The title of this blog post is terrible, I agree, but nothing pithy-yet-comprehensible came to mind. One way to see if a social science hypothesis is worth pursuing is to assume a ridiculous limit case and see if it leads to a significant result. If it does not, then the hypothesis is not worth pursuing. So that is what this post will do with the hypothesis that improved fertility technology caused the recent massive increase in the fertility of highly-educated women. (The credit for this hypothesis goes to Bitsy.)

Between 1998 and 2013, IVF procedures resulted in approximately 803,000 babies. Over the same period, postgraduate women born between 1970 and 1974 gave birth to about 4.61 million children. They had a completed fertility rate of 1.74 children per woman, up from 1.33 for postgraduate women born in 1950-54. If we assume that all 803,000 assisted fertility births were born to postgraduate women in that age cohort, then their non-assisted completed fertility rate would have been only 1.47.

So the hypothesis cannot be dismissed out of hand.

But there are a *lot* of women born before 1970 who would have gotten IVF over that period. (Our group of interest was aged only 24-28 in 1998.) We can effectively throw out the data before 2000, but that only cuts the number of IVF births 711,000. So the hypothesis still cannot be dismissed.

Given that we know the approximate age of IVF patients, we can guess that the maximum number of IVF births over the years 2000-13 that could have fallen to women in our cohort of interest was around 400,000. (This assumes that the age distribution at the link held in every year, a somewhat heroic assumption but one which does not, I think, have a particular bias.)

If *all* 400,000 of those births accrued to postgraduate women, then their non-IVF completed fertility would have been 1.59. IVF would account for 40% of the increase. But given that postgraduate women were only 13.8% of all women born in 1970-74, that also seems unlikely. We are still above a reasonable upper bound.

Let us say that half of all births accrued to them, say 200,000. In other words, imagine that postgraduate women resorted to IVF at a rate 3.6 times that of other women in their age group. That assumption gives us a non-IVF completed fertility of 1.66. In other words, IVF would be responsible of 20% of the increase.

This seems like a reasonable upper bound, but tell me if you think there is a logical or arithmetical mistake!

If we assume that a quarter of IVF births accrued to postgraduate women at a rate twice that of other women (for a total of 27.6% of all IVF births), then non-IVF fertility for postgraduate women jumps to 1.70. That is within spitting distance of the actual 1.74; IVF would account for only 10% of the increase from 1.33 children over the past two decades.

In short, IVF was a significant factor, but is unlikely to account for more than 20% of the increase in fertility.

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