A CHARACTERIZATION OF THE RAWLSIAN SOCIAL ORDERING OVER INFINITE UTILITY STREAMS

In this paper, we characterize a Rawlsian ordering over infinite utility streams using a fairness principle called Hammond Equity, as well as a weak efficiency principle, Sup Continuity, and a condition that links finite and infinite settings of distributive justice called Preference Continuity.     

Impossibility Theorems with Interpersonally Comparable Welfare Levels: The "Extended Sympathy Approach" Reconsidered

We re-examine a type of interpersonal welfare comparison, called the "extended sympathy" approach, which Arrow (1977), Hammond (1976) and Roberts (1980a) introduced in order to escape from Arrovian impossibility theorems. In particular, we extend the positional dictatorship theorem due to Roberts to the case where the domain of social choice rules satisfies the axiom of identity. We show that there is a positional dictator if the rule with the domain satisfies independence, Suppes unanimity and monotonicity
JEL Classification Numbers: 022, 025, 026     

The Pro‐Poorness,Growth and Inequality Nexus: Some Findings From a Simulation Study

An income growth pattern is pro‐poor if it reduces a (chosen) measure of poverty by more than if all incomes were growing equiproportionately. Inequality reduction is not sufficient for pro‐poorness. In this paper, we explore the nexus between pro‐poorness, growth, and inequality in some detail using simulations involving the displaced lognormal, Singh–Maddala, and Dagum distributions. For empirically relevant parameter estimates, distributional change preserving the functional form of each of these three‐parameter distributions is often either pro‐poor and inequality reducing, or pro‐rich and inequality exacerbating, but it is also possible for pro‐rich growth to be inequality reducing. There is some capacity for each of these distributions to show trickle effects (weak pro‐richness) along with inequality‐reducing growth, but virtually no possibility of pro‐poorness for growth which increases overall inequality. Implications are considered.     

Bivariate income distributions for assessing inequality and poverty under dependent samples

As indicators of social welfare, the incidence of inequality and poverty is of ongoing concern to policy makers and researchers alike. Of particular interest are the changes in inequality and poverty over time, which are typically assessed through the estimation of income distributions. From this, income inequality and poverty measures, along with their differences and standard errors, can be derived and compared. With panel data becoming more frequently used to make such comparisons, traditional methods which treat income distributions from different years independently and estimate them on a univariate basis, fail to capture the dependence inherent in a sample taken from a panel study. Consequently, parameter estimates are likely to be less efficient, and the standard errors for between-year differences in various inequality and poverty measures will be incorrect. This paper addresses the issue of sample dependence by suggesting a number of bivariate distributions, with Singh–Maddala or Dagum marginals, for a partially dependent sample of household income for two years. Specifically, the distributions considered are the bivariate Singh–Maddala distribution, proposed by Takahasi (1965), and bivariate distributions belonging to the copula class of multivariate distributions, which are an increasingly popular approach to modelling joint distributions. Each bivariate income distribution is estimated via full information maximum likelihood using data from the Household, Income and Labour Dynamics in Australia (HILDA) Survey for 2001 and 2005. Parameter estimates for each bivariate income distribution are used to obtain values for mean income and modal income, the Gini inequality coefficient and the headcount ratio poverty measure, along with their differences, enabling the assessment of changes in such measures over time. In addition, the standard errors of each summary measure and their differences, which are of particular interest in this analysis, are calculated using the delta method.     

Multidimensional generalized Gini indices

Summary. The axioms that characterize the generalized Gini social evaluation orderings for one-dimensional distributions are extended to the multidimensional attributes case. A social evaluation ordering is shown to have a two-stage aggregation representation if these axioms and a separability assumption are satisfied. In the first stage, the distributions of each attribute are aggregated using generalized Gini social evaluation functions. The functional form of the second-stage aggregator depends on the number of attributes and on which version of a comonotonic additivity axiom is used. The implications of these results for the corresponding multidimensional indices of relative and absolute inequality are also considered.Received: 20 August 2003, Revised: 26 May 2004, JEL Classification Numbers: D63. Correspondence to: John A. WeymarkWe are grateful to our referee for his or her comments.     

A general class of additively decomposable inequality measures

Summary. This paper presents and characterizes a two-parameter class of inequality measures that contains the generalized entropy measures, the variance of logarithms, the path independent measures of Foster and Shneyerov (1999) and several new classes of measures. The key axiom is a generalized form of additive decomposability which defines the within-group and between-group inequality terms using a generalized mean in place of the arithmetic mean. Our characterization result is proved without invoking any regularity assumption (such as continuity) on the functional form of the inequality measure; instead, it relies on a minimal form of the transfer principle – or consistency with the Lorenz criterion – over two-person distributions. Received: October 27, 1997; revised: March 25, 1998     

