Distorted Copulas: Constructions and Tail Dependence

Given a copula C, we examine under which conditions on an order isomorphism ψ of [0, 1] the distortion C _ψ: [0, 1]² → [0, 1], C _ψ(x, y) = ψ{C[ψ^?1(x), ψ^?1(y)]} is again a copula. In particular, when the copula C is totally positive of order 2, we give a sufficient condition on ψ that ensures that any distortion of C by means of ψ is again a copula. The presented results allow us to introduce in a more flexible way families of copulas exhibiting different behavior in the tails.     

Multivariate nonparametric methods in two-way balanced designs: performances and limitations in small samples

Investigations of multivariate population are pretty common in applied researches, and the two-way crossed factorial design is a common design used at the exploratory phase in industrial applications. When assumptions such as multivariate normality and covariance homogeneity are violated, the conventional wisdom is to resort to nonparametric tests for hypotheses testing. In this paper we compare the performances, and in particular the power, of some nonparametric and semi-parametric methods that have been developed in recent years. Specifically, we examined resampling methods and robust versions of classical multivariate analysis of variance (MANOVA) tests. In a simulation study, we generate data sets with different configurations of factor''s effect, number of replicates, number of response variables under null hypothesis, and number of response variables under alternative hypothesis. The objective is to elicit practical advice and guides to practitioners regarding the sensitivity of the tests in the various configurations, the tradeoff between power and type I error, the strategic impact of increasing number of response variables, and the favourable performance of one test when the alternative is sparse. A real case study from an industrial engineering experiment in thermoformed packaging production is used to compare and illustrate the application of the various methods.     

Concentration functions and Bayesian robustness

The concentration function, extending the classical notion of Lorenz curve, is well suited for comparing probability measures. Such a feature can be useful in different issues in Bayesian robustness, when a probability measure is deemed a baseline to be compared with other measures by means of their functional forms. Neighbourhood classes Γ of probability measures, including well-known ones, can be defined through the concentration function and both prior and posterior expectations of given functions of the unknown parameter are studied. The ranges of such expectations over Γ can be found, restricting the search among the extremal measures in Γ. The concentration function can be also used as a criterion to assess posterior robustness, when considering sensitivity to changes in the likelihood and the prior.     

Family Dynamics and Child Outcomes: An Overview of Research and Open Questions

Previous research has documented that children who do not live with both biological parents fare somewhat worse on a variety of outcomes than those who do. In this article, which is the introduction to the Special Issue on “Family dynamics and children’s well-being and life chances in Europe,” we refine this picture by identifying variation in this conclusion depending on the family transitions and subpopulations studied. We start by discussing the general evidence accumulated for parental separation and ask whether the same picture emerges from research on other family transitions and structures. Subsequently, we review studies that have aimed to deal with endogeneity and discuss whether issues of causality challenge the general picture of family transitions lowering child well-being. Finally, we discuss whether previous evidence finds effects of family transitions on child outcomes to differ between children from different socioeconomic and ethnic backgrounds, and across countries and time-periods studied. Each of the subsequent articles in this Special Issue contributes to these issues. Two articles provide evidence on how several less often studied family forms relate to child outcomes in the European context. Two other articles in this Special Issue contribute by resolving several key questions in research on variation in the consequences of parental separation by socioeconomic and immigrant background, two areas of research that have produced conflicting results so far.     

Rectangular Patchwork for Bivariate Copulas and Tail Dependence

We present a method for constructing bivariate copulas by changing the values that a given copula assumes on some subrectangles of the unit square. Some applications of this method are discussed, especially in relation to the construction of copulas with different tail dependencies.     

Unequal transitions: Selection bias and the compensatory effect of social background in educational careers

Previous studies have shown that social background inequality differs among educational transitions and it is stronger for those transitions that involve a higher risk of social demotion. This paper focuses on two processes that may account for part of the observed differences in social background inequality across educational transitions. First, it studies how the family of origin might compensate for a ‘false step’ in the early stage of young people's educational careers. This compensatory effect of social background can be described as the likelihood of having ‘a second chance’ for unsuccessful educational transitions. Second, it focuses on two unobserved factors that might potentially bias the effect of social background across educational transitions. These are the students’ unobserved cognitive and non-cognitive skills and their unobserved anticipated choices of dropping out of the education system. Two issues – the compensatory effect of social background and selection bias in educational transitions – are addressed by estimating a probit model with sample selection for the transition to post-compulsory education in Spain.     

Rotten Parents and Disciplined Children: A Politico‐Economic Theory of Public Expenditure and Debt

This paper proposes a dynamic politico‐economic theory of fiscal policy in a world comprising a set of small open economies, whose driving force is the intergenerational conflict over debt, taxes, and public goods. Subsequent generations of voters choose fiscal policy through repeated elections. The presence of young voters induces fiscal discipline, that is, low taxes and low debt accumulation. The paper characterizes the Markov‐perfect equilibrium of the voting game in each economy, as well as the stationary equilibrium debt distribution and interest rate of the world economy. The equilibrium can reproduce some salient features of fiscal policy in modern economies.     

VERTICAL INTEGRATION AND TECHNOLOGY: THEORY AND EVIDENCE

We study the determinants of vertical integration. We first derive a number of predictions regarding the relationship between technology intensity and vertical integration from a simple incomplete contracts model. Then, we investigate these predictions using plant‐level data for the UK manufacturing sector. Most importantly, and consistent with the theoretical predictions, we find that the technology intensity of downstream (producer) industries is positively correlated with the likelihood of integration whereas the intensity of upstream (supplier) industries is negatively correlated with it. Also consistent with theory, both correlations are stronger when the supplying industry accounts for a large fraction of the producer's costs. These results are generally robust and hold with alternative measures of technology intensity, with alternative estimation strategies, and with or without controlling for a number of firm‐ and industry‐level characteristics. (JEL: L22, L23, L24, L60)