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Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality
, 1998
"... We derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare and inequality. This includes estimators of most of the poverty indices currently in use, as well as estimators of the curves used to infer stochastic dominance ..."
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Cited by 212 (32 self)
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We derive the asymptotic sampling distribution of various estimators frequently used to order distributions in terms of poverty, welfare and inequality. This includes estimators of most of the poverty indices currently in use, as well as estimators of the curves used to infer stochastic dominance of any order. These curves can be used to determine whether poverty, inequality or social welfare is greater in one distribution than in another for general classes of indices. We also derive the sampling distribution of the maximal poverty lines (or income censoring thresholds) up to which we may con dently assert that poverty or social welfare is greater in one distribution than in another. The sampling distribution of convenient estimators for dual approaches to the measurement ofpoverty is also established. The
The income component of the human development index
 Journal of Human Development
"... Issues and r esear ch strategies Human beings as ends and means The overarching understanding that has motivated the Human Development Reports (United Nations Development Programme, several years) since their inception in 1990 is the elementary recognition that human beings are the primary ends as ..."
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Cited by 53 (0 self)
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Issues and r esear ch strategies Human beings as ends and means The overarching understanding that has motivated the Human Development Reports (United Nations Development Programme, several years) since their inception in 1990 is the elementary recognition that human beings are the primary ends as well as the principal means of development. These two aspects of the ‘human ’ side of development are related but quite distinct, and recognizing the special demands of each is important for analytical clarity in this dif�cult subject. As it happens, both these roles were typically neglected in the analyses of growth and development that came into fashion in the years following the Second World War. Both needed correction, but they called for rather different types of recti�cation. The rhetoric on ‘the importance of human elements ’ in the process of development often confounds the disparate demands of the two emendations, each important in their own right, but
Aggregate Poverty Measures
 36 Dynamics in Algeria By Laabas Belkacem, Ph.D
, 1997
"... Abstract. The way poverty is measured is important for an understanding of what has happened to poverty as well as for antipoverty policy evaluation. Sen’s (1976) pathfinding work has motivated many researchers to focus on the way poverty should be measured. A poverty measure, argued by Sen, should ..."
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Cited by 37 (2 self)
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Abstract. The way poverty is measured is important for an understanding of what has happened to poverty as well as for antipoverty policy evaluation. Sen’s (1976) pathfinding work has motivated many researchers to focus on the way poverty should be measured. A poverty measure, argued by Sen, should satisfy certain properties or axioms and the desirability of a poverty measure should be evaluated by these axioms. During the last two decades, many researchers have adopted the axiomatic approach pioneered by Sen to propose additional axioms and develop alternative poverty measures. The objective of this survey is to provide a clarification on the extensive literature of aggregate poverty measures. In this survey, we first examine the desirability of each axiom, the properties of each poverty measure, and the interrelationships among axioms. The desirability of an axiom cannot be evaluated in isolation, and some combination of axioms may make it impossible to devise a satisfactory poverty measure; some axioms can be implied by other axioms combined and so are not independent; some others are ad hoc and are disqualified as axioms for poverty measurement. Based on the interactions among axioms, we identify the ‘core ’ axioms which together have a strong implication on the functional form of a poverty measure. We then review poverty measures that have appeared in the literature, evaluating the interrelationships among different measures, and examining the properties of each measure. The axioms each measure satisfies�violates are also summarized in a tabular form. Several ‘good ’ poverty measures, which have not been documented by previous surveys, are also included.
An axiomatic characterization of the Theil measure in income inequality
 Journal of Economic Theory
, 1983
"... This paper provides a characterization of a frequently used measure of income inequality. It has been known for some time that the Theil measure of income inequality (1) is consistent with the Lorenz criterion, when it applies, and (2) exhibits a simple and empirically useful decomposition by popula ..."
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Cited by 22 (1 self)
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This paper provides a characterization of a frequently used measure of income inequality. It has been known for some time that the Theil measure of income inequality (1) is consistent with the Lorenz criterion, when it applies, and (2) exhibits a simple and empirically useful decomposition by population subgroup into withingroup and betweengroup terms. The major theorem establishes the converse: the decomposability property defines the Theil measure uniquely (up to a positive multiple) among all Lorenzconsistent measures. Journal of Economic Literature Classification Number: 024. I.
has the literature on Gini’s index evolved in the past 80 years? Working paper
, 2003
"... Peking University for his encouragement and suggestions, and Zhiyong Huang, a student at Nan Kai University for correcting some errors in the earlier draft of this paper. In addition to what have been written here, the original plan also includes two sections on the generalization and statistical in ..."
