Measurement of Economic Distance Between Blacks and Whites

This article proposes new distribution-free methods for estimating the economic distance (advantage) between one group and another, especially for interval-to-interval comparisons, which can be more informative than a single aggregative measure. Novel techniques for computing projected quantiles, smoothing of empirical cumulative distribution functions, maximum entropy methods for finding the upper bound of the richest income interval, and statistical confidence intervals are described and applied to black-white income differences in 1967 and 1979.     

基于社会核算矩阵乘数的中国产业、居民相对收入分析

 本文使用社会核算矩阵(SAM)收入分配乘数及其分解方法,对中国2000年细分SAM进行了分析,研究了经济系统中产业部门、居民部门相对收入的变化,以及政府部门在收入分配过程中的作用,并分析了引起相对收入变化的构成。通过分析我们得出,从相对收入角度来说,大部分产业之间是非相互促进的;产业对居民相对收入的提高与居民的初始收入水平有较高的相关性;政府部门的投入会提高城镇居民的相对收入,但却会降低农村居民的相对收入。     

Income distribution in Italy: A nonparametric analysis

Using kernel density estimation, this paper describes the real income distribution and how it evolved over time in Italy. Data are cross-sectional samples from the population of Italian households during the period 1987–1998. A non parametric test is applied to asses whether the observed changes in the distribution are statistically significant, while the presence of more than one mode in the distributions is investigated by a bootstrap test. Empirical results show that the Italian income distribution significantly changed over time, accompanied by a decreasing inequality pattern until 1991 and a subsequent rise. No marked income gains were perceived, while the real “losers” of the decade seem to be households in the middle-upper income range. Supported by the MURST project 98-13-45. We would like to thank Nicholas Longford for his precious support and encouragement, two anonymous referees, the participants of the seminar at CEPS/INSTEAD in Luxembarg, and of the 40 ^th SIS Conference in Florence, for helpful comments and suggestions. The usual disclaimers apply.     

潜在流动性约束与城镇家庭消费

笔者认为,收入不平等与家庭消费的关系与信贷约束程度以及家庭社会地位偏好有关。住房是典型的地位性商品,收入差距扩大时,人们为了维持或提高现有的相对地位会努力改善居住条件,住房攀比最终会导致全社会住房面积标准提高和房价上涨。在信贷缺乏的环境中,购房标准提高和房价上涨意味着家庭未来遭遇流动性约束的风险加大,为此,家庭在增加购房预算的同时会抑制日常消费。利用2010年、2012年和2014年的微观跟踪调查数据所做的实证分析支持了我们的观点：（1）周围人群的住房面积的扩大,会促使家庭选择购买更大的房子。并且,攀比效应对住房需求的刺激作用明显大于房价上涨对住房需求的抑制作用。（2）家庭平均住房面积扩大和房价上涨都与收入不平等引发的住房攀比有关。（3）收入不平等对城镇家庭消费皆有拉动作用和抑制作用。（4）潜在流动性约束对家庭消费的抑制作用与家庭地位等级的高低有关。     

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.     

Some theoretical results regarding the polygonal distribution

Polygonal distributions are a class of distributions that can be defined via the mixture of triangular distributions over the unit interval. We demonstrate that the densities of polygonal distributions are dense in the class of continuous and concave densities with bounded second derivatives. Furthermore, we prove that polygonal density functions provide O(g^{? 2}) approximations (where g is the number of triangular distribution components), in the supremum distance, to any density function from the hypothesized class. Parametric consistency and Hellinger consistency results for the maximum likelihood (ML) estimator are obtained. A result regarding model selection via penalized ML estimation is proved.     

收入增长、收入波动与城镇居民财产积累

本文根据1995年和2002年住户调查数据,讨论了居民收入增长、收入波动以及住户特征对于城镇居民财产积累的影响。本文发现在1995年的家庭财产持有行为中已经具有明显的预防性动机,收入波动对于家庭的财产积累行为具有重要影响,而2002年中这种效应则有所下降。城镇居民在这一期间持有财产数量的增长主要是由收入增长所解释。此外,预防性动机在整个财产分布中的变化趋势在两个年份中是相反的,1995年财产分布低分位点钟具有更强的预防性动机,而2002年则相反,预防性动机随着财产分布分位点的上升而增强。如果控制收入、收入波动以及生命周期等储蓄性因素,户主特征对于财产积累的解释作用非常有限。     

