Income inequality games

The paper explores different applications of the Shapley value for either inequality or poverty measures. We first investigate the problem of source decomposition of inequality measures, the so-called additive income sources inequality games, based on the Shapley value, introduced by Chantreuil and Trannoy (1999) and Shorrocks (1999). We show that multiplicative inequality games provide dual results compared with Chantreuil and Trannoy’s ones. We also investigate the case of multiplicative poverty games for which indices are non additively decomposable in order to capture contributions of sub-indices, which are multiplicatively connected with, as in the Sen-Shorrocks-Thon poverty index. We finally show, in the case of additive poverty indices, that the Shapley value may be equivalent to traditional methods of decomposition such as subgroup consistency and additive decomposition.     

Constructing indices of multivariate polarization

Multivariate indices of polarization are constructed to measure effects of non-income attributes like wealth and education. Polarization is considered as the presence of groups which are internally homogeneous, externally heterogeneous, and of similar size. We propose a class of polarization indices which is built from measures of relative groups size and from decomposable indices of socio-economic inequality. For the latter, we employ the special inequality indices of Maasoumi (Econometrica 54:991–997, 1986), Tsui (J Econ Theory 67:251–265, 1995; Soc Choice Welf 16:145–157, 1999) and Koshevoy and Mosler (J Multivar Anal 60:252–276, 1997). Then, postulates for multidimensional polarization measurement are stated and discussed. The approach is illustrated by an empirical application to the population of the East and West Germany with polarization defined on income and education.     

Empirical issues in lifetime poverty measurement

Recently there has been increased interest in developing methods for measuring poverty in a way that takes into account the lifetime experience of individuals. We analyze some specific proposals that take the so-called spells approach and consider how they differ in the manner in which they address issues of lifetime poverty, most notably the measurement of chronic poverty. Comparing these specific measures by applying them to a US panel data set, we provide important insights for further research in conceptualizing and measuring lifetime poverty.     

Developing a child-focused and multidimensional model of child poverty for South Africa

This paper presents a new method of measuring child poverty in South Africa, based on a theoretically sound distinction between the conceptualization, definition, measurement, and enumeration of poverty. Conceptual frameworks, definitions, and measurements of poverty are briefly reviewed in the international and South African contexts. This paper presents a child-centered, multidimensional model of child poverty with both absolute and relative poverty components. The absolute core of this model follows the Copenhagen Declaration and includes basic needs such as food and shelter. This is complemented by a relative component, using a multidimensional conceptualization of poverty, and based on a child's ability to participate fully in South African society. The dimensions, or domains of deprivation, for both absolute core and relative aspects can be the same; eight exemplar domains are presented here. Located between the model's relative and absolute components and equally relevant to both components is found a ring of indicators relating to access to good-quality services. We argue that relative poverty can be defined both by consensually agreed upon necessities for societal inclusion and by research-delineated child needs. This approach, while presenting challenges for measurement, will provide policy makers with a better evidence base for combating child poverty.     

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.     

The Foster–Greer–Thorbecke (FGT) poverty measures: 25 years later

Twenty-five years ago, the FGT class of decomposable poverty measures was introduced in Foster, Greer, and Thorbecke (Econometrica 52:761–776, 1984). The present study provides a retrospective view of the FGT paper and the subsequent literature, as well as a brief discussion of future directions. We identify three categories of contributions: to measurement, to axiomatics, and to application. A representative subset of the literature generated by the FGT methodology is discussed and grouped according to this taxonomy. We show how the FGT paper has played a central role in several thriving literatures and has contributed to the design, implementation, and evaluation of prominent development programs; the breadth of its impact is evidenced by the many topics beyond poverty to which its methodology has been applied. We conclude with a selection of prospective research topics.     

Measuring opportunity inequality with monetary transfers

In this paper I consider the problem of measuring opportunity inequality when monetary transfers are possible. First, I consider the case in which agents have common evaluations (or identical preferences), as in the previous literature. I then propose an extension to the heterogeneous case. In both cases I identify an appropriate egalitarian benchmark relative to which inequality can be measured, and I establish that this yields a theory of measurement analogous to that of income inequality. Consequently, the introduction of money (or an infinitely divisible commodity) avoids the difficulty reported in Ok (J Econ Theory 77:300–329, 1997). The results of the paper are immediately applicable to the measurement of multidimensional economic inequality including economies with indivisible goods.     

