A TREATMENT OF ABSOLUTE INDICES OF POLARIZATION*

Absolute polarization indices remain unchanged under equal absolute augmentation in all incomes. This paper identifies the class of absolute polarization indices whose orderings of alternative income distributions agree with the rankings generated by nonintersecting absolute polarization curves. We explore the possibility of using the Kolm (1976) – Blackorby‐Donaldson (1980) ethical absolute inequality index in polarization measurement. We establish that although inequality and polarization are dissimilar concepts, different absolute inequality indices can be employed to design alternative absolute polarization indices. A numerical illustration is provided using Indian data and it is shown that inequality and polarization are different issues in income distribution analysis.     

A Class of Social Welfare Functions That Depend on Mean Income and Income Polarization

A well‐established strategy for evaluating alternative income distributions is based on the use of an abbreviated social welfare function that depends only on mean income and an inequality index. In keeping with this literature, we study the existence of social welfare functions that can be written as a trade‐off between efficiency and income polarization. This paper proposes a class of social welfare functions consistent with the Esteban and Ray, and Duclos, Esteban and Ray income polarization indices. For this result, we expand the domain for personal preferences to incorporate not only own income but also the well‐being of others. In addition, we link our proposal to the literature on relative satisfaction. The approach is illustrated by an empirical application using the CPS database for the United States in the period 1991–2010.     

Income distributions and decomposable divergence measures

Inequality indices evaluate the divergence between the income distribution and the hypothetical situation where all individuals receive the mean income, and are unambiguously reduced by a Pigou–Dalton progressive transfer. This paper proposes a new approach to evaluate the divergence between any two income distributions, where the latter can be a reference distribution for the former. In the case where the reference distribution is perfectly egalitarian – and uniquely in this case – we assume that any progressive transfer reduces the divergence, and that the divergence can be additively separated into inequality and efficiency loss. We characterize the unique class of decomposable divergence measures consistent with these views. We derive the associated relative and absolute subclasses, and we illustrate the applicability of our results. This approach extends the generalized entropy studied in inequality measurement.     

Unequal uncertainties and uncertain inequalities: an axiomatic approach

In this paper, we provide an axiomatic characterization of social welfare functions for uncertain incomes. Our most general result is that a small number of reasonable assumptions regarding welfare orderings under uncertainty rule out pure ex ante as well as pure ex post evaluations. Any social welfare function that satisfies these axioms should lie strictly between the ex ante and the ex post evaluations of income distributions. We also provide an axiomatic characterization of the weighted average of the minimum and the maximum of ex post and ex ante evaluations.     

Comparisons of heterogeneous distributions and dominance criteria

We are interested in the comparisons of standard-of-living across societies when observations of both income and household structure are available. We generalise the approach of A.B. Atkinson and F. Bourguignon (1987) [3] to the case where the marginal distributions of needs can vary across the household populations under comparison. We assume that a sympathetic observer uses a utilitarian social welfare function in order to rank heterogeneous income distributions. Insofar as any individual can play the role of the observer, we take the unanimity point of view according to which the planner?s judgements have to comply with a certain number of basic normative principles. We impose increasingly restrictive conditions on the household?s utility function and we investigate their effects on the resulting rankings of the distributions. This leads us to propose four dominance criteria that can be used for providing an unambiguous ranking of income distributions for heterogeneous populations.     

Restricted and Unrestricted Dominance for Welfare, Inequality, and Poverty Orderings

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.     

Redistributive effects of minimal equal sacrifice taxation

We examine the circumstances under which minimal equal sacrifice taxation reduces income inequality. Focusing on absolute sacrifice and relative inequality, we show that after tax incomes are more equally distributed than before tax incomes and that after tax inequality decreases with the revenue to be raised if and only if the elasticity of the marginal utility of income is decreasing. However, other things equal, after tax inequality is shown to decline as the utility function becomes more concave. We investigate next how these conclusions extend when one takes the absolute inequality view and considers that it is the relative loss in utility that has to be equalized across individuals.     

A metric for assessing the “goodness” of income distributions and the effect of price changes

Social welfare evaluation depends in part on value judgments as to income distribution. This paper proposes a metric for assessing the “goodness” of particular income distributions. That metric is then used to examine the effect of price changes on the “goodness” of a given distribution. Consider an increase in the price of a commodity that is disproportionately consumed by households with incomes that are high relative to the preferred income distribution. One naturally supposes that such a price increase will make the given income distribution appear less bad. Surprisingly, this is not invariably the case.     

Blackwell's ordering and public information

We characterize a precise comparative static on welfare and the amount of public information in an economy under uncertainty. Results dating to Hirshleifer (Amer. Econom. Rev. 61 (1971) 561) have suggested that information can have negative value in such a setting, but counterexamples using competitive equilibrium outcomes have suppressed general results to this effect. We show that under the solution concept of implementable allocations, the negative relationship between more public information in the sense of Blackwell and welfare is fully general. Furthermore, Blackwell's ranking is necessary as well as sufficient to obtain our ranking, and hence ours provides an equivalent characterization of his ordering.     

