Of course specific cities are going to show deviations from the national trend. Take a look at the Case-Shiller index[0]. You can add comparisons between the national index and major city indexes.
There is probably strong spatial autocorrelation (Minneapolis and St. Paul are more similar than Minneapolis and Atlanta) but cities that share characteristics (e.g. population size, density, etc.) would also share similar trends.
[0] http://us.spindices.com/indices/real-estate/sp-case-shiller-...
Looks like Detroit has actually been on the rebound since 2012, though still below original levels. Denver and Dallas are really taking off. You can really see the housing crash hammering Phoenix and Vegas.
My quick take is that there are some big trends that are correlated nationally, but they'll be more or less pronounced region by region, and some cities have their own special issues.
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.
Honest question.