Poverty measurement: the critical comparison value

The Foster–Greer–Thorbecke (FGT) family of poverty-measures is commonly used when comparing income distributions with respect to poverty. Within this framework, the poverty ranking will be sensitive to the choice of poverty aversion parameter (defining a particular FGT poverty-measure). If we content ourselves with applying a few specific parameter values, then we may demand too little in order to claim robustness in our poverty comparisons. On the other hand, we may demand too much if we only work with FGT poverty-measure quasi orderings established by considering every possible parameter value. An alternative approach may be to report the number of parameter values representing possible reversal points in our poverty ranking—what we call critical comparison values—and leave the final evaluative step to the relevant decision-makers. By applying a generalized version of Descartes’ Rule of Signs, we show that the number of critical comparison values depends on the number of times the cumulative distribution functions intersect.

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An Extension of a Measure of Polarization, with an application to the income distribution of five OECD countries

We introduce an extension of the Esteban and Ray [Econometrica, 62:819–851 1994] measure of polarization that can be applied to density functions. As a by-product we also derive the Wolfson [Am. Econ. Rev., 84:353–358 1994] measure as a special case. This derivation has the virtue of casting both measures in the context of a (statistically) unified framework. We study the polarization of the distribution of household income for five OECD countries (LIS database): US, UK, Canada, Germany and Sweden. The present paper is essentially based on Esteban, Gradín and Ray [9], published as #218 in the working papers series of the Luxembourg Income Study. Changes have been kept to a minimum. We have provided a brief reference to the literature on polarization measurement that has appeared since then and have updated the data of our application.     

Non-Governmental and Not-for-Profit Organizational Effectiveness: A Modern Synthesis

NGO/NPO effectiveness remains a prominent concern for scholars and practitioners, but the literature on this issue is increasingly fragmented along disciplinary lines. We address this problem by presenting a comprehensive and interdisciplinary review of the literature on NGO and NPO effectiveness using citation analysis. In order to uncover commonalities across disciplines concerned with similar questions, we deploy a structured literature review using snowball sampling within citation networks. This approach limits author biases, fosters an interdisciplinary perspective, and adds a different methodological approach to conventional content-based literature reviews. Our review uncovers three trends: (1) there is broad scholarly consensus that unidimensional measures of effectiveness are not useful—even though such measures are commonly used by NGO/NPO rating agencies; (2) the scholarship on NGO/NPO effectiveness is dominated by conceptual works, while empirical studies remain rare; (3) a consensus on how to operationalize effectiveness remains elusive. These results suggest that progress in our understanding of NGO/NPO effectiveness requires enhanced efforts at crossing disciplinary divides, adding empirical analyses, and increasing attention to develop shared categories and methodologies.     

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     

Multidimensional poverty indices

This paper explores the axiomatic foundation of multidimensional poverty indices. Departing from the income approach which measures poverty by aggregating shortfalls of incomes from a pre-determined poverty-line income, a multidimensional index is a numerical representation of shortfalls of basic needs from some pre-specified minimum levels. The class of subgroup consistent poverty indices introduced by Foster and Shorrocks (1991) is generalized to the multidimensional context. New concepts necessary for the design of distribution-sensitive multidimensional poverty measures are introduced. Specific classes of subgroup consistent multidimensional poverty measures are derived based on sets of reasonable axioms. This paper also highlights the fact that domain restrictions may have a critical role in the design of multidimensional indices. Received: 1 March 1999/Accepted: 1 August 2000     

The Measurement of Multidimensional Poverty

Many authors have insisted on the necessity of defining poverty as a multidimensional concept rather than relying on income or consumption expenditures per capita. Yet, not much has actually been done to include the various dimensions of deprivation into the practical definition and measurement of poverty. Existing attempts along that direction consist of aggregating various attributes into a single index through some arbitrary function and defining a poverty line and associated poverty measures on the basis of that index. This is merely redefining more generally the concept of poverty, which then essentially remains a one dimensional concept. The present paper suggests that an alternative way to take into account the multi-dimensionality of poverty is to specify a poverty line for each dimension of poverty and to consider that a person is poor if he/she falls below at least one of these various lines. The paper then explores how to combine these various poverty lines and associated one-dimensional gaps into multidimensional poverty measures. An application of these measures to the rural population in Brazil is also given with poverty defined on income and education.     

