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This paper demonstrates the implications of adopting an approach to measuring poverty that takes into account the lifetime experience of individuals rather than simply taking a static or cross-sectional perspective. Our approach follows the theoretical innovations in Hoy and Zheng (2008) which address various aspects of the specific pattern of any poverty spells experienced by an individual as well as a possible retrospective consideration that an individual might have concerning his life experience as a whole. For an individual, our perspective of 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. Using PSID data for the US, we demonstrate empirically the power of alternative axioms concerning how lifetime poverty should be measured when making pairwise comparisons of individual lifetime profiles of consumption (income) experiences. We also demonstrate the importance of taking a lifetime view of poverty in comparing poverty between groups by use of the classic FGT ‘snapshot’ poverty index in conjunction with period weighting functions that explicitly reflect concerns about the pattern of poverty spells over individuals’ lifetimes.

Historically, the measurement of poverty has been based on a set of key axioms but limited to a static framework. Features such as multidimensionality and the time factor have only recently been incorporated into poverty measurement. Several alternative approaches have been proposed. This chapter presents a review of the literature that proposes how to conceptualize or develop specific measures of inter-temporal or lifetime poverty, addressing measurement issues, alternative perspectives on frequency, and concerns about data availability. Reflecting this budding literature, the chapter presents alternative axioms that have been proposed to capture the various approaches to inter-temporal or lifetime poverty. A variety of combinations and alternative formulations of these axioms is considered. Concluding remarks underline the need for further research and focus on the role of empirical analysis in shedding light on issues such as mitigation and chronic poverty.

Utilizing results from partial poverty orderings, we characterize a class of generalized Sen poverty indices. A generalized Sen poverty index is defined as the weighted area between the line of zero-poverty and the censored generalized Lorenz curve. Unlike the original Sen index, the generalized Sen index can satisfy the key axioms for poverty measurement.

In this paper we make several contributions to the literature of poverty measurement. We first identify a plausible source for the fuzziness in poverty identification which renders a natural and direct estimation of the poverty membership function; we then provide an axiomatic characterization for an important class of fuzzy poverty measures; and we finally derive a set of crisp dominance conditions for fuzzy partial poverty orderings. We also illustrate the results with the US CPS data.

This paper presents an axiomatic framework for measuring life time 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 life time. Two obvious candidates for aggregation are to aggregate over time and then across individuals, or vice versa. For a society, we consider a path-independence requirement to make these two approaches of aggregation consistent. We axiomatically characterize classes of lifetime poverty indices and derive dominance conditions of poverty orderings for both individual and societal lifetime poverty measurements.

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.

Standard inference procedures for poverty comparisons require samples to be independent. For many commonly used income samples, however, this requirement is not fulÞlled since samples are rotated. This note introduces an easy-to-use method of correction for sample dependency. We also apply the method to test changes in U.S.poverty in the 1990s and evaluate the marginal effects of public assistance on poverty before and after the recent welfare reform.

The way poverty is measured is important for an understanding of what has happened to poverty as well as for anti-poverty 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.

Recently developed statistical inference procedures for the Sen index and its components – the headcount, income gap and Gini index among the poor – are used to test explicit hypotheses concerning aggregate poverty in the United States for the period 1989 to 1997. Changes in Sen measures of poverty are investigated for cash and comprehensive income using the official poverty line and six additional poverty lines drawn using thresholds set at 50, 75, 125, 150, 175 and 200 percent of the official level. The paper also reports on the effects of using comprehensive income on subgroup poverty rates and on the demographic composition of the poor.

Relative poverty lines such as one-half median income have been increasingly used in poverty studies. This paper contributes to the literature by developing statistical inference for testing decomposable poverty measures with relative poverty lines. The poverty lines we consider are percentages of mean income and percentages of quantiles. We show that the estimates of poverty indices with relative poverty lines are asymptotically normally distributed and that the covariance structure can be consistently estimated. As a consequence, asymptotically distribution-free statistical inference can be established in a straightforward manner.

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.

This paper introduces a measure of distribution-sensitivity, which is similar to Arrow-Pratt's measure of risk aversion, for a poverty index. The measure also gauges poverty aversion and has a clear and straightforward interpretation. Using this measure, we can define various classes of minimum distribution-sensitive poverty indices. We show that the ordering condition for such a class of poverty indices is simply a generalized (poverty) deprivation profile dominance. Properties and implications of this dominance condition are analyzed and poverty orderings by different classes of poverty measures are compared. Journal of Economic Literature Classification Number: I32.

Poverty in the United States varies greatly by location. The difference in poverty intensity among locations, however, has only been evaluated by the official poverty measure – the headcount ratio – which has several drawbacks. The official poverty statistics also suffer from use of a single, arbitrary poverty line. This paper uses a recently-developed distribution-sensitive measure of poverty and 1990 census data to reconsider the difference among central city, suburban, and nonmetropolitan poverty levels, as well as differences among US regions. Instead of using a single, arguable poverty line, this paper lets the poverty line vary over an income range so that conclusions are more robust. We check for significance of differences across locations by applying some recently-developed methods of statistical inference.

