Is there a direct, inverse relationship between per-capita economic productivity, and fertility rate? It seems intuitive to me: a major way per-capita economic

Is there a direct, inverse relationship between per-capita economic productivity, and fertility rate? It seems intuitive to me: a major way per-capita economic productivity goes up is by working more hours, both at school, and in the workplace. Since you're competing with other max-hours workers for stuff like housing, the price rises to match. Soon, you're in a situation where there's no space in the average budget/apartment for kids. Widespread misallocation of human resources (i.e. unemployment, part-employment, etc) would presumably drive in the opposite direction.