It could go the other way as well, fewer people are starting a family because of the cost of housing.
For example, people might have been willing to raise kids while sleeping in a single bed in a single room apartment, possibly having to move multiple times.
Now, you only have kids if you can secure a single family detached house with multiple bedrooms located amongst other similar or higher socioeconomic class neighbors (good school district), and at least one parent has reliable employment with health insurance benefits, which might mean living in a metropolitan area with limited housing supply.