INTRODUCTION There is wide agreement that the methodology underpinning official US government poverty statistics is flawed. Nevertheless, the official statistics retain considerable appeal due to the long time series of consistent annual measures of the number of poor persons. Isabel Sawhill (1988) identified a number of difficulties with the official measurement methodology, some of which understate while others overstate poverty. More recently a Panel of the National Research Council (Citro and Michael 1995) restate many of the problems and recommend wide-ranging revisions in the methods used in measuring poverty in the United States. A related but separate scientific literature emphasizes additional shortcomings of the official US poverty statistics, which would continue even if the recommendations of the National Research Council (NRC) were adopted. Beginning with the work of Sen (1976), academic researchers have stressed that a headcount of poor persons, which is the basis of both the official poverty statistics and the NRC's recommended measurement procedure, is a deficient indicator of poverty.(1) According to Sen (1976) and many other academic researchers (cf. Foster et al. 1984), aggregate poverty measures must be sensitive to the average level and distribution of well-being of the poor as well as the number of poor persons.(2) Any aggregate poverty measure influenced by the average shortfall of incomes below the poverty line (the income gap of the poor), inequality of incomes among the poor and the headcount of the poor is said to be "distribution sensitive". This paper uses the Sen index of poverty, the most appealing of the distribution sensitive measures, and builds upon the policy related literature that emphasize flaws and shortcomings in the official US measurement methodology. We correct for several major problems and estimate Sen indices of poverty measures that are easy to interpret and compare with the official poverty statistics collected over the past four decades. In addition, we incorporate recently developed statistical inference procedures (Bishop et al. 1997) and test explicit hypotheses concerning the effects of correcting for specific deficiencies and improving upon the official measurement methodology. We estimate and report new poverty measures that provide insights and knowledge concerning two very different sets of issues and questions. First, when distribution sensitive measures are used we wish to know how poverty in the US changed across time and how these more complete measures compare to the official poverty statistics. This aspect of the research focuses on the importance of adding income gap measures and an inequality index of the poor to the official headcount measures. Second, for a given year, how do distribution sensitive poverty statistics based upon comprehensive incomes and adjusted for differences in interarea costs of living compare to estimates based upon Census money incomes, which is the income metric underpinning the official poverty statistics. This aspect of the research addresses whether the failure to adjust for differences in costs of living and the use of a clearly outdated and deficient income concept distorts measures of poverty across urban areas. The remainder of the paper is organized as follows. The next section discusses the difficulties with the official poverty measurement methodology that we correct for in this paper. This section also discusses the Sen index of poverty and briefly summarizes the statistical inference procedures used in interpreting the results. The following section presents the empirical results relating to Sen indices of poverty across time and makes comparisons to official headcount statistics for the period 1961-1996. Next we present and discuss distribution sensitive measures of poverty based upon comprehensive incomes in eight major urban areas in 1990. The effect of using comprehensive incomes rather than Census money incomes on the location of the poor is investigated holding the poverty headcount constant. …

This paper comments on the work of Rector et al. (1999a, 1999b). The poverty lines implicit in their restrictive material deprivation approach are disputed and the claim that America has triumphed over poverty is rejected. Evidence is presented showing that poverty among the poorest Americans has significantly increased and is now near an all time high. The long economic expansion since the recession of 1990–1991 has left hardcore poverty essentially unchanged and relative deprivation among the poorest of the poor has increased

The paper develops simple statistical test procedures for generalized decomposable poverty measures. It is shown that the estimates of the decomposable poverty indices, including the overall and various subgroup poverty indices, have (asymptotic) jointly normal distributions. The full variance-covariance structure is derived and can be estimated consistently without prior specification of the population density underlying the sample data. The (overall/decomposed) poverty indices can thus be used as tools for statistical inference instead of simply as descriptive statistics. We illustrate the test procedure by examining the contributions of whites and non-whites to total US poverty in 1975 and 1985.

Although the first distribution-sensitive, decomposable poverty index, the Watts index has long been neglected by the profession even when it was searching for a decomposable index. This neglect is due partly to the lack of an axiomatic characterization for the Watts index. This paper adopts an axiomatic approach and complements the Watts index with such a characterization. Under a set of reasonable axioms, the Watts index is the unique index if a poverty index is perceived as the absolute amount of social welfare loss due to poverty. The Watts index is relatively easy to apply. It also satisfies all basic axioms for a good poverty index.

This paper investigates the possibility of increasing the ordering power of additively separable poverty measures beyond the condition of second degree stochastic dominance by considering third degree stochastic dominance. For a fixed poverty line, the ordering power can be significantly enhanced by using the third degree criterion. For a range of poverty lines, the marginal power of the third degree criterion over the second degree depends critically upon the lower bound of the range; if the lower bound poverty line is arbitrarily close to zero, the two criteria coincide. The implications of a strong version of the transfer sensitivity axiom are also considered.

Since President Lyndon Johnson declared the war on poverty three decades ago, scholars have devoted many volumes to analyzing characteristics of poverty, evaluating effectiveness of antipoverty policies, and measuring changes in poverty. Unfortunately, most poverty studies have focused primarily on the incidence of poverty rather than on both the incidence of poverty and the income distribution within the poor population. Although A. K. Sen's [23] seminal work on measurement of poverty demonstrated the importance of constructing and using a distribution-sensitive poverty measure in evaluating poverty, the U.S. Federal Government still uses the proportion of poor as virtually the only indicator of poverty. With few exceptions, such as Bishop, Formby, and Smith [5], most recent scholarly works on poverty issues, including Sawhill [21], Hanratty and Blank [17], and Slesnick [24], are also concerned exclusively with the incidence of poverty and use a single poverty line. In this study, we demonstrate that a more comprehensive look at poverty, using distribution-sensitive measures and multiple poverty lines, yields a different picture of poverty changes over time compared to what official U.S. statistics portray. Practically, the comparison of poverty changes can be decomposed into three parts: (1) setting a poverty line -an income threshold below which a person is defined as poor. This step is also called the identification of the poor and is very important in poverty study; (2) choosing a method to aggregate individual poverty into overall poverty. Different methods of aggregating may lead to different conclusions about poverty changes. Therefore an appropriate method is essential for poverty study; and (3) statistical inference-since conclusions about poverty changes are drawn from a random sample of the population, it is important to know whether the estimated poverty