Bayesian treatment effects models with variable selection for panel outcomes with an application to earnings effects of maternity leave

We propose two alternative Bayesian treatment effect modeling and inferential frameworks for panel outcomes to estimate dynamic earnings effects of a long maternity leave on mothers' subsequent earnings. Modeling of the endogeneity of the treatment and the panel structure of the earnings are based on the modeling tradition of the Roy switching regression model and the shared factor approach, respectively. We implement stochastic variable selection to test, for example, for the presence of different dynamics under the treatment. Exploiting a change in maternity leave policy and Austrian registry data we identify substantial negative but steadily decreasing earnings effects over a 5 years period.