Steve Levitt and John Donahue are unconvinced by the critics of their "more wanted and fewer unwanted children means happier families and less crime" hypothesis. In large part what is going on is "normal science"--Foote and Goetz are inducing Levitt and Donahue to focus and improve their arguments by finding better data. It's not (at least not in anything I've seen) that Foote and Goetz are coming up with empirical results that tightly estimate the effect of abortion availability on crime to be small. The most their empirical results showed was that Levitt and Donahue had not proved their case (and that their Table 7 was badly mislabeled):

Freakonomics: Back to the drawing board for our latest critics%u2026and also the Wall Street Journal and (Oops!) the Economist.... [A] working paper by Chris Foote and Chris Goetz that is sharply critical of John Donohue and me has gotten an enormous amount of attention.... Foote and Goetz criticized the analysis underlying one of the tables in our original article that suggested a link between legalized abortion and crime. (It is worth remembering that the approach they criticize was one of four distinct pieces of evidence we presented in that paper they offer no criticisms of the other three approaches.)

Foote and Goetz... correctly noted that the text of our article stated that we had included state-year interactions in our regression specifications, when indeed the table that got published did not include these state-year interactions... correctly argue that without controlling for changes in cohort size, the original analysis we performed provided a test of whether cohorts exposed to high rates of legalized abortion did less crime, but did not directly afford a test of whether "unwantedness" was one of the channels through which this crime reduction operated.... They found that once you made those changes, the results in our original Table 7 essentially disappear.

There is, however, a fundamental problem with the Foote and Goetz analysis. The abortion data... are... noisy. As one adds more and more control variables... the meaningful variation in abortion rates gets eaten away [while the noise remains].... That will lead the measured impact of abortions on crime to dwindle.... In light of this, it seems uncontroversial that one would want to do the best one could in measuring abortion when carrying out such an exercise....

What John Donohue and I have done (with fantastic research assistance from Ethan Lieber) is... the following [four corrections].... 4) The standard solution to measurement error is to perform instrumenal variables in which one uses one noisy proxy of the phenomenon that is poorly measured as an instrument for another noisy proxy. (I recognize that most readers of this blog will not understand what I mean by this.) In this setting, the CDC's independently generated measure of legalized abortions is likely to be an excellent instrument.... I think that just about any empirical economist would tend to believe that each of these four corrections we make to the abortion measure will lead us closer to capturing a true impact of legalized abortion on crime. So, the question becomes, what happens when we replicate the specifications reported in Foote and Goetz, but with this improved abortion proxy?...

Foote and Goetz... We are able to replicate their results.... [But] with our more thoughtfully constructed abortion measure... the estimated abortion impacts increase... are now statistically significant[ly different from zero at the .05 level] in all of the Foote and Goetz specifications.... The only difference between what Foote and Goetz did and what we report in row 2 is that we have done a better job of really measuring abortion....

[T]he results of instrumental variables estimates using the CDC abortion measure as an instrument... [produces] results... a little bigger, but are more imprecisely estimated....

The simple fact is that when you do a better job of measuring abortion, the results get much stronger. This is exactly what you expect of a theory that is true: doing empirical work closer to the theory should yield better results than empirical work much more loosely reflecting the theory.... The results we show in this new table are consistent with the impact of abortion on crime that we find in our three other types of analyses we presented in the original paper using different sources of variation. These results are consistent with the unwantedness hypothesis.

No doubt there will be future research that attempts to overturn our evidence on legalized abortion. Perhaps they will even succeed. But this one does not.