I've never bought the idea that welfare recipients would bear children strategically. Surely after the first child, they'd realize that this was a difficult way to increase their top-line income.
Not sure where I'd look for data on this, but my gut feeling is that poor people who have a bunch of poorly-cared-for-children get pregnant because they're bad at planning ahead, not because they've been inventivized by a subsidy.
I think you're mistakingly assuming the kind of person who would do this would provide a similar (or any kind of) quality of life to their kids that you would.
I know of 3 small children in my own life whose parents collect welfare, and are meth addicted.
