A matrix approach to the Gini index decomposition by subgroup and by income source

The literature offers two main ways of decomposing the Gini index: decomposition by population subgroup and by income source. This article proposes merging the two decomposition dimensions by suggesting a matrix formula for the Gini index which permits the simultaneous decomposition by subgroup and by income source. Using this multi‐decomposition, one can investigate the role of the interaction between the subgroup and the source components in determining the overall inequality. We apply the methodology to sample data on Italian household incomes collected in 2008.     

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.     

Cointegration with structural changes between per capita product and income inequality in Mexico

The long-run relationship between per capita product and income inequality in Mexico is assessed for the period 1963–2010. The methodology consists of stochastic unit root techniques with structural changes. The integration and cointegration tests suggest that it is not possible to understand this link if the possibility of structural changes is not taken into account. Causality, running from per capita product to income inequality, and a negative and significant overall effect are estimated. However, after the regime shifts – mainly estimated to occur in the 1980s – the connection is no longer meaningful. This result seems to be linked to the slow growth of the Mexican economy after these structural breaks, affecting, in turn, the reductions in income inequality.     

以基尼系数衡量的教育不平等与中国的实证研究

人力资本结构在经济增长中的作用已为人们所公认,而教育不平等是评价人力资本结构的重要内容。通过计算教育基尼系数得到我国教育不平等的基本状况。我国教育基尼系数从1982—2000年呈减少状态,与平均受教育年限和初中入学率负相关,同时人均GDP水平越高教育基尼系数越小。在整体教育不平等状况改善的情况下,以文盲率体现的性别受教育差异并未得到改善,甚至有扩大的趋向。     

The limitations of negative incomes in the Gini coefficient decomposition by source

Lerman and Yitzhaki (1985) developed a decomposition of the Gini coefficient by income source that has been extensively used in the literature. This method has strong limitations in the presence of negative incomes, which were not discussed by the original authors and have been widely overlooked in successive studies. Through theoretical argumentation and practical examples, this article shows that, when using negative incomes, (1) the original decomposition formulae become inappropriate, (2) the marginal effects analysis may yield erroneous results and (3) the Pigou–Dalton ‘principle of transfers’ is not always met. This has critical implications for policy development, given that strategies based upon incorrect analyses could actually result in undesired greater income inequalities. The Gini source decomposition should be carefully applied by researchers and policymakers, especially in rural developing areas, where negative incomes are common due to financial losses from agricultural activities.     

How large is income inequality in China: assessment on different estimates of Gini coefficient

The rising income inequality in China has attracted social attentions, especially since SWUFE published the unbelievably high Gini coefficient in December 2012. In order to answer the question how large income inequality in current China is, this paper compares existing different Gini coefficients estimated from four different household surveys, which are the NBS household survey, the CHIP survey, the CHFS of SWUFE, and the CFPS of Peking University, and then assesses these household surveys themselves. The relevant evidences indicate that the national Gini coefficient in current China is between 0.47~0.52. The sampling defects of the CHFS are significantly major and that the national Gini coefficient of 0.61 published by SWUFE is seriously overestimated.     

基尼系数的扩展与和谐社会的基石

笔者从稀缺资源的分配角度对基尼系数进行了有益的扩展,提出并论证了权力系数的合理性,结果表明:降低权力系数不仅能够促进社会公平,而且能够促进经济增长,开放的社会秩序是合适的权力系数的必然结果,也是国家长治久安、社会和谐、民族崛起的必然选择。借助于传统基尼系数的计算方法,论文给出了权力系数一种新的算法。针对中国当前转轨经济的现实,提出了实现和谐社会的必要步骤。     

吉林省区域经济差异分析

考虑到测算吉林省区域差异的必要性,在分析有关区域差异内涵和理论的基础上,从理论方面,提出一种有关区域差异形成机制的假设,在实证研究方面,运用Theil指数的空间分解和基尼系数的产业分解两种方法,分析了吉林省1993—2003年这段时间内其区域差异的变化情况,最后简要分析了上述结果产生的原因,并提出一些建议。     

A new approach to the decomposition of the Gini income inequality ratio

The purpose of this research is to introduce a new approach to the decomposition of the Gini ratio into three components, supporting them with economic and statistical rigorous interpretations. The three components are: (i) the Gini inequalitywithin subpopulations; (ii) thenet contribution of the extended Gini inequalitybetween subpopulations; and (iii) the contribution of theintensity of transvariation between subpopulations. These components are weighted by the product of the population shares times the income shares of the corresponding subpopulations where the weights add to one.The decomposition introduced in this research is applied to the 1990 U.S. family income distribution. The population of families is disaggregated by types into the following subpopulations: (a) married-couple families; (b) male householder, no wife present; and (c) female householder, no husband present.     

The distance to competitive balance: a cardinal measure

Competitive balance is a key variable in the analysis of sports competitions. There are several indexes that measure competitive balance but, either they are not a mathematical metric or they do not have the unit interval as a range. Therefore, these indexes do not indicate the magnitude of the differences, and the measurements cannot be interpreted as percentages. We characterize the space of all admissible configurations of the results of a competition. Then, we construct a new index, based on the concept of distance, whose range is the unit interval, and define it as a function in a metric space. So, it solves issues linked to the limited cardinality of most existing indexes, and we can answer this question: What is the meaning of the differences between the levels of competitive balance? We applied this index to the major European soccer leagues over the last twenty seasons.     

