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We document the contribution of skin color toward quantifying inequality of opportunity over a proxy indicator of wealth. Our Ferreira–Gignoux estimates of inequality of opportunity as a share of total wealth inequality show that once parental wealth is included as a circumstance variable, the share of inequality of opportunity rises above 40%, overall and for every age cohort. By contrast, the contribution of skin tone to total inequality of opportunity remains minor throughout.

This paper examines multidimensional poverty in Brazil in 2000 and 2010, based on the microdata of the Demographic Censuses. Our analysis is disaggregated into five classes of municipalities according to their degree of urbanisation and remoteness, highlighting wide rural–urban inequalities in the levels and dynamics of poverty. We compare estimates of traditional monetary poverty with multidimensional poverty measures based on two methods: (i) the Alkire-Foster counting identification approach; and (ii) the Permanyer two-stage poverty identification approach. The two-stage approach introduces the concepts of complementarity/substitutability within and across poverty dimensions, which enables a more precise identification of the population targeted by anti-poverty policies. All methods highlight substantial progress in poverty alleviation. In absolute terms, the reduction in the incidence of multidimensional poverty was significantly larger in the initially poorest areas—rural and intermediate municipalities, as well as those in the North and North–East regions. Important advances were made in standard of living, especially in the access to electricity, durable consumer goods and private bathroom in the households in rural and intermediate municipalities. However, remote municipalities remain relatively poorer from any perspective, facing more difficulties in reducing monetary poverty.

Some socioeconomic indicators can be represented in alternative ways. For example, as either attainments (e.g. child survival rates) or shortfalls (e.g. child mortality rates) if the variables are bounded. The literature has long been concerned with the consistency of inequality comparisons across such alternative representations. The case of bounded variables and their two alternative representations (attainments versus shortfalls) has been largely settled. This paper addresses the extent of the consistency problem in inequality comparisons involving ratio indicators which also have two potential representations (e.g. number of people per room or number of rooms per capita in the case of overcrowding). First, we probe welfare comparisons based on the generalised Lorenz curve and find that consistency can be secured in the presence of rank dominance. Second, we show that robust inequality comparisons based on all possible Zoli partial orderings (which include all relative and absolute inequality partial orderings, among others) are inconsistent across alternative representations of ratios. Third, with the identification of a class of inequality indices based on the ratio of the harmonic to the arithmetic mean, we show that complete orderings consistent across alternative representations of ratios do exist. Then we consider and ponder the pros and cons of three alternative solutions: defending one representation, using inequality indices that combine both representations, and functional transformations of the ratio variable. We find that the costs of these alternatives render them inferior to the class of indices based on the harmonic and arithmetic means. Both the consistency problem and its preferred proposed solution are illustrated with an empirical study of intergenerational changes in overcrowding inequality in Mexico.

The last few years have witnessed an increasing emphasis on going beyond GDP per capita when measuring a nation’s quality of life. Countries (e.g. UK, France, Canada, Germany, Italy, Japan, Korea, Spain) and international organizations (e.g. OECD) have been developing methods suitable for non-income indicators. However, this involves serious measurement challenges due to: (a) multidimensionality, and (b) ordinality (i.e. unlike income these indicators do not have a natural scale). This paper is the first summary of the methods developed in the last decade in the field of inequality and welfare measurement to address these challenges. Next, we utilize the presented methodology and provide evidence on the ranking of OECD countries in terms of welfare and inequality in education and happiness. We find that when dimensions are analysed separately, welfare dominance is frequent (42% of all comparisons in education and 31% in life satisfaction). The number drops to only 4.4% for bivariate dominance, which highlights the empirical relevance of multidimensional analysis. Greece, Portugal and Hungary feature the lowest joint welfare. Northern European countries are most often dominating and Southern European countries are most often dominated in both inequality and welfare analyses.

The notion of social inequality lends itself to different understandings. One of them is the measurement of inequality over non-monetary dimensions of well-being. The companion Chapter 17 in this Handbook by Lasso de la Vega discusses theoretically the methods to measure inequality when variables are ordinal, and the methods for inequality measurement with bounded continuous variables. The present authors provide empirical illustrations of research implementing this method. Another understanding of social inequality refers to inequality in an indicator of interest between or across socioeconomic groups. The authors explore several methods proposed for this latter purpose and provide empirical illustration.

We examine the performance of asymptotic inference as well as bootstrap tests for the Alphabeta and Kobus&ndash, Miłoś family of inequality indices for ordered response data. We use Monte Carlo experiments to compare the empirical size and statistical power of asymptotic inference and the Studentized bootstrap test. In a broad variety of settings, both tests are found to have similar rejection probabilities of true null hypotheses, and similar power. Nonetheless, the asymptotic test remains correctly sized in the presence of certain types of severe class imbalances exhibiting very low or very high levels of inequality, whereas the bootstrap test becomes somewhat oversized in these extreme settings.

International audience; The distinction between effort and other factors, such as family background, matters for correcting policies and normative reasons when we appeal to inequality of opportunity. We take advantage of a purposefully designed survey on secondary schools in rural Bangladesh to offer a comprehensive view of the importance of overall effort when measuring inequalities of opportunity in education. The analysis comprises decomposition exercises of the predicted variance of student performance in mathematics and English by source (effort, circumstances, etc.) and subgroup (within- and between-schools) based on parametric estimates of educational production functions. Pupils’ effort, preferences, and talents contribute between 31% and 40% of the total predicted variances in performance scores. The contribution of overall effort falls by 10% when the correlation between effort and circumstances is taken into account. These findings are robust to the choice of estimation strategy (i.e. combined within- and between-schools variation models versus multilevel random-effect models). All in all, these results advocate that social determinism in education can be mitigated by individual effort at school.

