1,720,987 research outputs found
Intersecting generalized Lorenz curves and the Gini index
No full textAs 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
Inverse stochastic dominance, inequality measurement and Gini index.
No full textWe investigate the relationship between the third degree inverse stochastic dominance criterion introduced in Muliere and Scarsini (1989)[A note on stochastic dominance and inequality measures. Journal of Economic Theory, 49, 314-323] and inequality dominance when Lorenz curves intersect. We propose a new definition of transfer sensitivity aimed at strengthening the Pigou-Dalton Principle of Transfers. Our definition is dual to that suggested by Shorrocks and Foster (1987) [Transfer sensitive inequality measures. Review of Economic Studies, 14 , 485-497]. It involves a regressive transfer and a progressive transfer both from the same donor, leaving the Gini index unchanged. We prove that finite sequences of these transfers and/or progressive transfers characterize the third degree inverse stochastic dominance criterion. This criterion allows us to make unanimous inequality judgements even when Lorenz curves intersect. The Gini coefficient becomes relevant in these cases in order to conclusively rank the distributions
Characterizing Inequality Equivalence Criteria WP Number: 32, November 2012, ISSN: 2036-2919, Dipartimento di Scienze Economiche, Università di Verona
No full textWe introduce an axiomatic framework to analyze the perception of inequality across distributions with different total income. The main result is the characterization of a new two parameters generalized version of the inequality equivalence criterion (IEC), the Flexible IEC (FIE). This criterion is able to encompass all the most used criteria of inequality equivalence and is sufficiently flexible to provide a perception consistent with recent evidence from questionnaire investigations, namely that the inequality perception goes from the relative view (focussing on income shares) to the absolute view (focussing on absolute income differentials) as incomes increase. One parameter of the FIE is associated with the Bossert and Pfingsten (Math. Soc. Sc. 1990) Intermediate IEC (IIE) while the other is shown to lead to an alternative single parameter version of the IEC, the Proportional IEC which is dual to the previous. We provide independent characterizations both of PIE and IIE. Also alternative IECs existing in the literature are characterized within the axiomatic framework suggested. These results are consistent with those obtained in the surplus sharing literature by Moulin (Int. J. Game Theory 1987), Young (Math. Op. Res. 1987, J. Econ. Theory 1988) and Pfingsten (Math. Soc. Sc. 1991), and with recent results in inequality measurement by Ebert (Math. Soc. Sc. 2004) and Zheng (Soc. Ch. Wel. 2007). We complete the analysis investigating the implications of extending the domain of the income distributions including negative incomes. The basic consistency properties suggested in order to characterize the IECs are sufficient to select the absolute IEC when unbounded negative incomes are included in the domain
Variable population welfare and poverty orderings satisfying replication properties, WP 69 2009, ISSN: 2036-2919, Dipartimento di Scienze Economiche, Università di Verona
No full textWe discuss and compare the variable population axioms of Critical Level (CL) and Population Replication Invariance (PRI) introduced in the economic and philosophical literature for evaluating distributions with different population size. We provide a common framework for analyzing these competing views considering a strengthening of the Population Replication Principle
(PRP) based on Dalton’s (1920) “principle of proportionate additions to persons” that requires an ordering defined over populations of the same size to be invariant w.r.t. replication of the distributions, not necessarily imposing indifference between the original distribution and the replica. The strong version of PRP extends the invariance condition to hold also when distributions of
di=erent population size are compared. We suggest ethically meaningful general specifications of the invariance requirement underlying the Strong PRP and characterize the associated classes of parameterized evaluation functions that include CL principles and PRI properties. Moreover, we identify a general class of evaluation functions satisfying the Strong PRP: the social evaluation
ordering will be represented by the simple formula considering the product of
the population size times a strictly monotonic function of the Equally Distributed
Equivalent Income (EDEI). Interesting ethical properties are shown to be
associated with the shape of the function transforming the EDEI. Implications
for poverty measurement are investigated
A generalized version of the inequality equivalence criterion: a surplus sharing characterization, complete and partial orderings
No full textWe consider an axiomatic characterization of the perception of inequality across distributions with different total income which is consistent with those obtained in a game theoretic context in surplus sharing literature by Moulin (Int. J. Game Theory
1987), Young (Math. Op. Res. 1987, J. Econ. Theory 1988) and Pfingsten (Math. Soc. Sc. 1991). Within this set-up we discuss a generalized version of the inequality equivalence concept introduced in Zoli (1998). This criterion is able to encompass all the most used criteria of inequality equivalence and is sufficiently
flexible to provide a perception consistent with recent evidence from questionnaire investigations shown in Amiel and Cowell (1997): namely, that the inequality perception goes from the realtive to the absolute as incomes increase. The class of inequality indices and dominance criteria, which are associated with the suggested generalized criterion, are completely characterized
Measuring Dissimilarity
