Rent & House Prices-Substitutes
Add to that the fact that rent increases were relatively modest during the bubble, and it becomes clear that the cost of the different forms of housing costs are negatively and not positively correlated.
This need not be the case. If there is a general increase in demand for housing, due to for example an increasing population or increased preference among the young for moving from their parents, or an increased preference among the wealthy for having multiple homes, then this should raise both rents and house prices.
However, if we look at another theoretical scenario where the focus is on housing consumers having big shifts in relative preference for owning and renting, then the two prices should indeed move in opposite direction. When the preference for owning increased due to low interest rates then demand for rented housing fell, putting a downward pressure on rents.
After the housing bubble bursted, people became increasingly reluctant to own houses and instead increasingly preferred renting their homes something which helped push up rents.
Now the preference for owned housing is again increasing, pushing upward pressure on house prices and downward pressure on rents.
So, we have two different theoretical scenarios, one concerning general demand for housing and one concerning relative demand for owned and rented housing. While it under under circumstances would be possible for the first scenario to be more important, it is clear that in the recent decade the second has been more important in America.