> The only discernible effect on female winners is that wealth increases their short-run (but not long-run) divorce risk.
Women still divorce their sucky husbands. It just takes longer. This could result in fewer kids, or it could result in kids whose homes are broken during later childhood or adolescence.
Reading the actual paper, this is, in fact, the conclusion the authors come to: "In contrast, the only exception to the pattern of null results for female winners is that lottery wealth almost doubles their short-run probability of divorce. One interpretation of the absence of a discernible long-run increase in divorce risk among these women is that wealth accelerates the dissolution of marriages that were already underway."
> We also report results which suggest that when married men win the lottery, the windfall has a tendency to stabilize their existing marriages
Winning a lottery helps men feel secure enough that they aren't as sucky to their spouse.
> lottery wins cause the largest increase in marriage rates and the biggest reduction in divorce rates among unmarried men with low incomes.
So if you want stable marriages that have children the best thing to do is make people wealthier, especially those of lower income. Make men wealthier and they'll get married more and have more children. Make women wealthier and the men they stick with will be ones they like sticking with. I can't see this latter leading to fewer children, on average. I'd expect it would lead to more.
Where'd you get your idea from?