It seems obvious to me that Swedish women, for instance, have had more 'choices' than impoverished women in impoverished countries have and they have chosen a smaller number of childbirths, so it is eminently reasonable to infer the reciprocal relationship between women's well-being and a smaller number of childbirths. The same applies to historical evidence.
That said, I think that in comparing the Scandinavian experience with the American one, we may infer that the less puritanical culture of sexuality and the absence of a well-organized anti-abortion movement contribute to a somewhat smaller number of abortions than otherwise and the ratio of earlier to later abortions will be higher. Therefore, in your research, you must take note of not just the number but the kind of abortions (earlier vs. later, for instance), as well as sexual culture & gender equality, if you suppose such research is necessary.
Last but not the least, the birth rate is *not* solely determined by what you call "social health." Childbirth is *mediated by women's own wishes and desires as to what they want to do with their lives*. That is why when women have more 'choices' (i.e. when they are empowered to become socially equal to men and when their economic lives are secure and prosperous), they tend to prefer a smaller number of children. This is borne out by both historical evidence and international comparisons. Most importantly, since no contraception is humanly perfect, there will always be abortions, for even the most aggressively "socially engineered" pro-natalist laws and programs can't diminish *women's desire to do something other than giving birth and becoming mothers*.
Yoshie