose the Generalized Variance (GV) of ICM to measure the composite Generalized Variance Inequality (GVI) level. Second, to evaluate the stratum-specific structure of the overall inequality, we suggest a new two-stage procedure. In the first stage, we divide the total GVI into between-groups and within-groups effects. Then, in the second stage the contributions of the strata to the within-groups inequality and, the contributions of the dimensions to the between-groups inequality are calculated. This GVI approach is sensitive to the correlation system, decomposable into stratum effects and, the number of dimensions is not limited. Moreover, including the log-dimensions in the analysis, GVI yields an Entropy Covariance Matrix giving a new Generalized Variance Entropy index. Finally, the GVI of censored poverty indicators means multidimensional poverty measurement. This special complex task is not yet solved in the traditional literature so far.

     

A Household-Based Distribution-Sensitive Human Development Index: An Empirical Application to Mexico, Nicaragua and Peru

In measuring human development, one of the main concerns relates to the inclusion of a measure that penalizes inequalities in the distribution of achievements across the population. Using indicators from nationally representative household surveys and census data, this paper proposes a straightforward methodology to estimate a household-based distribution-sensitive human development index aggregated through generalized means. The evidence shows that the losses in human development due to inequality reach up 22, 29 and 57% in Mexico, Peru and Nicaragua, respectively. Among dimensions, the loss in the income index reaches up 61% in Nicaragua, while the education index appears as the most sensitive in the case of Mexico and Peru, with a percentage of loss between 38 and 48%. The importance of household-level calculations is highlighted when we compare the indices computed from the entire distribution with those existing indices computed for quintiles of the distribution, which minimizes the losses due to inequality. Overall, the estimations evidence a higher sensitivity of the index to inequality, and therefore an important space for public action to reduce inequality that could involve positive development returns.     

Aversion to Local Wellbeing Inequality is Moderated by Social Engagement and Sense of Community

Our subjective wellbeing is a mix of our personal and community wellbeing. One indication of their close relationship is the strong negative correlation between our own subjective wellbeing and the degree of subjective wellbeing inequality within our community. This negative relationship reflects our innate and socialized inequality aversion and holds regardless of whether the group is large as in the case of countries or small in the case of local neighbourhoods. While the country case has been well documented in the subjective wellbeing literature, the relationship between the local community distribution of subjective wellbeing and individual subjective wellbeing has received little attention. In this paper we demonstrate the sensitivity of individual life satisfaction to the distribution of life satisfaction within electoral wards in urban New Zealand and explore several possible behavioural drivers. We find that having social support and feeling a sense of community both reduce the negative effects of local subjective wellbeing inequality, while being less socially engaged exaggerates them. Our results highlight the potential that programmes aimed at reducing wellbeing inequalities within local communities might play in raising individual as well as average wellbeing.

     

On Exact Statistical Properties of Multidimensional Indices Based on Principal Components,Factor Analysis,MIMIC and Structural Equation Models

Recent empirical literature has seen many multidimensional indices emerge as well-being or poverty measures, in particular indices derived from principal components and various latent variable models. Though such indices are being increasingly and widely employed, few studies motivate their use or report the standard errors or confidence intervals associated with these estimators. This paper reviews the different underlying models, reaffirms their appropriateness in this context, examines the statistical properties of resulting indices, gives analytical expressions of their variances and establishes certain exact relationships among them.      

A New Multidimensional Measure of Development: The Role of Technology and Institutions

This paper constructs four structural indices by using 42 socioeconomic variables for 129 countries and the 10 years period from 2003 to 2012. Each structural index can be considered as a measure of a certain dimension of development. The first two indices are the most useful in explaining gaps in development across countries. The first captures the role of technology and institutional quality while the second provides a measure of the basic level of development. The contrast between them signifies that the notion of development is not only multidimensional, but also changing with the stage of development. These two indices are combined to form a development index (DI). A comparison of DI to income per capita and the Human Development Index highlights the importance of institutions in the transition of countries from merely having high income to full development. A methodological contribution of the paper is to use a Jackknife approach within the factor analysis routine to test for the significance of the extracted factors/indices.     

Simplifying the Water Poverty Index

In this paper, principal components methodology is used to derive simplified and cost effective indexes of water poverty. Using a well known data set for 147 countries from which an earlier five-component water poverty index comprising of Resources, Access, Capacity, Use and Environment was constructed, we find that a simplified three-component composite index comprising of Access, Capacity, and Environment, with unequal weights, or its two-component counterpart comprising of Capacity and Environment with equal weights, would be more cost-effective to construct without much loss of information. These simplified indexes have high positive and negative correlations with the Human Development Index and the Human Poverty Index, respectively.     

Using Ranked Weights and Acceptability Analysis to Construct Composite Indicators: A Case Study of Regional Sustainable Society Index

A variety of published composite indicators, i.e., Energy Trilemma Index and Sustainable Society Index, are commonly aggregated with equal weights. However, this plausible scheme is criticized as eclecticism and ignores the discriminating power of the different indicators. Differing from the traditional methods that assign weights to each indicator for the purpose of aggregation, this paper proposes a new mechanism to construct composite indicators using ranked weights and stochastic multicriteria acceptability analysis. More specifically, this study comprehensively consider all possible preferences among the indicators. Under each preference, we develop a sophisticated mathematical transformation to calculate the least and most favorable scores of each entity, which formulates the lower and upper bounds of the intervals. Then an interval decision matrix, alternatively described as a stochastic decision problem, is formulated to construct the composite indicators. Holistic acceptability indices are generated and regarded as a new composite indicator, which is capable of providing a comprehensive and robust composite indicator with more discriminating power. We apply the proposed method to modify the regional sustainable society index and present the obtained results and comparisons.     

