Labor shortages do increase wages. Up to a point....
Wages ALWAYS fall behind inflation in keeping pace. Wage inflation has never kept pace with goods price inflation.
Henry Ford paid $5/day for unskilled labor which is equivalent to just under $200K/yr in today's wages.
Unskilled labor today is not even getting $45k/yr. But the goods (housing, food, energy) costs have risen keeping the unskilled labor from ever getting better. In fact made things much worse for them.
Even skilled labor has not kept pace with inflation.....their wages have fallen by comparison.
So....until people can afford to actually live there is going to be a lack of children and general unrest of the citizenry. Then the economic stability necessary for young men and women to have children will need to be held onto. Because otherwise we will have to have almost unregulated immigration to fill job demands. (Such as is currently happening)
People do not have children in economic difficult times. Children are seen as an unaffordable burden instead of a blessing. Hence the 1.6 live birth rate instead of a 2.6 needed for stasis. A 3 would give us population growth needed for a thriving economy.
As things currently sit, a 2 income household (unskilled labor) cannot afford even an apartment and 2 car notes...much less children.
Rent at $1800/MO or more when the 2 incomes combined are roughly $1200/wk is a huge problem.