基尼系数的区间估计及其应用

 本文给出了收入为离散分布的三种计算基尼系数的新方法。利用收入份额法导出了基尼系数协方差算法的离散形式,并因此产生了计算基尼系数的回归系数法。文章重点讨论了基尼系数进行区间估计的两种方法,这些方法也适用于集中度指数,因而它们在测度社会经济领域的不平等中具有着十分广泛的用途。实际应用表明,新算法有效地简化了对基尼系数区间估计的标准差估算。     

收入波动与基尼系数:关于收入不平等的一个讨论

 本文建立了一个考察收入波动与基尼系数关系的模型,并通过计算机模拟实验证实：给定任何终生收入不平等状况,收入波动性增加都将导致各期的基尼系数增大。即,在终生收入不平等状况不变的情况下,各期的基尼系数也可因收入波动性增加而增大。考虑到我国经济转轨进程中家庭收入波动性日益增加的事实,则本文结论意味着,仅以基尼系数为判断标准很可能在一定程度上高估我国的家庭收入不平等状况。     

收入分配差异状况的一种新测度方法

在衡量收入分配差异方面,基尼系数存在较大局限。设计新的测度收入分配差异状况的方法十分必要。本文提出的对称收入系数及其派生指标能很好地运用于研究收入分配的差异及其变化状况。本文还结合我国城镇居民的收入分配状况进行分析,得到了一些新的结论。     

拓展基尼系数及其居民消费应用研究

本文给出了拓展基尼系数的一个等价定义,给出拓展基尼系数组群、要素分解的统一形式。对2009年我国城乡居民食品消费数据进行结构性分析,结果表明：⑴拓展基尼系数是不平等厌恶参数的增函数,最小值为0、最大值为1-S1/p1;⑵随着不平等厌恶参数的增大,各个组群或要素对不平等边际效应的方向保持相对稳定;⑶城镇居民在外餐饮、肉禽及制品、水产品类支出份额的增加,对食品消费不平等产生消极的边际影响。     

Variance Estimators of the Gini Coefficient—Probability Sampling

An estimator of the Gini coefficient (the well-known income inequality measure) of a finite population is defined for an arbitrary probability sampling design, taking the sampling design into consideration. Alternative estimators of the variance of the estimated Gini coefficient are introduced. The sampling performance of the Gini coefficient estimator and its variance estimators is studied by means of a Monte Carlo study, using stratified sampling from a miniature population of Swedish households with authentic income data.     

Some Sampling Properties of a Model for Income Distribution

A recently proposed model for describing the distribution of income over a population, based on the Burr distribution, has been shown to fit better than the commonly used lognormal or gamma distributions. The current article extends that analysis by deriving the large-sample properties of the maximum likelihood estimates for this three-parameter model. Consequently, resulting confidence intervals for some measures of income inequality (including the Gini index) are used to further test the model's validity, as well as to examine apparent trends in inequality over time. Since these properties depend on the way the income data are grouped and censored, implications for choosing data-report intervals can be analyzed. Specifically, a choice between two common methods of reporting the data is shown to have an important impact on Gini index estimates.     

理论基尼系数及其社会福利含义的讨论

 内容提要：尽管关于基尼系数的经验估计与研究异常丰富,但是对于基尼系数的理论含义一直缺乏严格的推导。本文试图从收入分布函数的定义出发,严格探讨基尼系数的理论含义和性质,以澄清一些关于基尼系数的误解。本文认为,最优的基尼系数值不可能从基尼系数的定义本身找到答案,必然牵涉到关于社会福利的价值判断。此外,一旦得到具体的收入分布函数,基尼系数的计算可以通过分布函数的参数估计来实现,因此本文最后给出了产生收入分布函数以及计算基尼系数的一种简单法则。     

Posterior Distributions for the Gini Coefficient Using Grouped Data

When available data comprise a number of sampled households in each of a number of income classes, the likelihood function is obtained from a multinomial distribution with the income class population proportions as the unknown parameters. Two methods for going from this likelihood function to a posterior distribution on the Gini coefficient are investigated. In the first method, two alternative assumptions about the underlying income distribution are considered, namely a lognormal distribution and the Singh–Maddala (1976) income distribution. In these cases the likelihood function is reparameterized and the Gini coefficient is a nonlinear function of the income distribution parameters. The Metropolis algorithm is used to find the corresponding posterior distributions of the Gini coefficient from a sample of Bangkok households. The second method does not require an assumption about the nature of the income distribution, but uses (a) triangular prior distributions, and (b) beta prior distributions, on the location of mean income within each income class. By sampling from these distributions, and the Dirichlet posterior distribution of the income class proportions, alternative posterior distributions of the Gini coefficient are calculated.     

