Poverty orderings: A graphical illustration

This note graphically illustrates the power of various poverty ordering conditions. Using the Kolm three-person simplex, we are able to show that (1) for a fixed poverty line the power may be increased as higher degrees of stochastic dominance are considered, (2) for a single but variable poverty line the power is reduced as the line increases, and (3) for a range of poverty lines the power of the third degree ordering condition may be reduced to that of the second degree if the lower bound poverty line is arbitrarily close to zero. Received: 9 September 1998/Accepted: 11 January 2000     

Poverty orderings and welfare dominance

This paper examines the partial orderings of discrete distributions derived from various poverty indices and sets of welfare functions. The poverty ordering with respect to some indexP is the ordering obtained whenP ranks consistently over a range of admissible poverty lines. The poverty orderings derived from the headcount ratio, the per-capita income gap and another distribution-sensitive index are characterized in some detail when the poverty standard is allowed to take any positive value, and these orderings are shown to coincide with the natural interpretation of first, second and third degree welfare dominance, respectively. Additional results are then obtained for the situation in which the admissible poverty lines cannot exceed some finite upper bound.We are particularly indebted to Nick Kiefer for initial insights into the issues addressed in this paper. We have also had helpful comments from Amartya Sen, from an anomymous referee, and from many seminar audiences. Financial support from the Krannert Endowment Trust and the Leverhulme Trust is gratefully acknowledged.     

Inference for the measurement of poverty in the presence of a stochastic weighting variable

Empirical applications of poverty measurement often have to deal with a stochastic weighting variable such as household size. Within the framework of a bivariate distribution function defined over income and weight, I derive the limiting distributions of the decomposable poverty measures and of the ordinates of stochastic dominance curves. The poverty line is allowed to depend on the income distribution. It is shown how the results can be used to test hypotheses concerning changes in poverty. The inference procedures are briefly illustrated using Belgian data. An erratum to this article can be found at     

Richness orderings

An index of richness in a society is a measure of the extent of its affluence. This paper presents an analytical discussion on several indices of richness and their properties. It also develops criteria for ordering alternative distributions of income in terms of their richness. Given a line of richness, an income level above which a person is regarded as rich, and depending on the redistributive principle, it is shown that the ranking relation can be implemented by seeking dominance with respect to the generalized Lorenz curve of the rich or the affluence profile of the society. When the line of richness is assumed to be variable, we need to employ the stochastic dominance conditions for ordering the income distributions.     

A vulnerability approach to the definition of the middle class

Measurement of the middle class has recently come to the center of policy debate in middle-income countries as they search for the potential engines of growth and good governance. This debate assumes, first, that there is a meaningful definition of class, and second, that the thresholds which define relatively homogeneous groups in terms of pre-determined sociological characteristics can be found empirically. This paper aims at proposing a view of the middle class based on vulnerability to poverty. Following this approach the paper exploits panel data to determine the amount of comparable income -associated with a low probability of falling into poverty— which could define the lower bound of the middle class. It looks at absolute thresholds, challenging the view that people just above the poverty line are actually part of the middle class. In an analogy with poverty measurement, there is a degree of arbitrariness in the definition of specific thresholds, but the concept behind them is clear and economically meaningful. The estimated lower-threshold is used in cross-section surveys to quantify the size and the evolution of middle classes in Chile, Mexico, and Peru over the past two decades. The evidence also shows that the middle class has increased significantly in all three countries. There is an important group of people, however, who cannot be defined as middle class from this perspective, but remain vulnerable to fall back into poverty.     

Elitism and stochastic dominance

Stochastic dominance has been typically used with a special emphasis on risk and inequality reduction something captured by the concavity of the utility function in the expected utility model. We claim that the applicability of the stochastic dominance approach goes far beyond risk and inequality measurement provided suitable adaptations be made. We apply in this article the stochastic dominance approach to the measurement of elitism which may be considered the opposite of egalitarianism. While the usual stochastic dominance quasi-orderings attach more value to more equal and more efficient distributions, our criteria ensure that, the more unequal and the more efficient the distribution, the higher it is ranked. Two instances are provided by (i) comparisons of scientific performance across institutions like universities or departments, and (ii) comparisons of affluence as opposed to poverty between countries.     