Income Mobility, Inequality and Social Welfare

It is often argued that an observation of rising annual income inequality need not have negative normative implications. The argument is that if there has been a sufficiently large simultaneous increase in mobility, the inequality of income measured over a longer time period can be lower despite the rise in annual inequality. In this paper, it is shown by example that if normative implications are drawn from a standard social welfare function, the set of circumstances put forward in the above argument are not sufficient to guarantee that social welfare will improve. The reason is that even though rising mobility does reduce longer term inequality, it also increases the variability of income profiles over time and the latter has a detrimental social welfare effect. Hence, there are two types of mobility: one which reduces inequality (regression to the mean), but another that increases inequality (relative movements uncorrelated with incomes). Further, if individuals' aversion to income variabiltiy is sufficiently larger than the social welfare judge's aversion to inequality, then an increase in mobility, no matter how large, cannot offset the negative normative effect of rising annual inequality.     

The subgroup decomposable intermediate indices of inequality

An inequality index is called subgroup decomposable if it can be expressed as a weighted sum of inequality values calculated for population subgroups plus inequality arising from differences among subgroup means. This paper derives the class of subgroup decomposable inequality indices that satisfies the Bossert–Pfingsten type intermediate inequality invariance. When the intermediate inequality equivalence concept coincides with the relative notion of inequality, the derived class becomes the Cowell–Shorrocks generalized entropy family. For comments and suggestions, we are grateful to Peter J. Lambert and two anonymous referees. We thank Chranjib Neogi for drawing the only figure of the paper.     

Comparing Income Distributions Using Atkinson's Measure of Inequality

This article is aimed at undergraduate and graduate economics students, and public sector economists, who are interested in inequality measurement. It examines the use of the Atkinson inequality measure to compare income distributions. A major feature of this measure is that distributional value judgements are made explicit, via the use of a particular form of social welfare function. Emphasis is given to the interpretation of changes in inequality and the role of the relative inequality aversion parameter, which reflects an important feature of those value judgements.     

Monte Carlo simulation of macroeconomic risk with a continuum of agents: the general case

In large random economies with heterogeneous agents, a standard stochastic framework presumes a random macro state, combined with idiosyncratic micro shocks. This can be formally represented by a random process consisting of a continuum of random variables that are conditionally independent given the macro state. However, this process satisfies a standard joint measurability condition only if there is essentially no idiosyncratic risk at all. Based on iteratively complete product measure spaces, we characterize the validity of the standard stochastic framework via Monte Carlo simulation as well as event-wise measurable conditional probabilities. These general characterizations also allow us to strengthen some earlier results related to exchangeability and independence. Parts of this work were done while Yeneng Sun was visiting Stanford University in July 2003, March–May 2005 and July 2006, and while Peter Hammond was visiting the National University of Singapore in March–April 2004. An early version was presented at the World Congress of the Econometric Society in 2005.     

Transfer principles in income redistribution

Dalton's principle of transfer for income redistribution says that society will be better off when a unit of income in transferred from a richer to a poorer individual. This paper investigates the conjunction of a natural extension of Dalton's principle — which says that any combination of a socially desirable transfer with its inverse at uniformly higher levels of income will have positive social benefit — and a traditional utilitarian-egalitarian formulation of social welfare. The transfer principles involved in the extension of Dalton's rule correspond to stochastic dominance relations between income distributions with a common mean, and lead to the conclusion that, when ? and g are income distributions, the social welfare of ? is larger than that of g if $\text{Σe}{}^{\mathrm{-ax}}\text{?(x)<Σe}{}^{\mathrm{-ax}}\text{g(x)}$ for all positive a. This conclusion is intimately connected with a measure of income inequality studied by Kolm.     

HOW DO EUROPEANS EVALUATE INCOME DISTRIBUTIONS? AN ASSESSMENT BASED ON HAPPINESS SURVEYS

The purpose of this paper is to measure the evaluation of income inequality by European citizens. Starting from the concept of a social welfare function defined on income distributions the paper estimates the degree and nature of inequality aversion of Europeans. It uses subjective well-being (SWB) as an empirical measure of welfare and estimates how SWB is related to average income and measures of income inequality (from an appropriate class). The estimated relationship is used to determine those inequality measures which qualify as proper representations of people's inequality aversion.     

One Measure of Segregation*

This article considers the problem of deriving a numerical measure of segregation, i.e., a measure of inequality in the distribution of people across groups. It proposes a list of eight desirable properties for a good numerical measure of segregation. These properties yield a class of segregation indexes that are related to generalized entropy indexes of income inequality. Moreover, one and only one index—termed the square root index—satisfies seven of the properties.     

Arrovian aggregation in economic environments: how much should we know about indifference surfaces?

Arrow's celebrated theorem of social choice shows that the aggregation of individual preferences into a social ordering cannot make the ranking of any pair of alternatives depend only on individual preferences over that pair, unless the fundamental weak Pareto and non-dictatorship principles are violated. In the standard model of division of commodities, we investigate how much information about indifference surfaces is needed to construct social ordering functions satisfying the weak Pareto principle and anonymity. We show that local information such as marginal rates of substitution or the shapes “within the Edgeworth box” is not enough, and knowledge of substantially non-local information is necessary.     

