Optimal distribution-free confidence bands for a distribution function

Distribution-free confidence bands for a distribution function are typically obtained by inverting a distribution-free hypothesis test. We propose an alternate strategy in which the upper and lower bounds of the confidence band are chosen to minimize a narrowness criterion. We derive necessary and sufficient conditions for optimality with respect to such a criterion, and we use these conditions to construct an algorithm for finding optimal bands. We also derive uniqueness results, with the Brunn–Minkowski Inequality from the theory of convex bodies playing a key role in this work. We illustrate the optimal confidence bands using some galaxy velocity data, and we also show that the optimal bands compare favorably to other bands both in terms of power and in terms of area enclosed.     

受教育程度与城镇居民收入不平等—基于基尼系数的分解研究

基于2008年中国综合社会调查的数据,本文运用基尼系数分解的方法研究城镇居民受教育程度对收入不平等的影响。基于回归的不平等分解研究发现受教育程度是导致城镇居民职业收入不平等的最主要因素。对基尼系数的亚组分解研究发现受教育程度不同的人群之闻的收入不平等对总体收入不平等的贡献率为8.65％,城镇居民职业收入不平等主要表现为各个受教育程度人群内部的收入不平等。分地区来看,中西部地区受教育程度较低的人群其组内差距的贡献率要远高于东部地区。实证研究的结果表明,提供平等的受教育机会、缩小受教育程度的不平等、加大对中西部地区义务教育的投入可以有效缩小收入不平等。     

Neoliberalism,Inequality and Politics: The Changing Face of Australia

Since the early 1980s Australian public policy has undergone the most major transformation since Federation. This transformation has been underwritten by two key principles: liberalism – the view that citizens are autonomous individual actors whose interests are best served when they are free from coercive government interventions into individual action; and marketisation – the belief that free markets are arenas which best enable individual autonomy and produce efficient economic outcomes. These principles define ‘neoliberalism’ or ‘hard liberalism‘. After summarising the major policy changes identified with neoliberalism in Australia, the paper introduces a new research project that examines its impact on socioeconomic inequality, gender inequality and politics and culture. Inspection of relevant data indicates that there are important trends in inequality, public opinion and political behaviour that warrant this investigation.     

Beyond Piketty: A new perspective on poverty and inequality in India

The socio-economic literature has focused much on how overall inequality in income distribution (frequently measured by the Gini coefficient) undermines the “trickle down” effect. In other words, the higher the inequality in the income distribution, the lower is the growth elasticity of poverty. However, with the publication of Piketty’s magnum opus (2014), and a subsequent study by Chancel and Piketty (2017) of evolution of income inequality in India since 1922, the focus has shifted to the income disparity between the richest 1% (or 0.01%) and the bottom 50%. Their central argument is that the rapid growth of income at the top end of millionaires and billionaires is a by-product of growth. The present study extends this argument by linking it to poverty indices in India. Based on the India Human Development Survey 2005–12 – a nationwide panel survey-we examine the links between poverty and income inequality, especially in the upper tail relative to the bottom 50%, state affluence (measured in per capita income) and their interaction or their joint effect. Another feature of our research is that we analyse their effects on the FGT class of poverty indices. The results are similar in as much as direction of association is concerned but the elasticities vary with the poverty index. The growth elasticities are negative and significant for all poverty indices. In all three cases, the disparity between the income share of the top 1% and share of the bottom 50% is associated with greater poverty. These elasticities are much higher than the (absolute) income elasticities except in the case of the poverty gap. The largest increase occurs in the poverty gap squared – a 1% greater income disparity is associated with a 1.24% higher value of this index. Thus the consequences of even a small increase in the income disparity are alarming for the poorest.     

