It seems like the apartment markets in Detroit, San Francisco, and Eudora are all going to be very different, hinging on radically different factors.
Some US economic trends will affect all three, sure, but... my instinct is that they won't resemble each other very much at all. Apartments that are hundreds or thousands of miles away aren't exactly fungible commodities.
I don't know much about this area though, so it was an honest question, maybe they're all more linked than I realized.
If the US national average for interest rates drops from 5% to 4%, you would expect to see downward pressure on rental prices across all markets. Sure, not every landlord is refinancing or getting a new mortgage, but as long as some contingent of landlords is able to undercut the going rate of rentals, they will exert downward pressure on the rental price in their local market.
For example, if a bank has to repossess a house in the valley, it will not have much problems finding a new buyer. For a house in Detroit, that likely is different.
That likely doesn't have much effect on deltas in the short term, though, as those factors are relatively stable.