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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.

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.

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.

The U.S. Department of Transportation (DOT) defines a flight as “delayed” if it arrives 15+ minutes late. The DOT “flight counting” delay definition is used to rank airline/airport service quality. An obvious caveat of counting flight delays is that the duration of delay plays no role in the delay count. The purpose of this article is to propose an aggregate delay measure that is sensitive to the distribution of time delayed among passengers. The importance of this work is that our derived delay measure reflects passenger preferences rather than the arbitrary delay cutoff established by the DOT. We model passengers' preference ordering using the criteria that passengers prefer fewer, shorter, and more equal delay times.

This paper introduces a new approach to rank and measure socioeconomic inequality in health. A novel feature of the approach is the use of an income-health matrix that relates socioeconomic class with health status; each row of the matrix corresponds to a socioeconomic class and contains the respective probability distribution of health. By invoking a monotone assumption on the income-health matrix, which is a direct translation of the well-known hypothesis of social gradients in health outcomes, we derive a set of welfare-dominance and inequality-dominance conditions for ranking health distributions. Unlike other existing health inequality measures, our conditions require no cardinal specification of ordinal heath data and, hence, are robust. We then apply the dominance conditions to compare socioeconomic health inequality in the US and Canada using the newly released JCUSH data.

This article contributes to the literature of pro-poor growth measurement by introducing and characterizing a growth-rate consistency axiom. The axiom states that if one growth pattern is judged to be more pro-poor than another growth pattern at a given growth rate, then the pro-poor ranking between the two growth patterns should remain the same at a higher growth rate. We show that summary pro-poor measures such as poverty-growth elasticities may violate this axiom. We then characterize a special dominance condition under which a given summary pro-poor measure will satisfy the growth-rate consistency axiom. Finally, we establish a general growth-rate dominance condition under which all summary pro-poor measures will respect the growth-rate consistency axiom.

The paper examines the implications of the newly proposed unit consistency axiom for partial inequality orderings. We first show that some intermediate Lorenz dominance conditions violate the axiom. We then characterize a class of intermediate Lorenz orderings and demonstrate that the only unit-consistent member is the one related to Krtscha (Models and measurement of welfare and inequality. Springer, Heidelberg, 1994)’s intermediate notion of inequality which has recently been investigated by Zoli (A surplus sharing approach to the measurement of inequality. Discussion paper no. 98/25, University of York, 1998; Logic, game, theory and social choice. Tilburg University Press, Tilburg, 1999) and Yoshida (Soc Choice Welf 24:557–574, 2005). Finally, we provide a general characterization for unit-consistent Lorenz orderings and the Krtscha-type dominance again turns out to be the only one that is intermediate and unit-consistent.

This paper introduces a new axiom-the unit consistency axiom-into inequality measurement. This new axiom requires the ordinal inequality rankings (rather than the cardinal indices) to be unaffected when incomes are expressed in different units. I argue that unit consistency is an indispensable axiom for the measurement of income inequality. When unit consistency is combined with decomposability, I show that the unit-consistent decomposable class of inequality measures is a two-parameter extension of the one-parameter generalized entropy class. The extended class accommodates a variety of value judgments and includes different types of inequality measures.

The justification for using Lorenz dominance as an inequality ranking condition has been based on the aggregate social welfare comparison and the Pigou–Dalton principle of transfers. Since both the aggregating aspect of the social welfare function and certain implications of the principle of transfers are debatable, ordering conditions stronger than Lorenz dominance are worth exploring. A particularly interesting direction to pursue is to follow the frequently invoked notion that inequality is the “gap” between the rich and the poor. This paper follows this notion to formally propose a unified utility-gap concept and characterizes several utility-gap based conditions as general stronger-than-Lorenz-dominance ranking criteria. Specifically, we propose utility-gap dominance which requires all pair-wise utility-gaps in one distribution to be uniformly smaller than those of the other distribution. We then explore a conceptually weaker dominance concept – quasi dominance – which imposes conditions only on the gap between each person’s utility and some reference utility point of the distribution.

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.

Simple random sampling has been assumed in most statistical inference procedures developed to test Lorenz dominance and other partial ordering conditions. This note, using the Bahadur representation, derives the (asymptotic) covariance structures of the Lorenz and generalized Lorenz ordinates for stratified, cluster and multistage samples. The comparison of these covariance structures illustrates the necessity of taking the sampling method into account in inference testing.