中国城镇居民家庭收入流动性及其对收入差距的影响

本文从收入位次和收入份额两个角度分析中国城镇家庭收入流动性,重点探讨收入流动性能否缓和长期收入不平等。本文提出了流动性影响长期收入不平等的测度方法,给出了家庭等值收入的估算方法,然后利用中国家庭收入项目调查（CHIPS）的四轮城镇住户数据,实证分析了城镇家庭收入流动性。实证结果表明,1993-1995年、1997-1999年、2000-2002年和2011-2013年四个阶段的收入位次流动性逐渐下降,收入位次的固化现象愈加突出;四个阶段低收入家庭的收入份额都降低了,收入流动没有缓和长期收入不平等。     

中国城乡居民消费差距与收入差距的误差修正模型研究

在以绝对收入假说为基础的消费函数分析中发现,消费倾向差距对城乡居民消费差距的影响不显著,收入差距对城乡居民消费差距影响显著。在此基础上,通过构造城乡居民消费差距与收入差距的误差修正模型,发现他们之间还存在着长期稳定的均衡关系。格兰杰因果检验表明:在10%的显著性水平下,城乡居民消费差距与收入差距有双向的因果关系。为此,要有效缩小城乡居民消费差距,需要消费政策与收入政策协同并进。     

最低工资政策的城镇家庭收入分配效应研究

家庭在福利分析中具有重要地位，但家庭收入如何受最低工资政策影响却很少得到关注。本文采用2005-2015年中国综合社会调查（CGSS）数据，利用多时期双重差分和再中心化影响函数回归方法实证考察了最低工资政策对我国城镇家庭收入及其分布的影响。研究发现：①最低工资标准上涨显著提升了处于贫困标准1~2倍家庭的收入水平，对贫困标准以下或高于贫困标准2倍以上的家庭收入没有影响；②最低工资标准提升可有效减缓城镇家庭收入不平等，尤其对家庭收入分布较低分位部分的不平等程度有明显改善；③最低工资政策对家庭收入的最终影响取决于工资溢出效应和就业挤出效应的比较，且其对不同收入等级家庭中成员的收入和就业影响存在明显的异质性。政府在制定最低工资政策时，应针对低收入女性劳动力出台相应的配套措施，以保证各类低收入家庭均能从最低工资标准提升中受益。     

A generalization for two-sided power distributions and adjusted method of moments

A new rich class of generalized two-sided power (TSP) distributions, where their density functions are expressed in terms of the Gauss hypergeometric functions, is introduced and studied. In this class, the symmetric distributions are supported by finite intervals and have normal shape densities. Our study on TSP distributions also leads us to a new class of discrete distributions on {0, 1, …, k}. In addition, a new numerical method for parameter estimation using moments is given.     

Uniform stochastic orderings and total positivity

Uniform stochastic orderings of random variables are expressed as total positivity (TP) of density, survival, and distribution functions. The orderings are called uniform because each is a stochastic order that persists under conditioning to a family of intervals—for example, the family consisting of all intervals of the form (-∞,x]. This paper is concerned with the preservation of uniform stochastic ordering under convolution, mixing, and the formation of coherent systems. A general TP₂ result involving preservation of total positivity under integration is presented and applied to convolutions and mixtures of distribution and survival functions. Log-concavity of distribution, survival, and density functions characterizes distributions that preserve the various orderings under convolution. Likewise, distributions that preserve orderings under mixing are characterized by TP₂ distribution and survival functions.     

中国收入流动性再探讨

 本文利用“中国营养健康调查”(1989-2006)数据,从不同角度测度了中国收入流动性,分析了其对社会福利的影响,并按不同收入阶层对收入流动性进行分解,最后考察了个体的教育特征对收入流动性的影响。研究发现,城市和农村的收入流动性都先上升后下降,在收入分配差距较大的背景下,收入流动性降低加固了现有收入分层,形成“穷者越穷、富者越富”的马太效应,收入流动性并未改善社会福利;低收入阶层对总体收入流动性贡献最大,但大都在中低收入阶层内部变动;同时,受教育程度较高的个体不易向下流动,城市个体尤为显著。因此,在制定收入分配、教育政策时对低收入群体进行扶持,将有利于促进合理的收入流动进而缩小收入分配差距。     

