Thanks all for your responses.
I agree the consensus is it depends on how much rent increases (wage driven) vs market demand for CAP rate. However, without historical numbers, it will be hard argue one way or another.
In my original post, I had a hypothetical change of 20% wage/rent, and treasury rate going from 3 to 8. I think 3 to 6% is more realistic associated with a 20% wage/rent increase. So redoing the numbers:
10% CAP at 3% treasury (7% premium for multiunit)
13% CAP at 6% treasury (same 7% premium), and 20% rent increase. 100K unit at 10%, would be worth 92K at 13%, so a drop still. I think numbers for SFHs generally give the same results, i.e. under typical scenarios, wage growth won't be able to keep up with rate change in residential (what Bruce Norris believes as well). So affordability goes down and a net negative effect on SFHs.
But I'll try to get some charts together. It is easy to find interest rates, harder to find historical wage changes. anybody has a good chart already on rent vs interest rate going back at least 30 years?