Economists have long speculated that envy and malice play important roles in economic decisions. Surprisingly little empirical evidence has been offered in support of such claims. This paper uses experimental and multinomial logit techniques to estimate the effects of envy and malice in economic decisions involving Pareto efficiency. Envy and malice turn out to be powerful motivations with strong differential impacts across countries and relative positions. In some cases, opposition to Pareto gains reaches 60%. Behind a veil of ignorance, however, opposition falls to 10% overall. Pareto efficiency thus garners its greatest support under conditions which can lay claim to greatest legitimacy, those free of situational and personal bias. "... the greater part of human actions have their origin not in logical reasoning but in sentiment. This is particularly true for actions that are not motivated economically.... Man, although impelled to act by nonlogical motives, likes to tie his actions logically to certain principles; he therefore invents these a posteriori in order to justify his actions." V. Pareto in The rise and fall of the elites (1968, p. 27)

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.

This article derives large-sample properties and provides asymptotically distribution-free statistical inference procedures for an alternative approach to inequality orderings—normalized stochastic dominance (NSD). NSD is a straightforward extension of standard dominance techniques. As such, it can be generalized to higher orders of dominance, thereby providing a more powerful technique for ranking distributions. We illustrate the NSD method by applying it to Current Population Survey data for 1970–1990.

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

There exists a close tie between the coefficient of variation (CV) and a recently proposed inequality ranking criterion. We show that 1 2 (CV)2 is the area between the second-degree normalized stochastic curve and the line of perfect equality.

Distribution-free statistical inference procedures for changes in Lorenz- and Gini-based indexes of tax progressivity are developed and applied. Related but distinct tests for the Reynolds–Smolensky index of residual progression and the Kakwani index of liability progression are provided. The inference procedures are illustrated by applying them to Luxembourg Income Study microdata for Sweden, the United Kingdom, and the United States before and after periods of tax reform. In each country a finding of significant change depends on the choice among progressivity indexes. No single index exhibits a consistent pattern of significant change in all countries across time.

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.

Intergenerational disparity in income and health violates the norm of equal opportunity and deserves the attention of researchers and policy makers. To understand changes in intergenerational disparity, we created the intergenerational mobility index (IMI), which can simultaneously measure changes in income rankings and in health outcomes across two generations. We selected obesity as one health outcome to illustrate the application of IMI due to its severe health and financial consequences for society and the significant changes in the distribution of obesity across income groups. Although obesity has increased in all income groups in the last four decades, higher income groups have tended to have a faster increase in obesity, which has reduced the disparity in obesity across income groups. The strength of our intergenerational approach within families is to control the genetic influence, which is one of the strongest determinants of obesity. The decomposition of the IMI illustrates that it captures changes in obesity distribution (holding constant income rankings between generations) and changes in income rankings (holding constant the obesity distribution across generations), simultaneously. We used the data of the Panel Study of Income Dynamics (PSID), which have been collected since 1967, is the longest longitudinal survey in the U.S. The PSID surveyed respondents’ height and weight were recorded in 1986 and from 1999 to 2007. We selected respondents from 1986 as the parental generation and respondents from 2007 as the adult children’s generation. To make the adult children’s body weight status and income comparable to their parents’, we stratified the analysis by gender. For the pairs of fathers and adult sons, we found the intergenerational disparity in overweight, a less severe indicator of excessive fatness, across income was decreasing. This was partially due to the up-swing in the adult children’s income status. For the pairs of mothers and adult daughters, we found a similar decrease in socioeconomic disparity in obesity. However, decomposition of the IMI indicated that changes in income distributions between mothers and adult daughters contributed smaller effects than that between fathers and adult sons. Our study has demonstrated that the IMI and its decomposition are useful tools for analyzing intergenerational disparity in income and health.

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.

This paper provides distribution-free inferences for testing marginal rank dominance and Lorenz, and generalized Lorenz dominances. Marginal dominances refer to ordinary dominance relationships holding between an income distribution and its dependent after-event distribution. Using the elegant Bahadur representation, I establish the asymptotic normal distributions of sample marginal changes and derive the variance-covariance structures. I also show that the inference procedures can be modified and applied to more general cases where samples are (partially) dependent. The approaches are illustrated by re-evaluating the marginal impacts of working wives on the U.S. family income distribution using 1990 census data.

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