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I studied this question, and the paper is forthcoming in the Journal of Labor Economics. I find that child support policies adopted in the 1970s-90s reduced the abortion rate. (thread 1/)
The economics behind this is pretty straightforward: child support lowers the cost of raising a child as a single mom, so when women are more likely to receive support, they are less likely to terminate a pregnancy. 2/
For context, the abortion rate declined over the last several decades, particularly in the 1990s. 3/ 
Meanwhile, child support enforcement increased, largely because of new technologies promoting paternity establishment such as genetic testing, and also those facilitating payments, such as wage withholding. (The figure below is for never-married moms.) 4/
Here's the main result on abortions: when states strengthened their child support policies, the abortion rate fell in the following 1-2 years. (The abortion series in the figure is offset by 1 year for visual clarity: time 0 is 1 year after the policy change.) 5/
How large is the effect? Large: I find that the full rollout of child support policies from 1977 to 1992 reduced the abortion rate by 1-2 per 1000 women. This is large relative to the baseline rate of 28. (It's also large relative to the decline over this period). 6/
I will do a full thread on the paper at some point! Here is the paper: docs.google.com/viewer?a=v&pid… 7/
