I strongly recommend that report to anyone interested, there is a lot of interesting work in it, even just to skim the pictures like I did. That said, I have to say I really don't think "Early childhood public spending as a percentage of GDP has a strong positive correlation with fertility" is a useful takeaway from it. True, yes. Useful no.

Firstly, assuming we're looking at pg 50, seems to be correlation not causation - causation could be reversed (no children -> no need to spend). Secondly, there are so many correlations in that report that picking out any specific one is a bit random.

Also it isn't immediately clear if they're population weighting since the graph makes the US look like an equal to LUX instead of a 300 million person behemoth. To me that seems to make the correlation a minor curio.