Ecological Validity and Age-Related Change in Emotion Recognition

Isaacowitz and Stanley (Journal of Nonverbal Behavior, 2011) argue that typical measures of emotion recognition used to compare young and older adults—still photos—lack ecological validity. There are many aspects to this argument. In this commentary, I address the main points raised by Isaacowitz and Stanley and argue that they raise a number of valid and interesting points. Nevertheless, I believe that recognition of emotion in still photos provides important information about young-old differences, and has sufficient ecological validity to explain age differences in a number of social insights.     

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.     

Using ordinal variables to measure multidimensional poverty in Egypt and Jordan

This paper examines the empirical relevance of recent methodological refinements to the “counting approach” to multidimensional poverty measurement. It provides an empirical illustration based on data available in the Demographic and Health Surveys of Egypt and Jordan. The paper relies on the general framework proposed by Silber and Yalonetzky (2013) to compare multidimensional poverty measures, such as the Multidimensional Poverty Index (MPI) and others that are sensitive to the distribution of deprivation counts among individuals. It thus computes the measures introduced by Chakravarty and D’Ambrosio, 2006 and Rippin (2010) as well as indices based on the extension of the Aaberge and Peluso (2012), suggested by Silber and Yalonetzky (2013). It appears that it is useful to consider several multidimensional poverty measures when analyzing national poverty trends and when making a distinction between urban and rural areas.     

What’s so special about Euclidean distance?

In this paper, we provide an application-oriented characterization of a class of distance functions monotonically related to the Euclidean distance in terms of some general properties of distance functions between real-valued vectors. Our analysis hinges upon two fundamental properties of distance functions that we call “value-sensitivity” and “order-sensitivity”. We show how these two general properties, combined with natural monotonicity considerations, lead to characterization results that single out several versions of Euclidean distance from the wide class of separable distance functions. We then discuss and motivate our results in two different and apparently unrelated application areas—mobility measurement and spatial voting theory—and propose our characterization as a test for deciding whether Euclidean distance (or some suitable variant) should be used in your favourite application context. We would like to thank an editor and especially two anonymous referees for very useful comments which helped us to improve the paper substantially.     

The measurement of gender wage discrimination: the distributional approach revisited

This paper presents the advantages of taking into account the distribution of the individual wage gap when analyzing female wage discrimination. Several limitations of previous approaches such as the classic Oaxaca–Blinder and the recent distributive proposals using quantile regressions or counterfactual functions are thoroughly discussed. The methodology presented here relies on Jenkins’ (J Econom 61:81–102, 1994) work and supports the use of poverty and deprivation literature techniques that are directly applicable to the measurement of discrimination. In an empirical illustration, we quantify the relevance of the glass ceiling and sticky floor phenomena in the Spanish labor market.     

A model based approach for predicting annual poverty rates without expenditure data

The primus inter pares of the UN-approved Millennium Development Goals is to reduce poverty. The only internationally accepted method of estimating poverty requires a measurement of total consumption based on a time-consuming and resource-demanding measure of household expenditure in an integrated survey over 12 months. Rather than measuring poverty, say, only every fifth year, a model is presented to predict poverty based on a small set of household variables to be collected annually between two 12-monthly household surveys. Information obtained from these “light” surveys might then be used to predict poverty rates. The key question is whether the inaccuracy in these predictions is acceptable. It is recommended that these models be tested at a country level and if the test results are similar to those found here, that this approach be adopted.      

Multidimensional time and income poverty: well-being gap and minimum 2DGAP poverty intensity – German evidence

This paper focuses on interdependent multidimensional poverty of time and income with its incidence and intensity. We introduce a Two Dimensional Minimum Poverty Gap (2DGAP) measure, which quantifies the shortest path to escape multidimensional poverty. The 2DGAP disentangles single poverty attribute gaps while assuring their interdependence; an important issue for targeted antipoverty policies. Besides income, we include genuine personal leisure time with social participation reflecting Sen’s capability approach. The interdependence of multidimensional poverty is estimated by a CES-type well-being function with individual German data. The empirical results of Germany’s “working poor” emphasize the importance of time with social participation aspects in the multidimensional poverty discussion.