Just thinking out loud here… Let’s limit the analysis to SFR rentals.
If people cash out in favor of renting, who’s buying their house? Is it someone currently renting? If so, then the demand for rentals does not increase, it’s just a swap. Although, I could be convinced that few people currently renting a SFR are likely to be buying any time soon.
Let’s consider population flux: I’d guess that if we start to see significant housing price declines, very few people coming to town who would normally buy, will do so. So this is an argument for an increase in demand for rentals. However, some portion of the people leaving town will be owners and have to make the choice of either; a) selling in an unfavorable market possibly under distress; b) Grit their teeth, hang on to the property waiting for the cycle to come back… and of course rent out that property. So, at least some will choose option b thus putting more SFR inventory on the market for rent. This could have a balancing effect on supply/demand. It really depends on the flux rate. I bet there will not be as many people coming to town as leaving.
If the psychological effects of the loss of all that paper wealth cause people to spend less, resulting in a real impact on the local economy, people will become much more cost conscience and this could put downward pressure on the SFR rental market. (Wow, that was a long sentence… Sorry to the grammar police out there…)
I think I can convince myself that the SFR rental market could stay flat or decline. Knowing what happened in the last downturn would be interesting. Is there any historical record of rental prices out there?