Reducing poverty and inequality through tax-benefit reform and the minimum wage: the UK as a case-study

Atkinson’s book Inequality: What Can Be Done? (Harvard University Press, 2015) sets out a range of concrete proposals aimed at reducing income inequality, which cover a very broad span but include major changes to the income tax and social transfers system and the minimum wage. These are framed with specific reference to the UK but have much broader relevance in demonstrating how substantial the impact on inequality of such measures could be. This paper assesses the first-round effects of these tax, transfer and minimum wage reforms on income inequality and poverty based on a microsimulation approach using EUROMOD. The reforms involve a significantly more progressive income tax structure, a major increase in the minimum wage to the level which is estimated to represent the ‘Living Wage’, and alternative routes to reforming social transfers – either to strengthen the social insurance element or to restructure the entire system as a Participation Income (a variant of Basic/Citizen’s Income). The results show how the first-round effects of either set of tax and transfer proposals would be to substantially reduce the extent of income inequality and relative income poverty and the paper draws out how the two approaches differ in their effects. The additional impact of raising the minimum wage to the Living Wage is modest, reflecting in particular the position of beneficiaries in the household income distribution and the offsetting effects on household income of the withdrawal of means-tested cash transfers.     

Approximate confidence intervals for the weighted kappa coefficient of a binary diagnostic test subject to a case–control design

Case–control design to assess the accuracy of a binary diagnostic test (BDT) is very frequent in clinical practice. This design consists of applying the diagnostic test to all of the individuals in a sample of those who have the disease and in another sample of those who do not have the disease. The sensitivity of the diagnostic test is estimated from the case sample and the specificity is estimated from the control sample. Another parameter which is used to assess the performance of a BDT is the weighted kappa coefficient. The weighted kappa coefficient depends on the sensitivity and specificity of the diagnostic test, on the disease prevalence and on the weighting index. In this article, confidence intervals are studied for the weighted kappa coefficient subject to a case–control design and a method is proposed to calculate the sample sizes to estimate this parameter. The results obtained were applied to a real example.     

A note on the Cauchy-type mixture distributions

An interesting class of continuous distributions, called Cauchy-type mixture, with potential applications in modelling erratic phenomena is introduced by Soltani and Tafakori [A class of continuous kernels and Cauchy type heavy tail distributions. Statist Probab Lett. 2013;83:1018–1027]. In this work, we provide more insights into the Cauchy-type mixture distributions, involving certain characterizations, connections with the generalized Linnik distributions and the class of discrete distributions induced by stable laws. We also prove that the Laplace transform of Cauchy-type mixture distributions when normalized by constant terms become as a density functions in terms of distributional conjugate property.     

A new Bayesian wavelet thresholding estimator of nonparametric regression

The methods of estimation of nonparametric regression function are quite common in statistical application. In this paper, the new Bayesian wavelet thresholding estimation is considered. The new mixture prior distributions for the estimation of nonparametric regression function by applying wavelet transformation are investigated. The reversible jump algorithm to obtain the appropriate prior distributions and value of thresholding is used. The performance of the proposed estimator is assessed with simulated data from well-known test functions by comparing the convergence rate of the proposed estimator with respect to another by evaluating the average mean square error and standard deviations. Finally by applying the developed method, density function of galaxy data is estimated.     

A new log-location regression model: estimation,influence diagnostics and residual analysis

We introduce a log-linear regression model based on the odd log-logistic generalized half-normal distribution [7 G.M. Cordeiro, M. Alizadeh, R.R. Pescim, and E.M.M. Ortega, The odd log-logistic generalized half-normal lifetime distribution: Properties and applications, Comm. Statist. Theory Methods (2015), accepted for publication. [Google Scholar]]. Some of its structural properties including explicit expressions for the density function, quantile and generating functions and ordinary moments are derived. We estimate the model parameters by the maximum likelihood method. For different parameter settings, proportion of censoring and sample size, some simulations are performed to investigate the behavior of the estimators. We derive the appropriate matrices for assessing local influence diagnostics on the parameter estimates under different perturbation schemes. We also define the martingale and modified deviance residuals to detect outliers and evaluate the model assumptions. In addition, we demonstrate that the extended regression model can be very useful in the analysis of real data and provide more realistic fits than other special regression models. The potentiality of the new regression model is illustrated by means of a real data set.     