Trends in inequality in infant mortality in the north of England, 1921–1973, and their association with urban and social structure

Summary.  The paper analyses a time series of infant mortality rates in the north of England from 1921 to the early 1970s at a spatial scale that is more disaggregated than in previous studies of infant mortality trends in this period. The paper describes regression methods to obtain mortality gradients over socioeconomic indicators from the censuses of 1931, 1951, 1961 and 1971 and to assess whether there is any evidence for widening spatial inequalities in infant mortality outcomes against a background of an overall reduction in the infant mortality rate. Changes in the degree of inequality are also formally assessed by inequality measures such as the Gini and Theil indices, for which sampling densities are obtained and significant changes assessed. The analysis concerns a relatively infrequent outcome (especially towards the end of the period that is considered) and a high proportion of districts with small populations, so necessitating the use of appropriate methods for deriving indices of inequality and for regression modelling.     

Inequality and negative income

Summary This note deals with some problems in the measurement of inequality when negative incomes are allowed. A new axiom is defined, called the Greatest Gets More axiom. Using this axiom it can be shown that the properties of some inequality measures depend on whether there are negative incomes or not. In this paper, for the intermediate measures of Eichhorn and the centrist inequality measures of Kolm a threshold value is given above which the Greatest Gets More axiom holds. I am indebted to two anonymous referees for their helpful comments.     

U-Statistics and Their Asymptotic Results for Some Inequality and Poverty Measures

U-statistics form a general class of statistics that have certain important features in common. This class arises as a generalization of the sample mean and the sample variance, and typically members of the class are asymptotically normal with good consistency properties. The class encompasses some widely used income inequality and poverty measures, in particular the variance, the Gini index, the poverty rate, the average poverty gap ratios, the Foster-Greer-Thorbecke index, and the Sen index and its modified form. This paper illustrates how these measures come together within the class of U-statistics, and thereby why U-statistics are useful in econometrics.     

Cauchy-Schwarz不等式的应用及推广

Cauchy-Schwarz不等式是异于均值不等式的另一个重要不等式,不仅在数学分析、高等代数中应用比较广泛,在竞赛数学和工程实际计算中也有广泛的应用.研究Cauchy-Schwarz不等式的几种特殊形式,并分别给出了它们的证明,最后给出了Cauchy-Schwarz不等式的推广形式.     

Globalization, the structure of the world economy and economic development

How does the structure of the world economy determine the gains from participation therein? In order to answer this question, we conduct a state of the art network analysis of international trade to map the structure of the international division of labor (IDL). We regress cross-national variation in economic growth on positional variation and mobility of countries within the IDL from 1965 to 2000. We find that the highest rates of economic growth occurred to countries in the middle of the IDL over the course of globalization. Second, we find that upper tier positions in the IDL are converging with each other, but diverging from the lower tier. This suggests that the mechanism underlying the rapid economic growth in intermediate positions was their uniquely high rates of upward mobility, in turn a function of their middling position. Taken together, these findings suggest that a country’s long-term economic development is conditioned by its position in the IDL.     

Foreign-born health integration during the transition to adulthood: The case of weight

Nativity differences in youths’ health in the United States are striking—the children of foreign-born parents often have healthier outcomes than those of native-born parents. However, very little is known about how immigrant-native differences evolve within the same individuals over time, or about life cycle aspects of the health-related integration of youth with migration backgrounds. Using data from the National Longitudinal Study of Adolescent Health, I examine nativity differences in trajectories of weight gain during adolescence and early adulthood, as well as the degree to which temporal patterns are stratified by race/ethnicity and socioeconomic status. I examine whether nativity differences converge, diverge or remain stable over time, and whether patterns are socially stratified within and across nativity groups. I find that first-generation adolescents begin at a lower weight than their third generation peers and gain weight at a significantly slower pace, resulting in meaningful differences by early adulthood. More complex examination of the relationship between nativity and weight gain reveals additional differences by ethnicity: the foreign-born advantage over time does not extend as strongly to Hispanic adolescents. The findings demonstrate how the health-related integration of foreign-born youth is tied to race/ethnicity and socioeconomic circumstances, and suggest the need to examine the ways in which social circumstances and health change together.