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1.
This paper is concerned with the problem of ranking Lorenz curves in situations where the Lorenz curves intersect and no unambiguous
ranking can be attained without introducing weaker ranking criteria than first-degree Lorenz dominance. To deal with such
situations, Aaberge (Soc Choice Welf 33:235–259, 2009) introduced two alternative sequences of nested dominance criteria for Lorenz curves, which proved to characterize two separate
systems of nested subfamilies of inequality measures. This paper uses the obtained characterization results to arrange the
members of two different generalized Gini families of inequality measures into subfamilies according to their relationship
to Lorenz dominance of various degrees. Since the various criteria of higher degree Lorenz dominance provide convenient computational
methods, these results can be used to identify the largest subfamily of the generalized Gini families, and thus the least
restrictive social preferences, required to reach unambiguous ranking of a set of Lorenz curves. We further show that the
weight-functions of the members of the generalized Gini families offer intuitive interpretations of higher degree Lorenz dominance,
which generally has been viewed as difficult to interpret because they involve assumptions about third and higher derivatives.
To demonstrate the usefulness of these methods for empirical applications, we examine the time trend in income and earnings
inequality of Norwegian males during the period 1967–2005. 相似文献
2.
Patrick Moyes 《Journal of Economic Inequality》2007,5(3):279-303
It is well-known that, when the Lorenz curves do not cross, the ranking of distributions provided by the Gini index is identical
to the one implied by the Lorenz criterion. This does not preclude inequality as measured by the Gini index to increase while
the Lorenz curves cross. A suitable modification of the Gini coefficient allows the Lorenz quasi-ordering to coincide with
the ranking generated by the application of unanimity over the class of extended Gini indices. Recently the Lorenz quasi-ordering
and the underlying principle of transfers have come under attack, while new criteria – the differentials, deprivation and
satisfaction quasi-orderings – have been proposed for providing unambiguous rankings of distributions. We suggest to weaken
the principle of transfers by imposing additional restrictions on the progressive transfers, which take into account the positions
on the income scale of the donors and beneficiaries. We identify the subclasses of extended Gini indices that satisfy these
weaker versions of the principle of transfers and we show that the application of unanimity among these classes generate rankings
of distributions that coincide with those implied by the differentials, deprivation and satisfaction quasi-orderings.
相似文献
3.
Several recent studies have suggested that the distribution of income (earnings, jobs) is becoming more polarized. Much of
the evidence presented in support of this view consists of demonstrating that the population share in an arbitrarily chosen
middle income class has fallen. However, such evidence can be criticized as being range-specific—depending on the particular
cutoffs selected. In this paper we propose a range-free approach to measuring the middle class and polarization, based on
partial orderings. The approach yields two polarization curves which, like the Lorenz curve in inequality analysis, signal unambiguous
increases in polarization. It also leads to an intuitive new index of polarization that is shown to be closely related to
the Gini coefficient. We apply the new methodology to income and earnings data from the U.S. and Canada, and find that polarization
is on the rise in the U.S. but is stable or declining in Canada. A cross-country comparison reveals the U.S. to be unambiguously
more polarized than Canada. 相似文献
4.
Gini’s nuclear family 总被引:1,自引:0,他引:1
Rolf Aaberge 《Journal of Economic Inequality》2007,5(3):305-322
The purpose of this paper is to justify the use of the Gini coefficient and two close relatives for summarizing the basic
information of inequality in distributions of income. To this end we employ a specific transformation of the Lorenz curve,
the scaled conditional mean curve, rather than the Lorenz curve as the basic formal representation of inequality in distributions
of income. The scaled conditional mean curve is shown to possess several attractive properties as an alternative interpretation
of the information content of the Lorenz curve and furthermore proves to yield essential information on polarization in the
population. The paper also provides asymptotic distribution results for the empirical scaled conditional mean curve and the
related family of empirical measures of inequality.
相似文献
5.
A large number of functional forms has been suggested in the literature for estimating Lorenz curves that describe the relationship between income and population shares. The traditional way of overcoming functional-form uncertainty when estimating a Lorenz curve is to choose the function that best fits the data in some sense. In this paper we describe an alternative approach for accommodating functional-form uncertainty, namely, how to use Bayesian model averaging to average the alternative functional forms. In this averaging process, the different Lorenz curves are weighted by their posterior probabilities of being correct. Unlike a strategy of picking the best-fitting function, Bayesian model averaging gives posterior standard deviations that reflect the functional-form uncertainty. Building on our earlier work (Chotikapanich and Griffiths, 2002), we construct likelihood functions using the Dirichlet distribution and estimate a number of Lorenz functions for Australian income units. Prior information is formulated in terms of the Gini coefficient and the income shares of the poorest 10% and poorest 90% of the population. Posterior density functions for these quantities are derived for each Lorenz function and are averaged over all the Lorenz functions. 相似文献
6.
W. Henry Chiu 《Social Choice and Welfare》2007,28(3):375-399
This paper clarifies the conceptual distinction of downside inequality aversion (or transfer sensitivity) as a normative criterion
for judging income distributions from the Pigou-Dalton principle of transfers. We show that when the Lorenz curves of two
income distributions intersect, how the change from one distribution to the other is judged by an inequality index exhibiting
downside inequality aversion often depends on the relative strengths of its downside inequality aversion and inequality aversion.