Strategy-proof preference aggregation: Possibilities and characterizations

An aggregation rule maps each profile of individual strict preference orderings over a set of alternatives into a social ordering over that set. We call such a rule strategy-proof if misreporting one's preference never produces a different social ordering that is between the original ordering and one's own preference. After describing two examples of manipulable rules, we study in some detail three classes of strategy-proof rules: (i) rules based on a monotonic alteration of the majority relation generated by the preference profile; (ii) rules improving upon a fixed status-quo; and (iii) rules generalizing the Condorcet–Kemeny aggregation method.     

Sharing a River

A group of agents located along a river have quasi-linear preferences over water and money. We ask how the water should be allocated and what money transfers should be performed. The core lower bounds require that no coalition should get less than the welfare it could achieve by using the water it controls. The aspiration upper bounds demand that no coalition enjoy a welfare higher than what it could achieve in the absence of the remaining agents. Exactly one welfare distribution satisfies the core lower bounds and the aspiration upper bounds: it is the marginal contribution vector corresponding to the ordering of the agents along the river. Journal of Economic Literature Classification Numbers: D62, C71.     

Self‐Assessed Social Position and Poverty

In this article, we use microlevel data extracted from the 2006 Japanese General Social Surveys to analyze the relationships between self‐assessed social position and socioeconomic factors such as income and poverty. We provide the posterior results of the estimation of the Bayesian multivariate ordered probit model and propose an inequality measure for self‐assessed social position on the basis of the posterior results. We call the inequality measure “regret” and show that the distributions of regret differ for people above and below the poverty line.     

INEQUALITY OF OPPORTUNITIES VS. INEQUALITY OF OUTCOMES: ARE WESTERN SOCIETIES ALL ALIKE?

This paper analyzes the relationship between income inequality and inequality of opportunities for income acquisition in nine developed countries during the 1990s. Equality of opportunity is defined as the situation where income distributions conditional on social origin cannot be ranked according to stochastic dominance criteria. We measure social origin by parental education and occupation and use the database built by Roemer et al. (2003 ). Stochastic dominance is assessed using nonparametric statistical tests. Our results indicate strong disparities in the degree of equality of opportunity across countries and a strong correlation between inequality of outcomes and inequality of opportunity. The U.S. and Italy show up as the most unequal countries in terms of both outcome and opportunity. At the opposite extreme, income distributions conditional on social origin are almost the same in Scandinavian countries even before any redistributive policy. We complement the ordinal comparison by resorting to an original scalar “Gini” index of opportunities, which can be decomposed into a risk and a return component. In our sample, inequality of opportunity is mostly driven by differences in mean income conditional on social origin, and differences in risk compensate the return element in most countries.     

ESTIMATING INCOME INEQUALITY IN CHINA USING GROUPED DATA AND THE GENERALIZED BETA DISTRIBUTION

There are two main types of data sources of income distributions in China: household survey data and grouped data. Household survey data are typically available for isolated years and individual provinces. In comparison, aggregate or grouped data are typically available more frequently and usually have national coverage. In principle, grouped data allow investigation of the change of inequality over longer, continuous periods of time, and the identification of patterns of inequality across broader regions. Nevertheless, a major limitation of grouped data is that only mean (average) income and income shares of quintile or decile groups of the population are reported. Directly using grouped data reported in this format is equivalent to assuming that all individuals in a quintile or decile group have the same income. This potentially distorts the estimate of inequality within each region. The aim of this paper is to apply an improved econometric method designed to use grouped data to study income inequality in China. A generalized beta distribution is employed to model income inequality in China at various levels and periods of time. The generalized beta distribution is more general and flexible than the lognormal distribution that has been used in past research, and also relaxes the assumption of a uniform distribution of income within quintile and decile groups of populations. The paper studies the nature and extent of inequality in rural and urban China over the period 1978 to 2002. Income inequality in the whole of China is then modeled using a mixture of province-specific distributions. The estimated results are used to study the trends in national inequality, and to discuss the empirical findings in the light of economic reforms, regional policies, and globalization of the Chinese economy.     

Growth and distribution in an AK-model with endogenous impatience

This paper combines the classical approach to inequality, based on the division of society into classes with different saving propensities, and the social conflict approach, in which inequality inflicts costs to growth. We assume that each consumer’s discount factor is endogenously determined through two channels: (1) it is positively related to the consumer’s relative wealth, and (2) negatively affected by an aggregate measure of social conflict. Unlike in models with exogenous discount rates, steady state equilibria are indeterminate and the set of equilibria is a continuum parameterized by an index of income inequality. Under reasonable assumptions, the relationship between growth and inequality has an inverted-U shape.