Background
Paternity leave is often discussed as a policy measure to reduce the gender earnings gap.  Due to earmarked paternity leave, mothers could spend more time focusing on their careers, while fathers spend more time with their family. This shift in household time allocation might set off a different dynamic between parents in the first months after birth, resulting in substantial changes in the household income division in the long run. 

In this paper, we investigate the causal effects of paternity leave on the gender earnings gap, measured by the relative labor income of women within a couple. We exploit Dutch longitudinal administrative register data together with a reform of the Dutch paternity leave system implemented in 2020: the Wet Invoering Extra Geboorteverlof (WIEG). By this reform, fathers could receive up to 5 weeks of additional paternity leave if their child is born on or after the first of July 2020. During those weeks, fathers receive a benefit equal to 70 percent of their wage. This reform provides a natural experiment due to exogenous variation in the access to paternity leave. After all, it is practically impossible to strategically time the exact date of birth of the child around the first of July.

Results
Using a fuzzy Regression Discontinuity Design (RDD), we find a small but positive effect of the take-up of paternity leave on the relative labor income of women in the first three months after birth. However, this is not the result of an improvement of the labor market position of mothers: no significant increase in the level of wages or labor supply of mothers is observed. In fact, the effect in the first months can be fully explained by the significant drop in wages of fathers due to the leave take-up (as a result of the 70 percent benefit level). Thereafter, no effect of the paternity leave take-up is observed. We also use a Difference-in-Difference approach to estimate the effects of the reform itself and find only a significant effect of the reform one month after birth. Overall, we conclude that that paternity leave does not improve women’s labor income share within the household and, in that sense, does not reduces the gender earnings gap.