The Lorenz zonotope and multivariate majorizations

 The distribution of d commodities among n individuals is described by an n×d row stochastic matrix. We present a geometric approach to order such matrices. For a row stochastic matrix the Lorenz zonotope is investigated, which is a higher dimensional generalization of the Lorenz curve. The Lorenz zonotope is a convex polytope. The inclusion of Lorenz zonotopes defines an ordering between row stochastic matrices, which is a multivariate majorization. For a cone in nonnegative d-space, a cone extension of the Lorenz zonotope and the respective inclusion ordering are introduced. We study this class of orderings and establish equivalence with known majorizations. It is provided a finite set of inequalities to which the ordering is equivalent. Received: 16 February 1994/Accepted: 22 May 1996     

Sequential procedures for poverty gap dominance

Poverty evaluations differ from welfare evaluations in one significant aspect, the existence of a threshold or reference point, the poverty line. We build up normative evaluation models in which comparisons are made taking distances from this reference point rather than from the origin to be ethically relevant, by focussing upon poverty gaps and not incomes. When poverty lines differ for different groups in a socially heterogeneous population, choosing poverty gaps instead of incomes as the relevant indicator brings in normatively appealing classes of poverty indices not previously accommodated, for which poverty comparisons are implemented through sequential poverty gap curves (or poverty gap distributions) dominance. These conditions are logically related to those suggested by Atkinson and Bourguignon (Arrow and the foundations of the theory of economic policy, Macmillan, London, 1987) and Bourguignon (J Econom 42:67–80, 1989) for welfare comparisons. However, the proportion of poor individuals in the society and their average poverty gap play a role in our comparisons, though they do not in the existing poverty dominance criteria for heterogeneous populations.     

Economic Growth and Poverty Reduction by Region: Chile 1990‐96

This article examines the evolution of poverty in Chile during 1990‐96, a period of rapid economic growth. It shows that Chile has embarked on a significant poverty‐reduction trajectory. The robustness of this result is examined by using nonparametric estimates of the income distribution and a stochastic dominance test. Growth is an important factor in explaining the poverty reduction that has occurred. Using the Datt‐Ravallion decomposition, it accounts for over 85% of poverty reduction at the national level. However, the pattern varies significantly across regions. Both growth, and its contribution to poverty reduction, vary significantly among regions. This seems to reflect the sectoral composition of growth across regions, with export‐oriented activities producing a larger poverty‐reduction impact.     

Measuring the cohesiveness of preferences: an axiomatic analysis

In this paper, we axiomatically study how to measure the similarity of preferences in a group of individuals. For simplicity, we refer to this as the cohesiveness. First, we provide axioms that characterize a family of linear and additive measures whose intersection is a partial ordinal criterion similar to first order stochastic dominance. The introduction of some additional properties isolates a one-parameter subfamily. This parameter evaluates the effect on the cohesiveness if one individual changes his ranking on a single pair of objects, as a function of how many of the remaining individuals in the group rank the first object over the second and vice versa. Finally, we characterize the focal measures of this subfamily separately showing that they coincide with measures constructed using two, at first sight, totally different approaches suggested in the literature.     

Size and distribution trade-offs for the leximin ordering

A relative invariant and an absolute invariant inequality ordering satisfying extreme bottom-sensitivity, are proposed. It is shown that the leximin social welfare ordering can be expressed in terms of a ranking of distributions on the sole basis of their size, measured by the mean, and the degree of inequality, measured according to these inequality concepts. Leximin thus exhibits extreme bottom-sensitivity. This property does not withstand that leximin prefers a larger size of the cake at the cost of higher inequality in a number of cases. These trade-offs between size and equality are characterised in terms of degrees of dominance of the lower parts of the ordinary and absolute Lorenz curves that are accepted by leximin for a given increase in the mean.     

Strategic behaviour and a notion of ex ante efficiency in a voting model

A person is said to prefer in the stochastic dominance sense one lottery-over-outcomes over another lottery-over-outcomes if the probability of his (at least) first choice being selected in the first lottery is greater than or equal to the analogous probability in the second lottery, the probability of his at least second choice being selected in the first lottery is greater than or equal to the analogous probability in the second lottery, and so on, with at least one strict inequality. This (partial) preference relation is used to define straightforwardness of a social choice function that maps profiles of ordinal preferences into lotteries over outcomes. Given a prior probability distribution on profiles this partial preference ordering (taking into account the additional randomness) is used to induce a partial preference ordering over social choice functions for each individual. These are used in turn to define ex ante Pareto undominated (efficient) social choice functions. The main result is that it is impossible for a social choice function to be both ex ante efficient and straightforward. We also extend the result to cardinal preferences and expected utility evaluations.This work was supported by Grant #SOC 77-27403 and #SES 80-26086 from the National Science Foundation. It has been prepared at the University of Illinois and the University of Pennsylvania. We want to thank Steve Matthews and an anonymous referee for helpful comments     