Self-rated economic welfare in Russia

Most of those Russian adults who feel that they are poor are not classified as such in the poverty statistics, and most of those who are classified as poor don't feel that way. We study the determinants of peoples’ perceptions of their economic welfare in an unusually rich socioeconomic survey. While income is a highly significant predictor, subjective economic welfare is influenced by many other factors including health, education, employment, assets, relative income in the area of residence and expectations about future welfare. Insights are obtained into how objective data should be weighted in assessing economic welfare.     

Direct evidence on income comparisons and their welfare effects

This paper provides direct evidence that income comparisons exert a significant impact on subjective well-being. It also evaluates the relative importance of different types of benchmarks. Internal comparisons to one's own past living standard outweigh any other comparison benchmarks. Local comparisons (to one's parents, former colleagues or high school mates) are more powerful than self-ranking in the social ladder. The impact of comparisons is asymmetric: under-performing one's benchmark always has a greater welfare effect than out-performing it (in absolute value). Comparisons, which reduce satisfaction also increase the demand for income redistribution, but there, the relative impact of subjective ranking is preponderant.     

A SYNTHESIS OF POVERTY LINE DEFINITIONS*

A fundamental point of discussion in poverty research is whether poverty is an absolute or a relative concept. If poverty is seen to be a situation of absolute deprivation, a poverty line will usually be defined to be independent of the general style of living in society. If poverty is considered to be a situation of relative deprivation, a poverty line will be defined in relation to the general style of living in society. The choice for one of these two approaches has important consequences for social policy, as absolute poverty may be reduced by economic growth, while relative poverty will only decrease when income inequality decreases. This paper suggests a poverty line definition that is not a priori meant to be either absolute or relative, but depends on the perception of poverty in society. If the poverty line is higher in countries with higher median income (as an indicator of “general style of living”) the poverty line is said to be relative; if the poverty line does not vary with median income, it is said to be absolute. The poverty line definition suggested appears to be a generalization of almost all well-known poverty line definitions. Poverty lines thus defined are estimated for eight European countries on the basis of a 1979 survey. The resulting lines appear to have an elasticity with respect to median income of 0.51, and hence can be said to be halfway on the scale between absolute and relative.     

Household inequality, social welfare, and trade

Working with Sen social welfare functions (meaning explicit separability between mean income and income dispersion), we develop a generalized dual approach to tracking household inequality aspects of social welfare in general equilibrium. We highlight how household equity can be examined analytically alongside production efficiency in duality-based models, using our dual framework to explore potential trade-offs between efficiency and equity effects of trade policy. Our results complement the set of standard inequality results in trade theory focused on functional rather than household inequality. We also find that the relative distributional impact of tariffs on welfare is conditional on the initial level of inequality.     

Proximity-sensitive individual deprivation measures

We characterize a generalization of the linear index of individual deprivation. Our class allows for an income increase of a higher-income individual to have a stronger impact the closer they occur to the income of the person under consideration.     

RANKING INCOME DISTRIBUTIONS WHEN NEEDS DIFFER

We derive criteria for ranking income distributions where households differ in equity-relevant non-income characteristics ('needs'). using methods which do not require cardinal specifications of equivalence scales. We consider comparisons for situations where the distributions of needs differ (eg. Cross nationally or intertemporally), building on the results of Atkinson and Bourguignon (1987) and Atkinson (1992). The modifications required when the individual rather than the household is the income-receiving unit are also discussed. We illustrate the methods with an analysis of changes in social welfare and poverty in the U.K. between 1981 and 1986.     

THE INCOME UNIT AND THE ANATOMY OF INCOME DISTRIBUTION*

This paper focuses on a neglected aspect of the treatment of the income unit in the construction of size distributions of income. If the size distribution is to be an indicator of the distribution of economic welfare, and if the economic welfare of each individual in society is to count equally, then conventional distributions are inconsistent with individualistic welfare functions. We estimate size distributions with each person's welfare weighted equally, and contrast these results with those weighting each household unit's welfare equally. The choice of weights is shown to affect both the level and the trend in income inequality.     

New unit-consistent intermediate inequality indices

This paper introduces a class of intermediate inequality indices that is, at the same time, ray-invariant and unit-consistent. These measures allow us to make possible keeping some of the good properties of Krtscha’s (Models and measurement of welfare and inequality. Springer, Heidelberg, 1994) index while maintaining the “centrist” attitude no matter howmuch the income increases.By doing so, we approach the intermediate inequality concept suggested by Del Río and Ruiz-Castillo (Soc Choice Welfare 17:223–239, 2000) and generalize it in order to extend the range of income distributions that are comparable according to this ray-invariance criterion.     

DUAL‐INDEX MEASUREMENT OF INCOME INEQUALITY

This study introduces the concept of unequally distributed income and proposes a dual‐index measurement of income inequality that evaluates the magnitude and dispersion of unequally distributed income. We use the Rawlsian index as a magnitude index and employ current income inequality indices as a dispersion index. We describe the properties of the Rawlsian and dispersion indices, and apply these indices to real income data. Further, we show that the Gini dispersion index is a weighted average of Rawlsian indices for the sub‐distributions of the unequally distributed income distribution.     

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.