A common argument against safety net social welfare for people with children is that it can incentivise people without better options to have children. This could be considered a problem if it means people who aren't fit to be parents continue having children.
For example in New Zealand the the Domestic Purposes Benefit (a benefit paid to people with children, if child support from the other parent does not exceed the base rate) pays about the same rate as a minimum wage full time job.
An argument could be made that the economically rational decision for an uneducated person is to have children, where they can't be fired, aren't subject to starting times or drug tests etc.
Is there any evidence for what the effect of welfare payments for children has?
In particular I'm interested in any situation where the entitlement has either increased or decreased, and what the effects on birthrate or people applying for the benefit has been after that.