A global count of the extreme poor in 2012: data issues,methodology and initial results

The 2014 release of a new set of purchasing power parity (PPP) conversion factors (PPPs) for 2011 has prompted a revision of the World Bank’s international poverty line. In revising the line, we have sought to minimize changes to the real purchasing power of the earlier $1.25 line (in 2005 PPPs), so as to preserve the integrity of the goalposts for international targets such as the Sustainable Development Goals (SDGs) and the World Bank’s twin goals – which were set with respect to that line. In particular, the new line was obtained by inflating the same fifteen national poverty lines – originally used by Ravallion et al. (World Bank Econ. Rev. 23(2): 163–184 2009) to construct the $1.25 line – to 2011 prices in local currency units, and then converting them to US dollars using 2011 PPP conversion factors. With a small approximation, this procedure yields a new international poverty line of $1.90 per person per day. In combination with other changes described in the paper, this revision leads to relatively small changes in global poverty incidence for 2011: from 14.5 % using the old method to 14.1 % using the new method. In 2012, the new reference year for the global count, we find 12.7 % of the world’s population, or 897 million people, are living in extreme poverty. There are changes in the regional composition of poverty, but they are also relatively small. This paper documents methodological decisions taken in the process of updating both the poverty line and the consumption and income distributions at the country level, including issues of inter-temporal and spatial price adjustments. It also describes various caveats and limitations of the approach taken.     

Poverty and poverty alleviation programmes in the urban areas of Mozambique

The first part of this paper provides an analysis of poverty and destitution in the cities of Mozambique. The second part summarises the existing programmes for poverty alleviation and the social safety net. The last part describes in some detail the only organisation and programme which has had significant impact in terms of alleviating poverty and destitution: the Gabinete de Apoio a População Vulnerável (GAPVU) Cash Transfer Scheme.A poverty profile of Mozambique's urban centres shows that over half of all households are living in poverty. It distinguishes between absolutely poor and destitute households. The latter have expenditures less than two thirds of the poverty line, are at risk of malnutrition, high child mortality and low life expectancy and comprise nearly a third of the population. A distinction is made between structural and conjunctural causes of poverty and used as a basis for classifying households in different situations, in order to identify appropriate types of intervention. Existing policies and programmes to reduce poverty and alleviate destitution are reviewed and their strengths and weaknesses identified. The cash transfer scheme designed and operated by the GAPVU is described in more detail, and its effectiveness in reaching destitute households assessed. Finally, its administrative efficiency and financial and institutional sustainability are evaluated. It is shown to be a well designed programme which succeeds in reaching increasing numbers of vulnerable households because of its use of decentralised health and community administrative structures, and strong political and institutional backing.     

Global poverty estimates based on 2011 purchasing power parity: where should the new poverty line be drawn?

This paper aims to present a new global poverty line based on the 2011 Purchasing Power Parity (PPP). To calculate a new global poverty threshold based on 2011 PPP, this paper moves away from the World Bank’s method of anchoring a single global poverty line on the national poverty lines of the 15 poorest countries. It instead proposes an alternative method of using equivalent poverty lines. Each country is shown to have a different equivalent poverty line. This paper finds that there is no single international poverty line in 2011 PPP that is equivalent to $1.25 in 2005 PPP. Single poverty lines vary for each region because countries have experienced different inflation rates and have different PPP conversion rates between 2005 and 2011. To calculate a single poverty line in 2011 PPP, this paper measures the weighted average of equivalent poverty lines of 101 countries around the globe with weights proportional to their populations. Based on the new method, the corresponding poverty line is estimated at $1.93 in 2011 PPP. The World Bank has officially adopted the poverty line of $1.90 in 2011 PPP. This paper demonstrates that our proposed poverty line performs better than the World Bank’s in terms of preserving the real purchasing power of the previous line of $1.25 in 2005 PPP. Given the new poverty threshold of $1.93, the number of poor worldwide is reduced by 6.42 million, with the reduction largely occurring in South Asia and Sub-Saharan Africa.     

