There might be a confounder though, with the causality working backwards.

Rural housing is way cheaper than urban housing.

Urban cultural offering is way more lively than rural cultural offering.

If you want kids you need space, and have no time for fun, so you optimize. You stop paying for cultural offering you don't need, and opt for cheaping housing you do need.

Doesn't mean that urban/rural life makes you have children, rather the opposite. The choice in having children dictates whether you choose rural or urban life.

Not saying it's like this, just offering an alternative theory.

From my observations, its more the friends that never left rural village we grew up in that have children. My urban friends don't really have children maybe because urban life i stressed but you also have so much stuff to do so maybe kids isn't really a thing one think about, it's more about building up a network.