For additive inequality indices or their monotonic transformations, a measure characterizing the strength of an index’s downside
inequality aversion against its inequality aversion is shown to determine the ranking by the index of two distributions whose
Lorenz curves cross once. The precise condition under which the same result generalizes to the case of multiple-crossing Lorenz
curves is also identified. The results are particularly useful in understanding the distributional impact of tax reforms.
I received exceptionally helpful comments from Mike Hoy, Peter Lambert, the Editor, Buhong Zheng, and an anonymous referee.
The remaining errors and shortcomings are my own – W.H. Chiu 相似文献
7.
Rolf Aaberge 《Social Choice and Welfare》2000,17(4):639-653
The purpose of this paper is to propose and justify the use of a few measures of inequality for summarizing the basic information
provided by the Lorenz curve. By exploiting the fact that the Lorenz curve can be considered analogous to a cumulative distribution
function it is demonstrated that the moments of the Lorenz curve generate a convenient family of inequality measures, called
the Lorenz family of inequality measures. In particular, the first few moments, which often capture the essential features
of a distribution function, are proposed as the primary quantities for summarizing the information content of the Lorenz curve.
Employed together these measures, which include the Gini coefficient, also provide essential information on the shape of the
income distribution. Relying on the principle of diminishing transfers it is shown that the Lorenz measures, as opposed to
the Atkinson measures, have transfer-sensitivity properties that depend on the shape of the income distribution.
Received: 20 July 1998/Accepted: 10 September 1999 相似文献
8.
9.
An index of richness in a society is a measure of the extent of its affluence. This paper presents an analytical discussion on several indices of richness and their properties. It also develops criteria for ordering alternative distributions of income in terms of their richness. Given a line of richness, an income level above which a person is regarded as rich, and depending on the redistributive principle, it is shown that the ranking relation can be implemented by seeking dominance with respect to the generalized Lorenz curve of the rich or the affluence profile of the society. When the line of richness is assumed to be variable, we need to employ the stochastic dominance conditions for ordering the income distributions. 相似文献
10.
Buhong Zheng 《Social Choice and Welfare》2007,28(2):255-280
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.
I am grateful to two anonymous referees and Peter Lambert for their very constructive comments and suggestions on an earlier
version of the paper. The usual caveat applies. 相似文献
11.
Intersecting generalized Lorenz curves and the Gini index 总被引:5,自引:0,他引:5
Claudio Zoli 《Social Choice and Welfare》1999,16(2):183-196
As is well known, the use of the Gini coefficient in comparisons is inconsistent with an utilitarian approach. This paper
analyzes the Gini coefficient's normative significance in welfare comparisons evaluating income distributions according to
Yaari dual social welfare function. When generalized Lorenz curves cross once, the Gini coefficient is decisive in determining
welfare rankings if we strengthen the Principle of Transfers applying a Positional version of the Principle of Transfer Sensitivity.
This result can also be extended to the case of multiple crossings.
Received: 28 August 1996 / Accepted: 22 October 1997 相似文献
12.
The Journal of Economic Inequality - We propose an extension of the univariate Lorenz curve and of the Gini coefficient to the multivariate case, i.e., to simultaneously measure inequality in more... 相似文献
13.
We consider the problem of ranking distributions of opportunity sets on the basis of equality. First, conditional on a given
ranking of individual opportunity sets, we define the notion of an equalizing transformation. Then, assuming that the opportunity
sets are ranked according to the cardinality ordering, we formulate the analogues of the notions of the Lorenz partial ordering,
equalizing (Dalton) transfers, and inequality averse social welfare functions – concepts which play a central role in the
literature on income inequality. Our main result is a cardinality-based analogue of the fundamental theorem of inequality
measurement: one distribution Lorenz dominates another if and only if the former can be obtained from the latter by a finite
sequence of rank preserving equalizations, and if and only if the former is ranked higher than the latter by all inequality
averse social welfare functions. In addition, we characterize the smallest monotonic and transitive extension of our cardinality-based
Lorenz inequality ordering.
Received: 2 May 1995 / Accepted: 11 October 1996 相似文献
14.
Robert Sugden 《Social Choice and Welfare》2007,29(4):665-682
Most work on measuring opportunity is directed at ranking opportunity sets. This paper addresses the more general issue of
assessing the opportunity provided by multi-period decision problems, focusing on the dynamic inconsistencies that can occur
if agent’s preferences are unstable. A principle is proposed by which a dominance relation among outcomes iteratively induces
a dominance relation among multi-period problems. This principle implies that opportunities to make sequences of individually
reasonable actions have positive value, even if, because of dynamic inconsistency, those sequences lead to unambiguous loss.
Opportunities which allow an agent to constrain herself are shown to have zero value. 相似文献
15.