The demographic and socio-economic characteristics of post-1965 immigrants to New York City: a comparative analysis by national origin

This article analyses and compares the demographic and socio‐economic characteristics of persons born abroad who immigrated to New York City after 1965 and still lived in the City in 1990. Using data from the 1990 Census, we classify persons into the twenty four largest national origin groups and compare their demographic and socio‐economic characteristics (sex, age, educational attainment, labour force participation, unemployment, occupation, income, and poverty). We pose and answer three empirical questions. The first question is: what are some of the main differences by national origin in the composition of persons immigrating to New York City after 1965? The second question is: what are some of the main differences in the location of post‐1965 immigrants in New York's socio‐economic structure? The third question is: what are some of the main differences in the economic rewards received by persons who immigrated to New York City since 1965? We find that immigrants with less than a high school education have higher labour force participation rates than the US‐born population in the same educational category and also have slightly higher earnings. Immigrants with a high school degree have labour force participation rates close to (or slightly higher than) the average for the US‐born population but their incomes are slightly lower than the average income for the US‐born population. Immigrants with a college degree have participation rates similar or slightly lower that those of the US‐born population while their earnings are significantly lower that those of US‐born college graduates.     

Complaints and inequality

Temkin (1986, 1993) set out a philosophical basis for the analysis of income inequality that provides an important alternative to the mainstream welfarist approach. We show that the Temkin principles can be characterised by a parsimonious axiomatic structure and we use this structure to derive a new class of inequality indices and an inequality ordering. This class of indices has a family relationship to well-known measures of inequality, deprivation and poverty. The ordering is shown to have properties analogous to second-order dominance results.We would like to acknowledge financial support by the Training and Mobility of Researchers Programme of the European Communities, grant #ERBFMRXC T980248 (Living Standards, Inequality and Taxation), and to thank STICERD for hosting Ebert in order to facilitate our collaboration. Ralph Bayer helped greatly in preparation of the figures. We are grateful for comments from Yoram Amiel, Kurt Devooght and Alain Trannoy and from participants at workshops in Warwick, Bocconi, the LSE and Venice. We also wish to acknowledge the helpful comments of the referees of this journal.     

RELATIVE WELL-BEING AMONG CHILDREN AND THE ELDERLY:

While recent decades have witnessed sharply divergent trajectories in the well-being of children and the elderly, little research explores the social-structural forces behind these trends. This study examines several key elements of Preston's theory relating relative age group size to the well-being of children and the elderly. First considered is the degree to which membership in a relatively large age group enhances well-being; second, the role of family structure in promoting well-being: third, differences between these processes for children and the elderly. An analysis of three indicators of group well-being—poverty, mortality, and suicide rates—for U.S. states provides mixed support for Preston's theory. Among the elderly, group size is inversely related to suicide and mortality, but unrelated to poverty. Contrary to Preston's view, larger group size diminishes the well-being of children. However. consistent with Preston's theory, family structure is substantially more important for the well-being of children than for the elderly.     

The ‘Extended’ Atkinson family: The class of multiplicatively decomposable inequality measures,and some new graphical procedures for analysts

This paper introduces and characterises a class of inequality measures which extends the Atkinson family. This class contains canonical forms of all aggregative inequality measures, each bounded above by one, provides a new dominance criterion for ordering distributions in terms of inequality and offers some new graphical procedures for analysts. The crucial axiom for the characterisation is an alternative to the standard additive decomposition property that we call ‘multiplicative decomposability,’ where the within-group component is a generalised weighted mean with weights summing exactly to one. An erratum to this article can be found at     

The concept and measurement of asset poverty: Levels, trends and composition for the U.S., 1983–2001

American prosperity in the second half of the 1980s together with the booming economy of the 1990s created the impression that American households have done well, particularly in terms of wealth acquisition. In this paper, we develop the concept of “asset poverty” as a measure of economic hardship, distinct from and complementary to the more commonly used concept of “income poverty.” We define a household with insufficient assets to enable it to meet basic needs (as measured by the income poverty line) for a period of three months to be asset poor. The results reveal that in the face of the large growth in overall assets in the U.S. and a fall in standard income poverty over the period from 1983 to 2001, the level of asset poverty increased from 22.4 to 24.5 percent. We also find that asset poverty rates for blacks and Hispanics are over twice those for whites; that asset poverty rates fall monotonically with both age and education; that they are much higher for renters than homeowners; and that by family type they range from a low of 5 percent for elderly couples to 71 percent for female single parents.