The Poverty-Growth-Inequality Triangle: Asia 1960s to 2010s

The main objective of this paper is to disentangle the poverty-growth-inequality triangle for Asia, its sub-regions and individual economies by constructing poverty and inequality profiles, decomposing poverty changes and modelling inequality. Due to a shortage of unit record data, analytical techniques are developed for estimating the poverty headcount ratio and regional inequality with minimum data requirements. Analytical results confirm significant reductions in poverty across the board due to fast growth, although the benign effect of growth on poverty was offset by worsening distributions in many economies. Furthermore, the poverty-reducing effect of growth has been diminishing over time and converging to 0 for many countries. Also, the cost of rising inequality in Asia was found to be surprisingly large in terms of missed poverty reduction. Looking ahead, Asia is expected to eradicate abject poverty soon but likely to continue facing high inequality, particularly income gaps between economies.

     

Explaining Accessibility and Satisfaction Related to Healthcare: A Mixed-Methods Approach

Accessibility and satisfaction related to healthcare services are conceived as multidimensional concepts. These concepts can be studied using objective and subjective measures. In this study, we created two indices: a composite healthcare accessibility index (CHCA) and a composite healthcare satisfaction index (CHCS). To calculate the CHCA index we used three indicators based on three components of multidimensional healthcare accessibility: availability, acceptability and accessibility. In the indicator based on the component of accessibility, we included an innovative perceived time-decay parameter. The three indicators of the CHCA index were weighted through the application of a principal components analysis. To calculate the CHCS index, we used three indicators: the waiting time after the patient arrives at the healthcare service, the quality of the healthcare, and the healthcare service supply. These three indicators making up the CHCA index were weighted by applying an analytical hierarchy process. Three kinds of regressions were subsequently applied in order to explain the CHCA and CHCS indices: namely the Linear Least Squares, Ordinal Logistic, and Random Forests regressions. In these regressions, we used different independent social and health-related variables. These variables represented the predisposing, enabling, and need factors of people´s behaviors related to healthcare. All the calculations were applied to a study area: the city of Quito, Ecuador. Results showed that there are health-related inequalities in regard to healthcare accessibility and healthcare satisfaction in our study area. We also identified specific social factors that explained the indices developed. The present work is a mixed-methods approach to evaluate multidimensional healthcare accessibility and healthcare satisfaction, incorporating a pluralistic perspective, as well as a multidisciplinary framework. The results obtained can also be considered as tools for healthcare and urban planners, for more integrative social analyses that can improve the quality of life in urban residents.     

The coefficient of variation: Weighting considerations

Some background notes on inequality indices are presented. Equality is seen not as a distribution in which each cell receives an equal share of a resource but as one in which each share is proportional to a criterion or weighting variable for the cell. Instances are noted where the coefficient of variation has been calculated without full consideration of the weighting variable. This can result in misleading comparisons between distributions. A specially constructed data set illustrates that an unweighted coefficient of variation fails to satisfy the Pigou-Dalton principle of transfers and is therefore invalid as an inequality index.     

A Discrepancy Index for the Study of Participation with an Application to the Case of Higher Education in Italy

This article proposes and applies a simple method to measure the distance from a situation of uniform participation. First, a discrepancy index based on the use of generalized Lorenz curves is presented. This index can be expressed in terms of means and Gini indices of relevant characteristics in the populations of participants and that of a control group. A multivariate extension is also illustrated. The discrepancy index is then used to analyse access into higher education in Italy during the nineties. Discrepancy between participants and non-participants is especially high in terms of parents’ wealth and education, less in terms of income. Also, discrepancy is higher during recessions. Multivariate analysis reveals that “cultural constrains” are more important than financial constraints. Hence, efforts to equalize opportunity for access into higher education should be as much focussed on motivation and social background as they are on financial constraints.

Examining the appropriateness of importance weighting on satisfaction score from range-of-affect hypothesis: hierarchical linear modeling for within-subject data

This study examines the range-of-affect hypothesis in a within-subject context using the weighting situation faced in quality of life (QOL) measurement. Data collected in Wu and Yao’s (2006b) study were used (332 undergraduates at National Taiwan University). The mean age was 19.80 years (std = 1.98). They completed a QOL questionnaire and indicated satisfaction, importance, and perceived have–want discrepancy on 12 life domains. Hierarchical linear modeling with a random-coefficients regression model was applied. At the first level (within-individual level), the satisfaction scores for each item were regressed on the have-want discrepancy, importance, and the interaction between have-want discrepancy and importance (have-want discrepancy ×  importance) of the same item. At the second level (between-individual level), the intercept, coefficients of have-want discrepancy, importance and the interaction between have-want discrepancy and importance at the first level were regarded as varying randomly over all participants. Results of this study supported the range-of-affect hypothesis, showing that the relationship between item have-want discrepancy and item satisfaction is stronger for high importance items than low importance items for a given individual. Implications for important weighting on item satisfaction scores were discussed.