Decomposing poverty changes into vertical and horizontal components

Variations in aggregate poverty indices can be due to differences in average poverty intensity, to changes in the welfare distances between those poor of initially unequal welfare status and/or to emerging disparities in welfare among those poor of initially similar welfare status. This note uses a general cost‐of‐inequality approach that decomposes the total change in poverty into a sum of indices of each of these three components. This decomposition can serve inter alia to integrate horizontal and vertical equity criteria in the poverty alleviation assessment of social and economic programmes. The use of these measures is briefly illustrated using Tunisian data.     

Unit-Consistent Poverty Indices

This paper characterizes unit-consistent poverty indices. The unit consistency axiom requires that poverty rankings (not poverty indices) remain unaffected when all incomes and the poverty lines are expressed in different measuring units. We consider two general frameworks of poverty measurement: the semi-individualistic framework that includes all decomposable indices and all rank-based indices; and the Dalton–Hagenaars framework that contains a subset of decomposable indices. Within the semi-individualistic framework, classes of unit-consistent poverty indices can be characterized for different value judgements about poverty measurement. Within the Dalton-Hagenaars framework, unit-consistent poverty indices are completely characterized without invoking any value judgement a priori. I thank Peter Lambert, Mike Hoy, Thesia Garner and an anonymous referee for their very helpful comments and suggestions.     

Absolute and Relative Deprivation and the Measurement of Poverty

This paper develops the link between poverty and inequality by focussing on a class of poverty indices (some of them well–known) 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 "relative–deprivation" 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.     

How Should We Measure Poverty in a Changing World? Methodological Issues and Chinese Case Study

This study asks whether, in a rapidly changing world, the estimated proportion of the world's population with income below US$1 (adjusted according to purchasing power parity) per day is still a good measure of trends in poverty. It argues that strong economic growth in nations such as China implies that the commonly accepted international poverty line definition of one half median national equivalent income is increasingly relevant and that poverty intensity (the normalized deficit or Foster–Greer–Thorbecke (FGT) index of order one) is a better summary index. This index has a convenient graphical representation—the “poverty box”. Using the proposed poverty line and the example of ranking the level of rural poverty in Chinese provinces, the study demonstrates how poverty intensity replicates the poverty rankings of the Sen family of poverty indices and captures most of the information content of higher‐order FGT indices.     

Africa is on time

We present evidence that the recent African growth renaissance has reached Africa’s poor. Using survey data on African income distributions and national accounts GDP, we estimate income distributions, poverty rates, and inequality indices for African countries for the period 1990–2011. We show that: (1) African poverty is falling rapidly; (2) the African countries for which good inequality data exists are set to reach the Millennium Development Goal (MDG) poverty target on time. The entire continent except for the Democratic Republic of Congo (DRC) will reach the MDG in 2014, one year in advance, and adding the DRC will delay the MDG until 2018; (3) the growth spurt that began in 1995, if anything, decreased African income inequality instead of increasing it; (4) African poverty reduction is remarkably general: it cannot be explained by a large country, or even by a single set of countries possessing some beneficial geographical or historical characteristic. All classes of countries, including those with disadvantageous geography and history, experience reductions in poverty. In particular, poverty fell for both landlocked as well as coastal countries; for mineral-rich as well as mineral-poor countries; for countries with favorable or with unfavorable agriculture; for countries regardless of colonial origin; and for countries with below- or above-median slave exports per capita during the African slave trade.     

TRENDS IN POVERTY IN THE UNITED STATES, 1967–84

The sensitivity of movements in poverty to the method used in measuring poverty is examined. The use of various poverty indices, and of various ways of setting the poverty lines, does not affect the conclusion that poverty followed a U-shaped pattern from 1967 to 1984. A model for a family's income/needs ratio is estimated and used to explore the factors that might lie behind this pattern. The results suggest that changes over time in the location of the income distribution are most relevant to the corresponding changes in poverty. Changes in the structure of families, and in labor supply within families, have also been relevant to recent movements in poverty.     