Lorenz curves and second-order dominance criteria, the fundamental tools for stochastic dominance, are known to be sensitive
to data contamination in the tails of the distribution. We propose two ways of dealing with the problem: (1) Estimate Lorenz
curves using parametric models and (2) combine empirical estimation with a parametric (robust) estimation of the upper tail
of the distribution using the Pareto model. Approach (2) is preferred because of its flexibility. Using simulations we show
the dramatic effect of a few contaminated data on the Lorenz ranking and the performance of the robust semi-parametric approach
(2). Since estimation is only a first step for statistical inference and since semi-parametric models are not straightforward
to handle, we also derive asymptotic covariance matrices for our semi-parametric estimators. 相似文献
16.
Bart Capéau 《Journal of Economic Inequality》2013,11(2):237-248
A relative invariant and an absolute invariant inequality ordering satisfying extreme bottom-sensitivity, are proposed. It is shown that the leximin social welfare ordering can be expressed in terms of a ranking of distributions on the sole basis of their size, measured by the mean, and the degree of inequality, measured according to these inequality concepts. Leximin thus exhibits extreme bottom-sensitivity. This property does not withstand that leximin prefers a larger size of the cake at the cost of higher inequality in a number of cases. These trade-offs between size and equality are characterised in terms of degrees of dominance of the lower parts of the ordinary and absolute Lorenz curves that are accepted by leximin for a given increase in the mean. 相似文献
17.
The aim of this paper is to empirically evaluate the effect of the length of the accounting period on indices of inequality of household income in Israel. There are three main findings: (1) The analysis of the impact of the accounting period on the Gini index of inequality can be done in a way which is identical to analyzing the effect of the accounting period on the coefficient of variation; (2) changing the accounting period from one to three months decreases, on average, the Gini index of inequality by about 1.7%. Furthermore, the Gini index calculated from a three-month accounting period was 3.9%–4.1% higher than the index based on a 12-month period. The change in the accounting period from 12 months to three months accounts for 27% to 37% of the increase in inequality in the last two decades, depending on the type of income considered. (3) The above relationship is stable over the years but is sensitive to the definition of income. 相似文献
18.
Kenneth D. Bailey 《Sociological inquiry》1985,55(2):200-211
Although sociologists have long been interested in the analysis of inequality, there have been relatively few systematic attempts to measure it. Most measurement has utilized popular existing measures such as the Gini coefficient, which unfortunately is relatively difficult to compute and interpret. This article presents a new measure of inequality (B) that is based upon the concept of entropy. The B measure is used for categorical data and complements Theil's (T) entropy measure for continuous data. The B measure is illustrated for both income and wealth data and successfully meets several criteria for evaluating measures of inequality. These include the criteria of scale invariance, sensitivity to transfers, and adequate upper bounds. A further advantage of sociological entropy measures of inequality is that they facilitate interdisciplinary comparison of work on inequality between sociology and other disciplines (such as economics) which use entropy measures of inequality. 相似文献
19.
Florent Bresson 《Journal of Economic Inequality》2010,8(1):71-100
Many authors have recently emphasized the crucial role of income inequalities in the design of efficient policies aimed at
reducing poverty. However, the link between variations in the degree of inequality and variations in poverty is not well documented.
The literature, for instance, does not provide any satisfying tool for predicting how a small relative variation in the Gini
index may be associated with a variation in the headcount index. In the present paper, we define a family of Lorenz curve
transformations that can directly be interpreted in terms of relative variations of known inequality measures. Then, we extend
Kakwani’s (Rev Income Wealth 39(2):121–139, 1993) methodology for the calculation of inequality elasticities of poverty. Improvements are threefold with respect to Kakwani’s
work. First, our formulas are not confined to the sole Gini index. Secondly, they embrace the uncertainty and the complexity
of the mechanical link between inequality and poverty. Third, using some flexible functional form, one can easily perform
an accurate estimation of the point inequality elasticities of poverty corresponding to observed variations of a given income
distribution. We also propose a simple measure that may be helpful to assess how “pro-poor” are inequality variations by comparing
the observed elasticities with the set of theoretical elasticities that could be obtained from the initial income distribution. 相似文献
20.
ATSUSHI ISHIDA 《International Journal of Japanese Sociology》2010,19(1):64-81
This study aims to measure the inequality of anticipated lifetime income and the inequality of annual income among the younger generation (24–29‐year‐old men), and to examine any trends that can be found in terms of inequality between 1955 and 2005 in Japan. Anticipated lifetime income is defined in this study as the present value of the total anticipated annual income that one is likely to earn each year between the ages of 24 and 59 years, assuming that there is no intragenerational class mobility. The anticipated lifetime income for each young male is estimated using the Social Stratification and Social Mobility Survey dataset, which is a Japanese national cross‐sectional survey of social stratification and social mobility. An inequality in the anticipated lifetime income can be regarded as an “inequality of outlook” among the younger generation. As a result of this analysis, it was found that the Gini coefficient, the most general measurement of income inequality, had significantly increased for anticipated lifetime income between 1995 and 2005. At the same time, the gap between the Gini coefficient of anticipated lifetime income and that of annual income had narrowed. It is suggested that “inequality of outlook,” which cannot be easily identified using a superficial index, has increased significantly. 相似文献