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

Child birth leads to a break in a woman's employment history and is considered one reason for the relatively poor labor market outcomes observed for women compared to men. However, the time spent at home after child birth varies significantly across mothers and is likely driven by observed and, more importantly, unobserved factors that also affect labor market outcomes directly. In this paper we propose two alternative Bayesian treatment modeling and inferential frameworks for panel outcomes to estimate dynamic earnings effects of a long maternity leave on mothers' earnings in the years following the return to the labor market. The frameworks differ in their modeling of the endogeneity of the treatment and the panel structure of the earnings, with the first framework based on the modeling tradition of the Roy switching regression model, and the second based on the shared factor approach. We show how stochastic variable selection can be implemented within both frameworks and can be used, for example, to test for the heterogeneity of the treatment effects. Our analysis is based on a large sample of mothers from the Austrian Social Security Register (ASSD) and exploits a recent change in the maternity leave policy to help identify the causal earnings effects. We find substantial negative earning effects from long leave over a 5 year period after mothers' return to the labor market, with the earnings gap between short and long leave mothers steadily narrowing over time.