Asymptotic distributions of weighted divergence between discrete distributions

A divergence measure between discrete probability distributions introduced by Csiszar (1967) generalizes the Kullback-Leibler information and several other information measures considered in the literature. We introduce a weighted divergence which generalizes the weighted Kullback-Leibler information considered by Taneja (1985). The weighted divergence between an empirical distribution and a fixed distribution and the weighted divergence between two independent empirical distributions are here investigated for large simple random samples, and the asymptotic distributions are shown to be either normal or equal to the distribution of a linear combination of independent X²-variables     

An analysis of quantile measures of kurtosis: center and tails

The consequences of substituting the denominator Q ₃(p)  −  Q ₁(p) by Q ₂  −  Q ₁(p) in Groeneveld’s class of quantile measures of kurtosis (γ ₂(p)) for symmetric distributions, are explored using the symmetric influence function. The relationship between the measure γ ₂(p) and the alternative class of kurtosis measures κ₂(p) is derived together with the relationship between their influence functions. The Laplace, Logistic, symmetric Two-sided Power, Tukey and Beta distributions are considered in the examples in order to discuss the results obtained pertaining to unimodal, heavy tailed, bounded domain and U-shaped distributions. The authors thank the referee for the careful review.     

On Mixture Failure Rates Ordering

Mixtures of increasing failure rate distributions (IFR) can decrease at least in some intervals of time. Usually, this property can be observed asymptotically as t → ∞. This is due to the fact that the mixture failure rate is “bent down” compared with the corresponding unconditional expectation of the baseline failure rate, which was proved previously for some specific cases. We generalize this result and discuss the “weakest populations are dying first” property, which leads to the change in the failure rate shape. We also consider the problem of mixture failure rate ordering for the ordered mixing distributions. Two types of stochastic ordering are analyzed: ordering in the likelihood ratio sense and ordering in variances when the means are equal.     

Top incomes in the UK over the 20th century

Summary.  Recent changes in the distribution of income need to be placed in historical context. The paper provides new evidence about the evolution of top incomes in the UK over the 20th century. Making use of published tabulations of the income tax statistics, and of microdata for recent years, we construct estimates of the shares of top income groups, giving for the first time an annual time series for gross incomes that spans more than 90 years. The paper pays particular attention to the problems of data construction and of the interpretation of tax-based evidence. The resulting statistics have evident limitations but throw light on periods, such as that between the First and Second World Wars, for which there is little other empirical material. The results bring out clearly how the major equalization of the first three-quarters of the century in the UK has been reversed, taking the shares of the top income groups back to levels of inequality found 50 years ago. A similar U-shaped pattern is found for the USA, but the post-war experience of France is different from that in the UK.     

On Non-Normal Invariance Principles for Multi-Response Permutation Procedures

A non-normal invariance principle is established for a restricted class of univariate multi-response permutation procedures whose distance measure is the square of Euclidean distance. For observations from a distribution with finite second moment, the test statistic is found asymptotically to have a centered chi-squared distribution. Spectral expansions are used to determine the asymptotic distribution for more general distance measures d, and it is shown that if d(x, y) = |x — y|^u, u? 2, the asymptotic distribution is not invariant (i.e. it is dependent on the distribution of the observations).     

Evolution and decomposition of income inequality in Italy, 1991–2004

The aggregate measures of inequality do not display any significant trend in the concentration of equivalent income among the Italian households in the early 2000s. Yet some sizeable shifts in the income distribution seem to suggest that the relative positions of groups of households have changed on the income scale. Through a decomposition analysis of Gini index by income source we find that in the more recent years the income from self-employment is the main disequalizing factor. The decomposition by social groups provides the evidence that it is the group of self-employed and managers who have gained more ground on the income scale. This work has been debated by the three Authors under the coordination of Claudio Quintano. Rosalia Castellano has written Sect. 1, while Andrea Regoli has written Sects. 2 to 6.     

Lorenz ranking of income distributions

Based on the stochastic comparison of the Lorenz curves of income distributions, five partial orderings of income distributions are obtained. Three of these orderings are the well known star shaped, stochastic and the Lorenz orderings. The other two are new and are studied in some detail. The weakest ordering which is called the Lorenz area ordering is of special importance since it enables us to compare interesting Lorenz curves. This latter ordering leads to a class of income inequality measures which are identical with the linear inequality measures considered by Mehran (1976). A discussion of these measures is presented together with an application to part of Kunzet's (1963) data.