Mexico is a country with high levels of inequality and low intergenerational social-mobility rates for those located at the bottom extremes of the wealth distribution. Although such low rates suggest that at least a share of the observed income inequality may be due to an unequal distribution of opportunities, this conjecture has not been thoroughly tested in the literature. The present article fills this gap estimating the lower bound of the contribution of unequal opportunities to income and wealth inequality in Mexico, with an operationalization of the “ex-ante” approach to the measurement of inequality of opportunity. Relying on a national representative survey designed for the analysis of social mobility, namely, the ESRU Survey on Social Mobility in Mexico (2011), we are able to define a broad set of circumstance groups (“types”), encompassing the wealth of the household of origin. This available information reduces the omitted variable bias of previous estimations and allows for a better account of the role of inequality of opportunity in income inequality. Our results show that the lower bound of the contribution of unequal opportunities to total income inequality and total wealth inequality is around 30 per cent, which is substantially higher than previous estimations for Mexico and ranks among the highest values in Latin America.

The multidimensional nature of wellbeing is now the widely accepted approach in frontier research on poverty, inequality and policy analysis. However, significant challenges and disagreement remain...

A recent literature on inequality of opportunity offers quantitative tools for comparisons and measurement based on stochastic dominance criteria and traditional inequality indices. In this paper I suggest an additional way of assessing inequality of opportunity with two indices of dissimilarity across distributions. The indices are based on a traditional homogeneity test of multinomial distributions and are similar to the square coefficient of variation (Reardon and Firebaugh, Sociol Method 32:33–67, 2002). Their properties are studied, as well as their usefulness and limitations in applications when both circumstances and advantages/outcomes are multidimensional. An empirical application measures changes in inequality of opportunity from an old to a young cohort in Peru. The importance of assessing the sensitivity of the results to group definitions and group proportions is highlighted.

Most non-monetary development indicators are bounded and many of them are presented in terms of either attainments or shortfalls. Whether an absolute approach or a relative approach should be undertaken to assess cross-country convergence of these indicators has been a subject of debate. Revisiting this debate, we provide three arguments explaining why a relative approach is misleading and, instead, an absolute approach is more appropriate. We assess the presence of absolute convergence across countries in several non-monetary development indicators by applying a number of absolute inequality indices. Although we find numerous instances of absolute convergence, these are rarely robust to alternative specifications of indices. We additionally contribute to the available methodological toolkit of convergence analysis by employing absolute-Lorenz curves to assess the robustness of absolute cross-country convergence, which is rarely conducted in the literature, and never to date with absolute-Lorenz curves. We also clarify the relationship between different relevant notions of egalitarian progress and elucidate how progress in these indicators relates to changes in their convergence using absolute Lorenz curves.

Dissimilarity indices quantify the differences between conditioned probability distributions of categorical variables. Traditionally they have been used to study social segregation in labor markets, housing, and school districts. Recently they have also been used to measure “horizontal” inequalities—that is, inequalities between groups—and inequality of opportunity concepts. The current methodological literature provides indices for unordered categorical variables and different indices suitable for ordered variables. Keywords: inequality; quantitative methods; stratification and inequality

Most methods for the analysis of distributional change rely on the changes in the income of a particular group of people, taking either the situation of this group in the previous period, or the average change in the population, as reference point. By contrast, we propose a measure of distributional change based on the comparison of a group’s wellbeing standard against a richer group, thereby capturing a notion of change in relative income, which embodies the influence of others’ wellbeing on the judgment of the group’s own situation. The indices, and related relative income change (RIC) curves, are based on ratios of generalized mean incomes between two groups, which render them closely related to Zenga’s inequality measures and Lorenz curve comparisons, when arithmetic means are used. We consider both relative and absolute income cut-offs for the group partitions. Differences and similarities between our measures of relative income change and the Growth Incidence Curve are also discussed. These are highlighted in an empirical illustration on European countries.

When measuring poverty with counting measures, it is worth inquiring into the conditions prompting poverty reduction which not only reduce the average poverty score further but also decrease deprivation inequality among the poor, thereby emphasizing improvements among the poorest of the poor. For comparisons of cross-sectional datasets of the same society in dierent

A long literature on inter-distributional inequality (IDI) has developed statistical tools for measuring the extent of inequality between two groups (e.g. men versus women). Firstly, I introduce the property of group-specific disadvantage focus (GDF). Indices satisfying this property are only sensitive to inequalities that are disadvantageous to one specific group. Then the paper reviews some of the most prominents IDI indices proposed in the last four decades. The assessment focuses on whether these indices satisfy GDF and, if not, how they react to inequalities that are disadvantageous to different groups. I also discuss whether these indices are informative, or not, regarding other interesting features related to IDI comparisons, e.g. distributional equality, absence of distributional overlap and presence of first-order stochastic dominance. Finally, I propose amendments to several of these indices in order to render them in fulfillment of GDF and more informative on the mentioned distributional features.

Purpose – We propose applying Reardon's approach to the measurement of ordinal segregation to the study of inequality in life chances in the case of ordinal variables. We also propose additional measures of inequality in life chances in such a case. Methodology – We state the desirable properties of measures of inequality in life chances when the variable under study is ordinal and check which properties are fulfilled by the various indices examined in this chapter. Findings – All the indices defined in this chapter seem suitable for the analysis of inequality in life chances with ordinal variables but we found some trade-off between indices fulfilling the population composition invariance and those fulfilling the group replication invariance. Originality – Besides extending the indices suggested by Reardon to the study of inequality of life chances, we propose, to analyze this issue, two additional sets of indices based on the notion of distributional dissimilarity.