Utilitarianism and discrimination

Since Becker (1971), a common argument against asymmetric norms that promote minority rights over those of the majority is that such policies reduce total welfare. While this may be the case, we show that there are simple environments where aggregate sum of individual utilities is actually maximized under asymmetric norms that favor minorities. We thus maintain that without information regarding individual utilities one cannot reject or promote segregation-related policies based on utilitarian arguments.     

Nonparametric estimation in the illness-death model using prevalent data

We study nonparametric estimation of the illness-death model using left-truncated and right-censored data. The general aim is to estimate the multivariate distribution of a progressive multi-state process. Maximum likelihood estimation under censoring suffers from problems of uniqueness and consistency, so instead we review and extend methods that are based on inverse probability weighting. For univariate left-truncated and right-censored data, nonparametric maximum likelihood estimation can be considerably improved when exploiting knowledge on the truncation distribution. We aim to examine the gain in using such knowledge for inverse probability weighting estimators in the illness-death framework. Additionally, we compare the weights that use truncation variables with the weights that integrate them out, showing, by simulation, that the latter performs more stably and efficiently. We apply the methods to intensive care units data collected in a cross-sectional design, and discuss how the estimators can be easily modified to more general multi-state models.     

Review article

Simonetta Soldani and Gabriele Turi (eds), Making Italians. School and Culture in Modern Italy. Vol. I, The Birth of the Nation‐State, Vol. II, A Mass Society (1993), 521 + 509 (Il Mulino, Bologna).     

Quantitative assessment of response shift in QOL research

Two assumptions which characterize the measurements of quality life (QOL) studies, are questioned by the present report: First, the assumption that QOL is the same thing for all subjects, is usually related to health problems and can easily be measured across subjects. Second, when this assumption is given up by introducing subjective base-rates in an intra-subject (before-after) design, researchers still tend to assume that no response shifts occur on the QOL scales, e.g., that these scales maintain the same meaning and values for subjects over time and interventions. In our study we found that QOL had different subjective interpretations [1--4]. While for some certain issues in their family-life determined their quality of life, for others these were issues at their workplace or of their health conditions. Second, when QOL was tested against a subjective base-line (for each individual according to their choices of domains), about eleven percent of the hypertensives and normotensives showed a clear response shift of scale-calibration over the period of one year. When the scores of these subjects were excluded, the significance of certain previously reported results changed. For example, the significant difference between normotensives and hypertensives concerning the change in their subjective evaluation of QOL over the year and their initial depression became more significant, while similar changes in their evaluation of sexual impairment and control at their work-place became insignificant. These results suggest that response shifts have to be traced and quantified, before one can claim any results (or lack of results) in 'before-after' designs, concerning subjective meaningful issues like quality of life.     

Gender Pay Gap and Employment Sector: Sources of Earnings Disparities in the United States, 1970–2010

Using data from the IPUMS-USA, the present research focuses on trends in the gender earnings gap in the United States between 1970 and 2010. The major goal of this article is to understand the sources of the convergence in men’s and women’s earnings in the public and private sectors as well as the stagnation of this trend in the new millennium. For this purpose, we delineate temporal changes in the role played by major sources of the gap. Several components are identified: the portion of the gap attributed to gender differences in human-capital resources; labor supply; sociodemographic attributes; occupational segregation; and the unexplained portion of the gap. The findings reveal a substantial reduction in the gross gender earnings gap in both sectors of the economy. Most of the decline is attributed to the reduction in the unexplained portion of the gap, implying a significant decline in economic discrimination against women. In contrast to discrimination, the role played by human capital and personal attributes in explaining the gender pay gap is relatively small in both sectors. Differences between the two sectors are not only in the size and pace of the reduction but also in the significance of the two major sources of the gap. Working hours have become the most important factor with respect to gender pay inequality in both sectors, although much more dominantly in the private sector. The declining gender segregation may explain the decreased impact of occupations on the gender pay gap in the private sector. In the public sector, by contrast, gender segregation still accounts for a substantial portion of the gap. The findings are discussed in light of the theoretical literature on sources of gender economic inequality and in light of the recent stagnation of the trend.     

Fast Computation by Block Permanents of Cumulative Distribution Functions of Order Statistics from Several Populations

The joint cumulative distribution function for order statistics arising from several different populations is given in terms of the distribution functions of the populations. The computational cost of our formula in the case of two populations is still exponential in the worst case, but it is a dramatic improvement compared to the general formula by Bapat and Beg. In the case when only the joint distribution function of a subset of the order statistics of fixed size is needed, the complexity is polynomial, for the case of two populations.     

A Second Look at the Process of Occupational Feminization and Pay Reduction in Occupations

Using the IPUMS-USA data for the years 1960–2015, this study examines trends in the effect of occupational feminization on occupational pay in the U.S. labor market and explores some of the mechanisms underlying these trends. The findings show that the (negative) association between occupational feminization and occupational pay level has declined, becoming insignificent in 2015. This trend, however, is reversed after education is controlled for at the individual as well as the occupational level. The two opposite trends are discussed in light of the twofold effect of education: (1) the entry of women into occupations requiring high education, and (2) the growing returns to education and to occupations with higher educational requirements. These two processes have concealed the deterioration in occupational pay following feminization. The findings underscore the significance of structural forms of gender inequality in general, and occupational devaluation in particular.     

Inequality in the family: The institutional aspects of women’s earning contribution

This paper examines the effect of employment-supportive policies and arrangements on women’s economic contribution to their family. Using samples of working-age couples in 21 countries we employ multilevel modeling to separate the effects of household and country-level variables on earnings. We distinguish two types of relevant contextual factors: those that support women’s employment while preserving their domestic roles and those that potentially reduce intra-family economic inequalities by allowing women to allocate more of their time to paid employment. The findings suggest that all employment-supportive policies and arrangements increase women’s relative contribution to the household income through their effect on female labor force participation. Among dual-earner families, however, higher rates of childcare facilities increase women’s contribution, while long maternity leave and part-time employment decrease it. These tendencies are more pronounced among mothers.     

The Scaled Uniform Model Revisited

Abstract

Sufficiency, conditionality, and invariance are basic principles of statistical inference. Current mathematical statistics courses do not devote much teaching time to these classical principles, and even ignore the latter two, in order to teach modern methods. However, being the philosophical cornerstones of statistical inference, a minimal understanding of these principles should be part of any curriculum in statistics. The scaled uniform model is used here to demonstrate the importance and usefulness of the conditionality principle, which is probably the most basic and less familiar among the three.     

Simulation-Based Confidence Intervals for Functions With Complicated Derivatives

In many scientific problems, the quantity of interest is a function of parameters that index the model, and confidence intervals are constructed by applying the delta method. However, when the function of interest has complicated derivatives, this standard approach is unattractive and alternative algorithms are required. This article discusses a simple simulation-based algorithm for estimating the variance of a transformation, and demonstrates its simplicity and accuracy by applying it to several statistical problems.