Joint GEEs for multivariate correlated data with incomplete binary outcomes

This study considers a fully-parametric but uncongenial multiple imputation (MI) inference to jointly analyze incomplete binary response variables observed in a correlated data settings. Multiple imputation model is specified as a fully-parametric model based on a multivariate extension of mixed-effects models. Dichotomized imputed datasets are then analyzed using joint GEE models where covariates are associated with the marginal mean of responses with response-specific regression coefficients and a Kronecker product is accommodated for cluster-specific correlation structure for a given response variable and correlation structure between multiple response variables. The validity of the proposed MI-based JGEE (MI-JGEE) approach is assessed through a Monte Carlo simulation study under different scenarios. The simulation results, which are evaluated in terms of bias, mean-squared error, and coverage rate, show that MI-JGEE has promising inferential properties even when the underlying multiple imputation is misspecified. Finally, Adolescent Alcohol Prevention Trial data are used for illustration.     

Marginal models for the association structure of hierarchical binary responses

Clustered binary responses are often found in ecological studies. Data analysis may include modeling the marginal probability response. However, when the association is the main scientific focus, modeling the correlation structure between pairs of responses is the key part of the analysis. Second-order generalized estimating equations (GEE) are established in the literature. Some of them are more efficient in computational terms, especially facing large clusters. Alternating logistic regression (ALR) and orthogonalized residual (ORTH) GEE methods are presented and compared in this paper. Simulation results show a slightly superiority of ALR over ORTH. Marginal probabilities and odds ratios are also estimated and compared in a real ecological study involving a three-level hierarchical clustering. ALR and ORTH models are useful for modeling complex association structure with large cluster sizes.     

Effects of some design factors on the distribution of similarity indices in cluster analysis

This article investigates the effects of number of clusters, cluster size, and correction for chance agreement on the distribution of two similarity indices, namely, Jaccard and Rand indices. Skewness and kurtosis are calculated for the two indices and their corrected forms then compared with those of the normal distribution. Three clustering algorithms are implemented: complete linkage, Ward, and K-means. Data were randomly generated from bivariate normal distributions with specified means and variance covariance matrices. Three-way ANOVA is performed to assess the significance of the design factors using skewness and kurtosis of the indices as responses. Test statistics for testing skewness and kurtosis and observed power are calculated. Simulation results showed that independent of the clustering algorithms or the similarity indices used, the interaction effect cluster size x number of clusters and the main effects of cluster size and number of clusters were found always significant for skewness and kurtosis. The three way interaction of cluster size x correction x number of clusters was significant for skewness of Rand and Jaccard indices using all clustering algorithms, but was not significant using Ward's method for both Rand and Jaccard indices, while significant for Jaccard only using complete linkage and K-means algorithms. The correction for chance agreement was significant for skewness and kurtosis using Rand and Jaccard indices when complete linkage method is used. Hence, such design factors must be taken into consideration when studying distribution of such indices.     

Computational approach test for inference about several correlation coefficients: Equality and common

In this article, we consider inference about the correlation coefficients of several bivariate normal distributions. We first propose computational approach tests for testing the equality of the correlation coefficients. In fact, these approaches are parametric bootstrap tests, and simulation studies show that they perform very satisfactory, and the actual sizes of these tests are better than other existing approaches. We also present a computational approach test and a parametric bootstrap confidence interval for inference about the parameter of common correlation coefficient. At the end, all the approaches are illustrated using two real examples.