Permutation Tests for Comparing Inequality Measures

ABSTRACT

Asymptotic and bootstrap tests for inequality measures are known to perform poorly in finite samples when the underlying distribution is heavy-tailed. We propose Monte Carlo permutation and bootstrap methods for the problem of testing the equality of inequality measures between two samples. Results cover the Generalized Entropy class, which includes Theil’s index, the Atkinson class of indices, and the Gini index. We analyze finite-sample and asymptotic conditions for the validity of the proposed methods, and we introduce a convenient rescaling to improve finite-sample performance. Simulation results show that size correct inference can be obtained with our proposed methods despite heavy tails if the underlying distributions are sufficiently close in the upper tails. Substantial reduction in size distortion is achieved more generally. Studentized rescaled Monte Carlo permutation tests outperform the competing methods we consider in terms of power.     

How consistent are perceptions of inequality?

Despite recent empirical evidence on the importance of perceived inequality, its analysis is still underexplored. In this paper we study whether unobserved perceptions of inequality are reflected in observed individual opinions in a consistent fashion. Inconsistency is relevant to ealuate the level of agreement that individuals share with respect to different domains of inequality.Using the wave from the 2009 International Social Survey Program in the US, we show that inequality is a complicated concept prone to inconsistencies and propose a testing procedure to an empirical appraisal. We find that inconsistencies exist though they may not extend to all the domains of inequality. This inconsistency also emerges by analyzing the relation between unobserved perceptions and political treatment suggesting the hypothesis that inconsistency may be associated with a set of relevant political preferences.     

外资进入与国内工资差异：基于工业行业面板数据的联立估计

 本文通过内生化熟练劳动力的相对工资与相对供给,建立两方程联立估计模型,利用1999-2006年我国36个工业行业数据实证考察了外资对我国工资不平等的影响。以科技人员相对工资作为熟练劳动力的代理指标,研究结果表明,外资进入一方面会通过技术外溢渠道促进我国内资企业偏向熟练劳动力的技术进步、从而扩大我国的工资不平等,另一方面其较高的劳动报酬会吸引更多的熟练劳动力流向外资企业、从而减少我国内资企业熟练劳动力的相对供给,进而进一步扩大我国的工资不平等。文章最后对估计结果的稳健性进行了较为细致的检验,检验结果表明本文的主要估计结果是稳健的。     

A Simple New Algorithm for Quadratic Programming with Applications in Statistics

Problems involving estimation and inference under linear inequality constraints arise often in statistical modeling. In this article, we propose an algorithm to solve the quadratic programming problem of minimizing for positive definite Q, where is constrained to be in a closed polyhedral convex cone , and the m × n matrix is not necessarily full row rank. The three-step algorithm is intuitive and easy to code. Code is provided in the R programming language.     

Admissible Linear Estimators with Respect to Inequality Constraints

Admissibility of linear estimators is characterized in linear models E(Y)=Xβ, D(Y)=V, with an unknown multidimensional parameter (β, V) varying in the Cartesian product C × ν, where C is a subset of space and ν is a given set of non negative definite symmetric matrices. The relation between admissibility of inhomogeneous and homogeneous linear estimators is discussed, and some sufficient and necessary conditions for admissibility of an inhomogeneous linear estimator are given.     

A Unified Approach to Likelihood Inference on Linear Inequality Constraints in Contingency Tables

In contingency table analysis, a likelihood ratio test for linear inequality constraints is discussed. The restriction condition considered in this article is much more general than usual stochastic order restriction conditions. Asymptotic property of test statistic is shown. Simulation study is conducted to compare the empirical power and size performed via the proposed method and others. Several real data sets are used to illustrate our theoretical result. The idea used in this article can be applied to test the problems with nonlinear inequality constraints.     

Admissibility of Linear Predictors in the Superpopulation Model with Respect to Inequality Constraints under Matrix Loss Function

Admissibility of linear predictors for the linear quantity Qy is investigated in a superpopulation model with respect to some inequality constraints. Necessary and sufficient conditions for a linear predictor to be admissible in the class of homogeneous linear predictors and the class of inhomogeneous linear predictors are obtained, respectively, under matrix loss function.     

Characterization of Admissible Linear Estimators in Multivariate Linear Model with Respect to Inequality Constraints under Matrix Loss Function

In this article, we study the characterization of admissible linear estimators in a multivariate linear model with inequality constraint, under a matrix loss function. In the homogeneous class, we present several equivalent, necessary and sufficient conditions for a linear estimator of estimable functions to be admissible. In the inhomogeneous class, we find that the necessary and sufficient conditions depend on the rank of the matrix in the constraint. When the rank is greater than one, the necessary and sufficient conditions are obtained. When the rank is equal to one, we have necessary conditions and sufficient conditions separately. We also obtain the necessary and sufficient conditions for a linear estimator of inestimable function to be admissible in both classes.     

Public Policy and Inequalities of Choice and Autonomy

Choice by service users has been promoted in social policy across many developed welfare states, often on the grounds that it will incentivize providers to enhance quality and efficiency. But this instrumental motivation for the promotion of choice overlooks the possibility that choice, understood in the deeper sense of autonomy, has intrinsic value, as suggested by egalitarian and capability‐based theories of social justice. This article argues that the narrow motivation of choice policies leads to a focus on services rather than outcomes for individuals and fails to address deep‐seated inequalities in the opportunities people have for real autonomy. We test this concept using newly collected data for the UK. Our empirical findings indicate that disabled people are more likely to experience constrained autonomy in all respects, while being from a low socio‐economic group and/or lacking educational qualifications is a risk factor across several components. We conclude that improving the ‘choice’ agenda for policy requires: (1) adopting a more sophisticated concept of ‘choice’ such as the conceptualization of ‘choice as autonomy’ outlined here; (2) developing a better understanding of existing inequalities in autonomy, such as we begin to explore in our empirical results; and (3) tackling these inequalities through, for example, the removal of obstacles to active decision‐making by providing effective support and advocacy, especially for disabled people, and addressing the major structural barriers – poverty, ill health and geographical inequality – which place significant restrictions on the autonomy of those who are already disadvantaged.