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Title: Additive density-on-scalar regression in Bayes Hilbert spaces with an application to gender economics Authors:  Eva-Maria Maier - Humboldt University of Berlin (Germany)
Almond Stoecker - Humboldt University of Berlin (Germany)
Bernd Fitzenberger - Institute for Employment Research (Germany)
Sonja Greven - Humboldt University of Berlin (Germany) [presenting]
Abstract: Motivated by research on gender identity norms and the distribution of the woman's share in a couple's total labor income, functional additive regression models for probability density functions as responses with scalar covariates are considered. To preserve nonnegativity and integration to one under summation and scalar multiplication, we formulate the model for densities in a Bayes Hilbert space with respect to an arbitrary finite measure. This enables us to not only consider continuous densities but also, e.g., discrete or mixed densities. Mixed densities occur in our application, as the woman's income share is a continuous variable having discrete point masses at zero and one for single-earner couples. We discuss the interpretation of effect functions in our model via odds-ratios. Estimation is based on a gradient boosting algorithm, allowing for potentially numerous flexible covariate effects. We show how to handle the challenging estimation for mixed densities within our framework using an orthogonal decomposition. Applying this approach to data from the German Socio-Economic Panel Study (SOEP) shows a more symmetric distribution in East German than in West German couples after reunification and a smaller child penalty comparing couples with and without minor children. These West-East differences become smaller but are persistent over time.