我国地区间公共福利基尼系数及其经济增长效应研究

本文采用1995—2007年我国31个省(市)的福利性财政支出数据,应用基尼系数方法测算了我国省(市)间的公共福利差距。通过分解计算基尼系数的地区构成,发现东、中、西部地区间的经济差距是我国福利性财政支出差异的主要表现方面。鉴于此,本文利用VAR模型和脉冲响应函数,计算并比较东、中、西部地区福利性财政支出基尼系数的经济增长效应差异性。结果表明:东、中部地区公共福利基尼系数的经济增长效应正负交替出现,但最终负向且趋于平稳;而西部地区公共福利的经济增长效应则一直是负向且稳定的。     

On competitive balance in the group stage of the UEFA Champions League*

This article examines competitive balance in the group stage of the UEFA Champions League over the last two decades (1999/2000–2017/2018). Competitive balance is considered both before and after a competition. Have the groups been designed in such a way as to ensure similar levels of competitive balance ex ante? Have the demonstrated strengths (ex post competitive balance) of the different groups been similar over each season? What is the relationship between the competitive balance in the designed groups and that achieved in the same groups after the competition? Are the performance achieved in terms of ex post competitive balance similar to ex ante competitive balance levels? We found that, despite expectations, the groups' ex ante competitive balance was not homogeneous. Although ex ante competitive balance serves as a good predictor, on average, of ex post competitive balance, we observed significant differences at the levels of group and seasons. Therefore, it is possible to improve the design mechanism of the groups that make up the group stage of the champions so that they are composed homogeneously in terms of ex ante competitive balance.     

Foreign players,team production,and technical efficiency: Evidence from European soccer

As on-field success is nowadays the main objective of European soccer clubs, good management needs to extract the highest sport success from the squad talent at hand. Because teams differ in their quality, performance needs to be compared with the best practice of comparable units. One remarkable source of heterogeneity across teams is the squad composition, which can produce gains from diversity together with communication costs. The paper studies the efficiency in sporting performance of soccer teams, paying attention to how the number of foreign players relates to productive inefficiency. Using data for 146 teams in the top 5 European leagues during 10 seasons, we estimate a double heteroskedastic True Random Effects Stochastic Frontier team production function. We find that (i) the number of passes, ball recoveries, and shots from the penalty area improve team efficiency, and (ii) a higher number of foreign players increase inefficiency. Our findings suggest that gains from squad diversity might be offset by communication costs.     

On the Limitations of Some Current Usages of the Gini Index

This note constructs a simple two class example in which the Gini index is held constant while the size of the rich and poor populations change, in order to illustrate how very different societies can have the same Gini index and produce very similar estimates of standard inequality averse Social Welfare Functions. The rich/poor income ratio can vary by a factor of over 12, and the income share of the top one per cent can vary by a factor of over 16, with exactly the same Gini index. Focussing solely on the Gini index can thus obscure perceptions—e.g. of important market income trends or large changes in the redistributive impact of the tax and transfer system. Hence, analysts should supplement the use of an aggregate summary index of inequality with direct examination of the segments of the income distribution which they think are of greatest importance.     

中国市域经济发展差异的空间分析

区域经济发展差异历来是学者和政府相关部门关注的重要课题。文章采用全国338个地、市、州,1990、1995、2000和2004年四期人均GDP数据(包括市辖县),定性定量分析了我国市域经济发展的差异和特征。结果显示,中国市域经济的发展有从沿海发达地区向中、西部逐步扩散的趋势,扩散的范围在扩大,但强度在减弱,而市域经济发展的差距总体上却有继续扩大的趋势。     

ICT and income inequality: a cross-national perspective

The importance of information and communications technology (ICT) for economic growth and development is widely researched and seemingly well understood, but the effect of such investments on income inequality is less well documented. On the one hand, improvements in infrastructure are expected to expand economic opportunities for previously underserved populations. On the other hand, ICT growth may exacerbate inequality due to differential access and skill premiums. We use panel data from 109 countries during the period 2001–2014 to examine the empirical connection between ICT and income inequality in a cross-national context. Our results suggest that the effect of ICT on income inequality depends both on the specific type of ICT and on the measure of income inequality. In addition, the magnitude of ICT’s effect on income inequality is comparable to that of more traditional forms of economic infrastructure. Finally, we find that the association between ICT and income inequality is conditional on other economic and political characteristics.     

Does economic freedom increase income inequality? Evidence from the EU countries

This paper examines the relationship between economic liberalization and income inequality in the EU using panel data for the 2000s. The empirical evidence suggests that economic freedom is strongly related to income inequality. However, not all areas of economic freedom affect income distribution similarly. Government size is robustly associated with inequality, and also when controlling for potential endogeneity in a dynamic panel data analysis. Regulation is linked to income inequality as well, whereas legal system and sound money have no significant effects on income distribution. In the case of freedom to trade internationally, the relationship differs between old (EU-15) and new (former socialist) EU countries.     

公平性指标:从基尼系数到收入满足度差距

本文通过对财富分配、生活方式和价格水平、货币边际效用递减、评价生活质量标准以及指标构造缺陷等方面的分析,揭示了基尼系数作为公平性指标的局限性.本文认为,公平是公众认为合理的、愿意接受的规范和准则,其结果是公众的满意和社会的和谐.根据这一观点,我们可以用收入满足度来反映公众的满意程度,从而建立能反映社会公平与和谐程度的指标--收入满足度差距指标,并用德国的经验数据加以验证.     

基于基尼系数的返利政策效果测评

制造商在制定来年的返利政策时,面临着对现有返利政策的效果测评问题。利用经销商个数累计百分比对应返利累计百分比的洛伦茨曲线及其衡量指标基尼系数,能在客观上对现有返利政策进行效果测评,从而为来年返利政策的调整指明方向。