Katie drew something to my attention yesterday: St. Louis and other cities are having a big problem with welfare, because a lot of families spend less on their children than the welfare check provides per child (this is very plausibly mistreatment of kids by parents), so they are incentivized to have many children, as many as a dozen or more.
There are a number of points to this:
firstly, St. Louis does not provide free contraception and abstinence-only education is common, and the cost of a first child is higher than the cost of subsequent children because you need to buy fixed supplies (a crib, for example). It's a safe bet that a number of these people never would have started down this track of many children intentionally if they hadn't accidentally had a first child unintentionally. So reducing abstinence only education for high schoolers and making contraception more available is one excellent possible solution.
Of course, this doesn't solve the current problem, and the solutions aren't pretty.
A policy of "for each additional child beyond three, you get paid less than the normal child allotment if any of them are over a certain age" (where less can be zero, and the age can be anything) has the effect of reducing incentives to keep having children to stay on welfare. By making the age flexible and the payment flexible, you can try and tune it so that you dont have children starving or turning to the drug trade to stay afloat.
Of course, then you have to be willing to enforce that - can you watch children not be fed enough because they're mistreated by their parents AND the government isn't giving them anything? It's a commitment you have to be willing to make if you want to disincentivize people from riding welfare rolls.
A way to minimize THAT problem is committing to checking on the welfare of children whose parents receive welfare money, and if the children are not receiving good care, committing to putting them in a home that does (of course, foster parents ALSO have terrible incentives that need to be changed, but that's for another post). If you made welfare money for kids contingent upon kids staying in school, that could significantly decrease school dropout rates, but it also creates massive problems with supplying people into the drug trade. You'd have to make this contingent on strong enforcement of drug laws.
It's not an easy problem.