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Cited by 9 (0 self)
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Peking University for his encouragement and suggestions, and Zhiyong Huang, a student at Nan Kai University for correcting some errors in the earlier draft of this paper. In addition to what have been written here, the original plan also includes two sections on the generalization and statistical inferences of the Gini index. This would make this paper too lengthy. The author chooses to leave those topics in another survey paper. A brief survey of this kind always runs the risk of inevitable omissions. The author wishes to thank all authors, cited and uncited, for their contributions to this large and significant literature. 1 The Gini coefficient or index is perhaps one of the most used indicators of social and economic conditions. From its first proposal in English in 1921 to the present, a large number of papers on the Gini index has been written and published. Going through these papers represents a demanding task. The aim of this survey paper is to help the reader to navigate through the major developments of the literature and to incorporate recent theoretical research results with a particular focus on different formulations and interpretations of the Gini index, its social welfare implication, and source and subgroup decomposition. 2 1
A general approach to sparse basis selection: Majorization, concavity, and affine scaling
 IN PROCEEDINGS OF THE TWELFTH ANNUAL CONFERENCE ON COMPUTATIONAL LEARNING THEORY
, 1997
"... Measures for sparse best–basis selection are analyzed and shown to fit into a general framework based on majorization, Schurconcavity, and concavity. This framework facilitates the analysis of algorithm performance and clarifies the relationships between existing proposed concentration measures use ..."
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Cited by 9 (5 self)
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Measures for sparse best–basis selection are analyzed and shown to fit into a general framework based on majorization, Schurconcavity, and concavity. This framework facilitates the analysis of algorithm performance and clarifies the relationships between existing proposed concentration measures useful for sparse basis selection. It also allows one to define new concentration measures, and several general classes of measures are proposed and analyzed in this paper. Admissible measures are given by the Schurconcave functions, which are the class of functions consistent with the socalled Lorentz ordering (a partial ordering on vectors also known as majorization). In particular, concave functions form an important subclass of the Schurconcave functions which attain their minima at sparse solutions to the best basis selection problem. A general affine scaling optimization algorithm obtained from a special factorization of the gradient function is developed and proved to converge to a sparse solution for measures chosen from within this subclass.
Absolute and Relative Deprivation and the Measurement of Poverty
, 2003
"... This paper develops the link between poverty and inequality by focussing on a class of poverty indices (some of them wellknown) which aggregate normative concerns for absolute and relative deprivation. The indices are distinguished by a parameter value that captures the ethical sensitivity of pover ..."
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Cited by 8 (1 self)
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This paper develops the link between poverty and inequality by focussing on a class of poverty indices (some of them wellknown) which aggregate normative concerns for absolute and relative deprivation. The indices are distinguished by a parameter value that captures the ethical sensitivity of poverty measurement to “exclusion” or “relativedeprivation” aversion. The indices can be readily used to predict the impact of growth on poverty. An illustration using LIS data finds that the United States show more relative deprivation than Denmark and Belgium whatever the percentiles considered, but that overall deprivation comparisons of the four countries considered will generally depend on the intensity of the ethical concern for relative deprivation. The impact of growth on poverty also depends on the presence of and on the attention granted to concerns over relative deprivation.
Restricted and Unrestricted Dominance for Welfare, Inequality and Poverty Orderings
 DEPARTMENT OF ECONOMICS, UNIVERSITÉ LAVAL
, 2002
"... This paper extends the previous literature on the ethical links between the measurement of poverty, social welfare and inequality. We show inter alia, how, when the range of possible poverty lines is unbounded above, a robust ranking of absolute poverty may be interpreted as a robust ranking of so ..."
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Cited by 7 (2 self)
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This paper extends the previous literature on the ethical links between the measurement of poverty, social welfare and inequality. We show inter alia, how, when the range of possible poverty lines is unbounded above, a robust ranking of absolute poverty may be interpreted as a robust ranking of social welfare, and a robust ranking of relative poverty may be interpreted as a robust ranking of inequality, and this, for any order of stochastic dominance.
ON THE DESIGN OF EQUALOPPORTUNITY POLICIES
"... We study in this paper mechanisms to construct equalopportunity policies for resource allocation. In a model where individuals enjoy welfare as a function of the e�ort they expend, and the amount of a socially provided resource they consume, the aim is to allocate the social resource so that the in ..."
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Cited by 6 (1 self)
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We study in this paper mechanisms to construct equalopportunity policies for resource allocation. In a model where individuals enjoy welfare as a function of the e�ort they expend, and the amount of a socially provided resource they consume, the aim is to allocate the social resource so that the inequality of welfare across individuals at the same relative e�ort level is minimized. In doing so, and as opposed to other existing mechanisms for the design of equalopportunity policies, we account for the hypothetical relative deprivation among equallydeserving individuals. Besides studying these mechanisms generically, we analyze their performance in the context of the delivery of health care resources.
Measuring inequalities without linearity in envy: Choquet integral for symmetric capacities
 Journal of Economic Theory
, 2002
"... The (generalized) Gini indices rely on the social welfare function of a decision maker who behaves in accordance with Yaari’s model, with a function f that transforms frequencies. This SWF can also be represented as the weighted sum of the welfare of all the possible coalitions in the society, where ..."
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Cited by 6 (0 self)
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The (generalized) Gini indices rely on the social welfare function of a decision maker who behaves in accordance with Yaari’s model, with a function f that transforms frequencies. This SWF can also be represented as the weighted sum of the welfare of all the possible coalitions in the society, where the welfare of a coalition is defined as the income of the worstoff member of that coalition. We provide a set of axioms (Ak) and prove that the three following statements are equivalent: (i) the decision maker respects (Ak), (ii) f is a polynomial of degree k, (iii) the weight of all coalitions with more than k members is equal to zero. Journal of Economic Literature Classification Number: D63