We propose a generic Bayesian framework for inference in distributional regression models in which each parameter of a potentially complex response distribution and not only the mean is related to a structured additive predictor. The latter is composed additively of a variety of different functional effect types such as nonlinear effects, spatial effects, random coefficients, interaction surfaces or other (possibly nonstandard) basis function representations. To enforce specific properties of the functional effects such as smoothness, informative multivariate Gaussian priors are assigned to the basis function coefficients. Inference can then be based on computationally efficient Markov chain Monte Carlo simulation techniques where a generic procedure makes use of distribution-specific iteratively weighted least squares approximations to the full conditionals. The framework of distributional regression encompasses many special cases relevant for treating nonstandard response structures such as highly skewed nonnegative responses, overdispersed and zero-inflated counts or shares including the possibility for zero- and one-inflation. We discuss distributional regression along a study on determinants of labour incomes for full-time working males in Germany with a particular focus on regional differences after the German reunification. Controlling for age, education, work experience and local disparities, we estimate full conditional income distributions allowing us to study various distributional quantities such as moments, quantiles or inequality measures in a consistent manner in one joint model. Detailed guidance on practical aspects of model choice including the selection of several competing distributions for labour incomes and the consideration of different covariate effects on the income distribution complete the distributional regression analysis. We find that next to a lower expected income, full-time working men in East Germany also face a more unequal income distribution than men in the West, ceteris paribus.

Data and its applications are increasingly ubiquitous in the rapidly digitizing world and consequently, students across different disciplines face increasing demand to develop skills to answer both academia's and businesses' increasing need to collect, manage, evaluate, apply and extract knowledge from data and critically reflect upon the derived insights. On the basis of recent experiences at the University of Ttingen, Germany, we present a new approach to teach the relevant data science skills as an introductory service course at the university or advanced college level. We describe the outline of a complete course that relies on case studies and project work built around contemporary data sets, including openly available online teaching resources.

This study addresses the much-discussed issue of the relationship between health and income. In particular, it focuses on the relation between mental health and household income by using generalized additive models of location, scale and shape and thus employing a distributional perspective. Furthermore, this study aims to give guidelines to applied researchers interested in taking a distributional perspective on health inequalities. In our analysis we use cross-sectional data of the German socioeconomic Panel (SOEP). We find that when not only looking at the expected mental health score of an individual but also at other distributional aspects, like the risk of moderate and severe mental illness, that the relationship between income and mental health is much more pronounced. We thus show that taking a distributional perspective, can add to and indeed enrich the mostly mean-based assessment of existent health inequalities.

We explore the application of structured additive distributional regression for the analysis of conditional income distributions in Germany following the reunification using the German Socio Economic Panel (SOEP) database. This methodology allows us to explore both between and within income inequality at a highly disaggregated level. Using a bootstrapped version of the Kolmogorov-Smirnov test, we find that conditional personal income distributions can generally be modelled using a mixture distribution entailing the three parameter Dagum distribution. JEL Classification: C13, C21, D31, J31

Using individual earnings data from university archives, we analyse the position of university professors within the aggregate income distribution over a time span covering the Kaiserreich, the Weimar Republic, the Third Reich as well as the Federal Republic of Germany. We find that not only did the earnings of professors deteriorate with respect to average incomes, due to the compression of the income distribution, but that professorial earnings no longer sufficed to lift professors into the top 1% of the aggregate income distribution.