[andrewla]

From the paper (preprint found here [1]), you are correct in how they reconstruct this information. They use birth data (including estimates of gestation period) to derive the pregnancy rate at a moment in the past. They also attempt to compensate for miscarriages and abortions.

I think your central conclusion is sound, though, namely that this cannot be used to predict the future because there's no reliable data source to give the pregnancy rate in the present.

On the other hand, it might be possible to show that even excluding your (1), (2), and (3), it would still make a reliable predictor. But I'm not sure that there are datasets that would allow any insight even into the number of reported pregnancies. Potentially pharmacies would have access to rudimentary proxies in the form of sales of pregnancy tests, or inverse proxies in the form of sales of contraceptives. Large companies might have information on parental leave, but in the lead-up to a recession, you might have the confounding variable that people are losing their jobs at a higher rate, leading to a direct correlation that might overstate the phenomenon.

[1] https://www3.nd.edu/~kbuckles/BHL_fertility.pdf