Testing Homogeneity of Gini Indices Against Simple-Ordered Alternative

Gini index is one of the most popular indices employed for measuring inequality in income and wealth. In this article, we propose a multi-sample test for testing Gini indices against simple-ordered alternatives. The exact critical points through simulation were computed for the proposed test in case of two-parameter exponential distribution; however, the proposed test can be applied even in case of other distributions like Pareto, Weibull, etc. Construction of simultaneous one-sided confidence intervals (SOCIs) was proposed along with an illustration. Power of the test is computed and some power comparisons are also made.     

The Asymptotic Distribution of the S–Gini Index

Several generalizations of the classical Gini index, placing smaller or greater weights on various portions of income distribution, have been proposed by a number of authors. For purposes of statistical inference, the large sample distribution theory of the estimators of those measures of economic inequality is required. The present paper was stimulated by the use of bootstrap by Xu (2000) to estimate the variance of the estimator of the S –Gini index. It shows that the theory of L –statistics (Chernoff, Gastwirth & Johns, 1967; Shorack & Wellner, 1986) makes possible the construction of a consistent estimator for the S –Gini index and proof of its asymptotic normality. The paper also presents an explicit formula for the asymptotic variance. The formula should be helpful in planning the size of samples from which the S –Gini index can be estimated with a prescribed margin of error.     

基尼加权回归分析：概念、方法及应用

普通最小二乘法是进行回归分析最常用的基本方法,但该方法要求满足若干经典假设,对于小样本或在与收入相关回归分析的参数估计中易受奇异值、高收入群体的影响。本文试图利用基尼加权回归弥补以上不足。基尼加权回归可分为参数方法与非参数方法两类,参数方法基于样本残差的基尼平均差最小原则对参数进行估计;非参数方法则是直接由两点间的斜率加权得到。基尼加权回归分析可以进行参数假设检验并定义拟合优度,其中的假设检验在实际应用中采用Jackknife重抽样方法估计方差。文中提出的样本拓展基尼平均差算法,弥补了现有算法对样本数据只能提供近似计算的不足,极大简化相应的计算公式。利用我国2015年省域截面数据、1994至2015年总量时间序列数据分别讨论入境旅游收入对收入基尼系数的影响,发现使用基尼加权回归的结果不仅符合理论预期,而且可以通过不平等厌恶参数的变化反映入境旅游收入对不同群体收入公平性的影响。     

Large Sample Theory for the Bounds on the Gini and Related Indices of Inequality Estimated From Grouped Data

The joint asymptotic distribution of the upper and lower bounds for the Gini index derived by Gastwirth for grouped data are obtained. From them a conservative asymptotically distribution-free confidence interval for the population Gini index is presented. The methods also yield similar results for other indices of inequality (e.g., Theil's and Atkinson's).     

A vector valued bivariate gini index for truncated distributions

Gini index is widely used in the study of inequality of income distribution. In the present paper we give a definition of the Gini index in the Bivariate set-up and look into the problem of characterizing probability distributions based on some relationship between this index and various other commonly used measures. We also generalized the Gini index to a situation where several attributes of the population are considered.     

Relative Price Changes and Inequality in the Size Distribution of Various Components of Income

This article uses a comprehensive model of economic inequality to examine the impact of relative price changes on inequality in the marginal distributions of various income components in which the marginal distributions are derived from a multidimensional joint distribution. The multidimensional joint distribution function is assumed to be a member of the Pearson Type VI family; that is, it is assumed to be a beta distribution of the second kind. The multidimensional joint distribution is so called because it is a joint distribution of components of income and expenditures on various commodity groups. Gini measures of inequality are devised from the marginal distributions of the various income components. The inequality measures are shown to depend on the parameters of the multidimensional joint distribution. It is then shown that the parameters of the multidimensional joint distribution depend on the relative prices of various commodity groups and several other specified exogenous variables. Thus, knowledge of how changes in relative prices affect the parameters of the multidimensional joint distribution is deductively equivalent to knowledge of how changes in relative prices affect inequality in the marginal distributions of various components of income. It is found that relative price changes have a statistically significant impact on inequality in various components of income.     

