Seems like it's more likely home prices are the key factor, not home values. Subtle but important difference I'd say. If you can't afford a place to live, you probably can't afford to have children.
Is it a difference? Home values are determined by looking at what comparable houses in the neighborhood are actually selling for. You can't value homes if no transactions are taking place because then you have no idea what it's worth. Asking prices are meaningless; prices of actual sales are all that matter.
It's more likely that people deciding not to have children have more money to spend, which, given supply constraints on housing, increases market clearing prices for housing.
