You would expect some effect though, yet Northern Europe and Japan continue to have extremely low birth rates despite the efforts of their governments.
Also, many European countries saw fertility rates drop a long time ago, often back when housing was much, much cheaper. IIRC countries like Sweden and Norway dropped below replacement levels in the late 1960s and early 1970s.
In countries I've been in, that period coincided with a move from farms, where land was ample, to cities, which were cramped. Big family housing wasn't really available; those cities had apartments which simply didn't really support larger families. Cost wasn't so much an issue for having a cramped 2 or 3 bedroom in the sixties, but beyond that, you moved into ultra-wealthy territory.
So I guess my question is whether you could write a little bit more about the Scandinavian countries. That's my own ignorance speaking.
Japanese cities are super-cramped. I would not want a big family in Tokyo.