MEASUREMENT OF POVERTY: POLAND IN THE 1980s

This paper presents results of an examination of poverty in Poland in the 1980s. The individual welfare measure is expenditure on consumption per equivalent adult. Household equivalence scales are estimated using a quasi-exact scales trans logarithmic model. Four poverty indices are calculated. These are intended to capture the following aspects of poverty: (1) incidence, (2) relative deprivation, acid (3) social ability to eliminate poverty by income transfers. The study revealed significant changes in poverty during the investigated period, from 9 to 30 percent with persistent poverty resulting for pensioners, farmers and low educated persons.     

Vulnerability Orderings for Expected Poverty Indices

Vulnerability to poverty refers to the risk of an individual or household falling below the poverty line. A partial vulnerability to poverty ordering is defined to indicate when a situation characterized by uncertainty means that people are more vulnerable to poverty than in another situation. The family of expected poverty indices used in this context contains versions under vulnerability of many well‐known poverty indices. The ordering resembles the Hardy et al. result on the Lorenz partial ordering. A separate ordering for the expected income gap ratio is also investigated. First‐order stochastic dominance is used to indicate when the expected value of the censored returns from the states increases.     

THE IMPORTANCE OF CONSECUTIVE SPELLS OF POVERTY: A PATH‐DEPENDENT INDEX OF LONGITUDINAL POVERTY

In this paper we propose a new index of individual poverty in the longitudinal perspective, taking into account the way poverty and non‐poverty spells follow one another along individual life courses. The Poverty Persistence Index (PPI) is based on all the pairwise distances between the waves of poverty. The PPI is normalized and it assigns a higher degree of (longitudinal) poverty to people who experience poverty in consecutive, rather than separated, periods, for whom the distances from the poverty line are larger along time and moreover, when the worst years are consecutive and/or recent. We also propose an aggregate index of persistence in poverty (APPI) in order to measure the distribution of the persistence of poverty in a society, and evaluate at once the diffusion of poverty, its depth, duration, and recentness. The indices are tested in comparison with other measures from the literature both at the individual as well as at the societal level.     

Poverty Intensity in Australia

Even though poverty indices with axiomatically sound properties have been advocated for several decades, most empirical studies of poverty in Australia and elsewhere continue to use the crude, but easily understood, head-count ratio. The difficulty of interpreting the axiomatically more desirable indices is a major reason why their use has been resisted in applied poverty measurement. This paper demonstrates how the more sophisticated poverty indices can be converted into a form that is readily interpreted as a measure of poverty intensity of a group, relative to the population to which the group belongs. The resulting poverty-intensity index is easy to understand and it retains the axiomatic properties of the poverty index on which it is based. We apply the method to Australian data. Poverty measures reported previously in the literature are converted into measures of poverty intensity and interpreted accordingly. We also calculate and interpret some new measures of poverty and poverty intensity using the 1996–97 Income and Housing Costs Survey, Australia (Australian Bureau of Statistics 1997). It is hoped our procedure will lead to wider use of poverty indices that are theoretically superior to the head-count ratio.     

SOCIALLY IMPROVING TAX REFORMS*

This article proposes graphical methods to determine whether commodity tax changes are “socially improving,” in the sense of improving social welfare or decreasing poverty for large classes of social welfare and poverty indices. It also shows how estimators of critical poverty lines and economic efficiency ratios can be used to characterize socially improving tax reforms. The methodology is illustrated using Mexican data.     

关于森的贫困度量方法及该领域最近的研究进展

在这篇文章中,我们应用贫困度量的公理化方法对森的贫困指数提出了一个统一的理论框架.这一理论框架清晰地表明,这些指数与一个特定的社会福利函数之间存有密切的联系,而且,我们发现这些指数具有相同的可分的乘积结构.因为这个性质,这些指数无论是从直观的角度还是从几何学的角度都更加便于理解,同时也更便于计算.这些发现使森的贫困指数可以直接在发达国家和发展中国家的扶贫政策分析和政策制定过程中得到应用.     

