This study has been prepared within the OPHI themes on missing dimensions and multidimensional measurement.

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This book, which was first published in 1973, presents a systematic treatment of the conceptual framework as well as the practical problems of the measurement of economic inequality. Alternative approaches are evaluated in terms of their philosophical assumptions, economic content, and statistical requirements. In a new annexe added in 1997, which is as large as the original book, Amartya Sen, jointly with James Foster, critically surveys the literature that followed the publication of the first edition of the book, and evaluates the main analytical issues in the appraisal of economic inequality and poverty. The technical and non‐technical sections of the book are not presented separately, but it is possible to skip or skim through the formal sections and go directly from the intuitive presentation of the axioms to the intuitive explanation of the results.

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Background: Human milk is a complex fluid comprised of myriad substances, with one of the most abundant substances being a group of complex carbohydrates referred to as human milk oligosaccharides (HMOs). There has been some evidence that HMO profiles differ in populations, but few studies have rigorously explored this variability.Objectives: We tested the hypothesis that HMO profiles differ in diverse populations of healthy women. Next, we examined relations between HMO and maternal anthropometric and reproductive indexes and indirectly examined whether differences were likely related to genetic or environmental variations.Design: In this cross-sectional, observational study, milk was collected from a total of 410 healthy, breastfeeding women in 11 international cohorts and analyzed for HMOs by using high-performance liquid chromatography.Results: There was an effect of the cohort (P < 0.05) on concentrations of almost all HMOs. For instance, the mean 3-fucosyllactose concentration was >4 times higher in milk collected in Sweden than in milk collected in rural Gambia (mean ± SEM: 473 ± 55 compared with 103 ± 16 nmol/mL, respectively; P < 0.05), and disialyllacto-N-tetraose (DSLNT) concentrations ranged from 216 ± 14 nmol/mL (in Sweden) to 870 ± 68 nmol/mL (in rural Gambia) (P < 0.05). Maternal age, time postpartum, weight, and body mass index were all correlated with several HMOs, and multiple differences in HMOs [e.g., lacto-N-neotetrose and DSLNT] were shown between ethnically similar (and likely genetically similar) populations who were living in different locations, which suggests that the environment may play a role in regulating the synthesis of HMOs.Conclusions: The results of this study support our hypothesis that normal HMO concentrations and profiles vary geographically, even in healthy women. Targeted genomic analyses are required to determine whether these differences are due at least in part to genetic variation. A careful examination of sociocultural, behavioral, and environmental factors is needed to determine their roles in this regard. This study was registered at clinicaltrials.gov as NCT02670278.

Multidimensional measures provide an alternative lens through which poverty may be viewed and understood. In recent work we have attempted to offer a practical approach to identifying the poor and measuring aggregate poverty (Alkire and Foster 2011). As this is quite a departure from traditional unidimensional and multidimensional poverty measurement -particularly with respect to the identification step -further elaboration may be warranted. In this paper we elucidate the strengths, limitations, and misunderstandings of multidimensional poverty measurement in order to clarify the debate and catalyse further research. We begin with general definitions of unidimensional and multidimensional methodologies for measuring poverty. We provide an intuitive description of our measurement approach, including a 'dual cutoff' identification step that views poverty as the state of being multiply deprived, and an aggregation step based on the traditional FGT measures. We briefly discuss five characteristics of our methodology that are easily overlooked or mistaken and conclude with some brief remarks on the way forward.Keywords: poverty measurement, multidimensional poverty, deprivation, FGT measures, decomposability, joint distribution, axioms. This publication is copyright, however it may be reproduced without fee for teaching or non-profit purposes, but not for resale. Formal permission is required for all such uses, and will normally be granted immediately. For copying in any other circumstances, or for re-use in other publications, or for translation or adaptation, prior written permission must be obtained from OPHI and may be subject to a fee. JEL classification: I3, I32, D63, O1

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Several recent studies have suggested that the distribution of income (earnings, jobs) is becoming more polarized. Much of the evidence presented in support of this view consists of demonstrating that the population share in an arbitrarily chosen middle income class has fallen. However, such evidence can be criticized as being range-specific -depending on the particular cutoffs selected. In this paper we propose a range-free approach to measuring the middle class and polarization, based on partial orderings. The approach yields two polarization curves which, like the Lorenz curve in inequality analysis, signal unambiguous increases in polarization. It also leads to an intuitive new index of polarization that is shown to be closely related to the Gini coefficient. We apply the new methodology to income and earnings data from the US and Canada, and find that polarization is on the rise in the US but is stable or declining in Canada. A cross-country comparison reveals the US to be unambiguously more polarized than Canada.