No full textThe analysis of many social phenomena requires to compare distributions of outcomes achieved by individuals belonging to different social groups, defined for instance by their gender, ethnicity, birthplace, education, age or parental background. When the groups are similarly distributed across classes of realizations, their members have equal chances to achieve any of the attainable outcomes. Otherwise, a form of dissimilarity prevails. We frame dissimilarity comparisons of sets of groups distributions by showing the equivalence between axioms underpinning information criteria, majorization conditions, agreement between dissimilarity indicators and new empirical tests based on Zonotopes and Path Polytopes inclusion. Multi-group comparisons of segregation, discrimination and mobility, as well as inequality evaluations, are embedded within the dissimilarity model
On the Measurement of Dissimilarity and Related Orders, WP ECINEQ 2012 – 274, October 2012
No full textWe consider populations partitioned into groups, whose members are distributed across a finite number of classes such as, for instance, types of occupation, residential locations, social status of fathers, levels of education, health or income. Our aim is to assess the dissimilarity between the patterns of distributions of the different groups. These evaluations are relevant for the analysis of multi-group segregation, socioeconomic mobility, equalization of opportunity and discrimination. We conceptualize the notion of dissimilarity making use of reasonable transformations of the groups' distributions, based on sequences of transfers and exchanges of population masses across classes and/or groups. Our analysis clarifies the substantial differences underlying the concept of dissimilarity when applied to ordered or to permutable classes. In both settings, we illustrate the logical connections of dissimilarity evaluations with matrix majorization preorders, and provide equivalent implementable criteria to test unambiguous reductions in dissimilarity. Furthermore, we show that inequality evaluations can be interpreted as special cases of dissimilarity assessments and discuss relations with concepts of segregation and discrimination
Ethnic Distribution, Effective Power and Conflict
No full textEthnic heterogeneity can potentially be related to the occurrence of conflicts with longlasting economic effects. Two main measures of ethnic heterogeneity are employed in the econometric literature on ethnic diversity and conflict: the Gini heterogeneity or fractionalization index and the discrete polarization index. However, still no broad consensus is reached on which distributional aspect of ethnic diversity is associated with the outbreak of conflict. In this paper we argue that the relative importance of each pattern of ethnic diversity depends on the trade-off between the groups' power and its interaction with other groups. Following the Esteban and Ray [On the measurement of polarization, Econometrica, 62(4), 1994] approach to social antagonism, we axiomatically
derive a parametric class of indices of conflict potential that combines the groups' effective power and the between-groups interaction. We use a discrete metric to define the distances between groups and we do not treat each group as a unitary actor. Moreover, we assume that the effective power of a group depends not only on its own relative size but also on the relative size of all the other groups in the population. We show that for certain parameter values the obtained indices reduce to the existing indices of ethnic diversity, while in general the derived indices combine in a non-linear way three different aspects of
ethnic diversity, namely the fractionalization, the polarization and the ethnic dominance. The power component of the extreme element of the class of indices is given by the relative Penrose-Banzhaf index of voting power. The results from our empirical exercise show that the derived extreme index outperforms the existing indices of ethnic diversity in the explanation of ethnic conflict onset
The evaluation of well-being in the functioning-capability space: a new criterion based on refined functionings
Full text linkIt is generally agreed that the identification of income wealth does not provide all the relevant information needed to evaluate the quality of life: income is but one component of overall individual wellbeing. Latest economic contributions focus on the multidimensional nature of well-being taking into account a number of life dimensions further than income (e.g.
health conditions, educational attainments). Moreover, as recently argued, freedom of choice plays a relevant role in the definition of quality of life. Which criterion could be the most appropriate to allow for the multidimensional nature of well-being? Can freedom of choice be included in such a comprehensive evaluation? This paper concerns a re-examination of the notion of well-being within the functioning-capability approach proposed by A.K. Sen. Following Sen’s framework we re-define the value of achieved functionings in a way that takes note of alternative opportunities.
We make operative a freedom-of-choice based refinement procedure by partitioning the population into different groups, homogeneous in some discriminating objective characteristic (e.g. age, sex, location). Our aim is to test whether the fact of showing a certain attribute poses an objective limit to a person’s opportunity to reach or exceed a given value of a functioning
From unidimensional to multidimensional inequality: a review
No full textWe review results concerning the representation of partial orders of univariate distributions via stochastic orders and investigate their applications to some classes of stochastic dominance conditions applied in inequality and welfare measurement. The results obtained in an unidimensional framework are extended to multidimensional analysis. We discuss difficulties arising from aggregation of multidimensional distributions into synthetic indicators that value both inequality in the distribution of each attribute and the association between the attributes. We explore the potential for multidimensional evaluations that are based on the partial orders induced by different criteria ofmajorization and organize related and equivalent inequality and welfare representations
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