Paternity leave may have a positive impact on the overall economic performance of women1. However, the policies to implement the leave must be developed considering the data. Non-mandatory paternity leave means there'll be a low adoption. In the case of Japan, the pay gets so much reduced that there is a net incentive for not taking paternity leave at all.
Countries with non-mandatory paternity leave (Sweden) had low adoptions until they changed the legislation for making it mandatory. Other countries should model legislation based on the available data and not reinvent the wheel.
These are the other notes that link to this one.