农村贫困、收入不平等与城镇化关系的实证研究——基于2000—2012年省际面板数据

城镇化进程对经济和社会产生了巨大影响。通过计算中国省际层面2000—2012年城镇化率、农村贫困发生率和农村基尼系数,利用面板数据固定效应模型,研究中国农村贫困、农村不平等和城镇化的关系。研究发现:农村贫困发生率随着城镇化率提高而下降,城镇化率每提高1%,农村贫困发生率会降低2.87%;农村收入不平等随城镇化水平提高呈弱倒U型变化。同时,不同地区城镇化对农村贫困、农村收入不平等的影响也呈现不同趋势。在未来城镇化战略中,实施农村减贫政策时应兼顾调整收入分配政策,降低农村收入不平等。     

Income inequality versus utility inequality

Bentham (1789 Bentham, J. (1789). Utilitarianism, reproduced by Nabu Public Domain Reprints. Available at: http://www.publicdomainreprints.org. [Google Scholar]) introduced utility as the pursuit of happiness, with happiness defined in his philosophical view as existing if “pleasure” predominated over “pain.” This paper is the first to derive and compare the relative frequency distributions of income and utility in Bentham's classical sense. A utility-based Gini coefficient is formulated from a utility distribution derived from the better known income distribution. A utility-based Lorenz curve is defined as the accumulated sum of pain and pleasure, as Bentham defined them. A utility-based polarization index is created as the ratio of accumulated pain to accumulated pleasure. If raw income data are unavailable, an income distribution can still be estimated from a summary inequality statistic such as the Gini coefficient using the maximum entropy method. In this study, a measure of true income inequality, utility inequality, and the “pain” suffered by the poorest group are quantified and estimated using National Tax Service data from Korea.     

我国社会保障基尼系数的讨论与估算

 内容提要：我国收入基尼系数的扩大已被大多数学者研究与认同,但基于收入“二次分配”的社会保障基尼系数的研究还十分欠缺。本文认为社会保障作为收入再分配的重要手段之一是对人均社会福利收入分配的补充与调整,在社会经济资源配置过程中起着重要作用。本文采用相对平均差的基尼系数方法对我国社会保障差异化程度进行离散型数据分析,发现我国社会保障基尼系数值较高,但总体上有缩小趋势;其中,主要表现在养老保险与其他社会保险项目发展的不平衡性与区域差异性,所以应进一步加强全民养老保险与医疗保险制度建设,促进工伤、失业保险制度的协同发展。建立全国统筹的社会保障制度,协调各社会保险项目的平衡发展关系对于缩小社会保险基尼系数有重要现实意义。     

中国城镇化的地域非均衡及其动态演进——来自基尼系数及核密度估计的经验证据

基于中国1995-2013年省域数据,采用基尼系数及其分解、核密度估计方法,从人口和土地城镇化入手,系统分析了中国城镇化的地域非均衡及其动态演化规律。结果发现,1.中国人口和土地城镇化分布均呈现出由东往西逐渐降低的规律,城镇化非均衡主要体现在土地城镇化,而人口城镇化则未出现明显分异。2.全国尺度人口城镇化基尼系数随时间不断下降,城镇化非均衡逐渐减小;土地城镇化基尼系数则呈倒"U"型,城镇化非均衡先增后减。3.东中西三大区域内人口城镇化基尼系数均呈直线下降,区域间非均衡东部最大,西部次之,中部最小;土地城镇化非均衡则是东部大于中部和西部,但近年来西部已超过东部。4.人口城镇化非均衡在1995-2001年间主要来自地区间重叠,而后2002-2013年主要由地区间差异驱动;土地城镇化非均衡则主要来源于地区间差异。5.核密度估计显示人口城镇化增速较快,波动较小,而土地城镇化则极化趋势明显,波动较大。新型城镇化的协调推进宜从人口和土地城镇化两方面着手,特别要注意土地城镇化的失衡发展问题。     

基尼系数合意值和警戒线的探讨

 近年来，很多学者对基尼系数的经验法则尤其是警戒线提出了质疑。本文首先分析了收入分配的合意类型，然后依据相对贫困、贫富差距及中等收入者的收入份额三个指标来界定合意的收入分配，最后根据合意收入分配确定基尼系数的合意值和警戒线。本文结论表明，0.3—0.4可以被认为是基尼系数的合意值,0.4作为基尼系数警戒线也是比较合理的。     

Contrasting the Gini and Zenga indices of economic inequality

The current financial turbulence in Europe inspires and perhaps requires researchers to rethink how to measure incomes, wealth, and other parameters of interest to policy-makers and others. The noticeable increase in disparities between less and more fortunate individuals suggests that measures based upon comparing the incomes of less fortunate with the mean of the entire population may not be adequate. The classical Gini and related indices of economic inequality, however, are based exactly on such comparisons. It is because of this reason that in this paper we explore and contrast the classical Gini index with a new Zenga index, the latter being based on comparisons of the means of less and more fortunate sub-populations, irrespectively of the threshold that might be used to delineate the two sub-populations. The empirical part of the paper is based on the 2001 wave of the European Community Household Panel data set provided by EuroStat. Even though sample sizes appear to be large, we supplement the estimated Gini and Zenga indices with measures of variability in the form of normal, t-bootstrap, and bootstrap bias-corrected and accelerated confidence intervals.