Measuring lifetime poverty

This paper presents an axiomatic framework for measuring lifetime poverty over multiple periods. For an individual, we argue that lifetime poverty is influenced by both the “snapshot” poverty of each period and the poverty level of the “permanent” lifetime consumption; it is also influenced by how poverty spells are distributed over the lifetime. We axiomatically characterize classes of lifetime poverty indices and derive dominance conditions of poverty orderings for both individual and societal lifetime poverty measurements.     

On multidimensional poverty rankings of binary attributes

We address the problem of ranking distributions of attributes in terms of poverty, when the attributes are represented by binary variables. To accomplish this task, we identify a suitable notion of “multidimensional poverty line” and characterize axiomatically the Head-Count and the Attribute-Gap poverty rankings, which are the natural counterparts of the most widely used income poverty indices. Finally, we apply our methodology and compare our empirical results with those obtained with some other well-known poverty measures.     

CALCULATING A PRICE INDEX FOR FAMILIES WITH CHILDREN: IMPLICATIONS FOR MEASURING TRENDS IN CHILD POVERTY RATES

This paper investigates the effects of varying consumption patterns for families with and without children on measured trends in child poverty. We first use data from consumer expenditure surveys to calculate price indices by family type. We next examine the effect of using these group-specific price indices on measured trends in child poverty. Although we find that, all else equal, children increase the cost of living, our calculations indicate that on average families with children experienced relatively lower inflation rates than families without children during the 1968 to 1987 period. While this result suggests that estimates of child poverty rates calculated using an average price index may have over-stated secular increases in child poverty, we find that child poverty rates calculated using a price index specific lo families with children are not substantively different from those calculated using an average index for all families.     

A Proposal to Compare Consistently the Inequality Among the Poor

A poverty index should be sensitive to the number of poor people, the extent of the shortfall of the poor, and the inequality among the poor. A difficulty arises when inequality among the poor needs to be assessed. The inequality may be analyzed in terms of either incomes or gaps. Depending on what side we focus on, the inequality level comparisons may be contradictory. This paper proposes a reinterpretation of the inequality component involved in the decompositions of well‐known poverty indices. The alternative indices we introduce measure equally the income and gap inequality among the poor. The comparisons in inequality as measured by these indices are then independent of the viewpoint. An empirical application illustrates the proposal.     

贫困按要素分解:方法与例证

本文构建了两个贫困分解框架,一个用于分解贫困的水平,另一个用于分解贫困的变化,这两个方法的独特之处是建立了贫困与生产要素(即资源禀赋)总量及其分配之间的数量关系。具体地说,一个给定的贫困发生率可以被分解为要素或资源短缺的贡献,外加要素分配不均等的贡献。贫困发生率的变化则可分解为由要素的水平变化引起的,或由要素的不均等分配变化引起的。将这两种分解方法用于中国农村的数据,我们发现要素的不均等分配而非资源短缺是导致贫困和贫困变化的主要原因。     

Testing for poverty dominance: an application to Canada

Abstract The paper proposes and applies statistical tests for poverty dominance that check for whether poverty comparisons can be made robustly over ranges of poverty lines and classes of poverty indices. This helps provide both normative and statistical confidence in establishing poverty rankings across distributions. The tests, which can take into account the complex sampling procedures that are typically used by statistical agencies to generate household‐level surveys, are implemented using the Canadian Survey of Labour and Income Dynamics (SLID) for 1996, 1999, and 2002. Although the yearly cumulative distribution functions cross at the lower tails of the distributions, the more recent years tend to dominate earlier years for a relatively wide range of poverty lines. Failing to take into account SLID’s sampling variability (as is sometimes done) can inflate significantly one’s confidence in ranking poverty. Taking into account SLID’s complex sampling design (as has not been done before) can also decrease substantially the range of poverty lines over which a poverty ranking can be inferred.     

ON MEASURING POVERTY

This paper investigates the properties of various measures of poverty and of the "difficulty of alleviation of poverty". It is found that the ranking properties of both kinds of indices can be quite counter-intuitive and that they could be misleading if used for policy evaluation. An alternative index is proposed; it is compared to the other indices and seems to fare rather well. To illustrate, a special reference is made to S. Anand's recent article on poverty in Malaysia.