A slow down in housing should have positive affects on the vacancy and rents in the multifamily apartment market.  Rising home prices drive some people to rent because they cannot afford homes.(See: Median Home Prices in Phoenix MSA) 

This is what happened in Greater Phoenix in the last few years.  As prices rose the rental rates increased as well.  This was true for the large apartment communities as well as the smaller fourplexes and the like.  This in should continue as home prices remain high and mortgages  become harder to get.  This should drive more people to rent, reduce the vacancy and increase rents. 
But, because there were so many speculators in the Phoenix real estate market who go left with vacant homes and condos when the market faltered, the number of homes and condos for rent have created a shadow market which affect rents through the rental market from top to bottom. 

No one knows the exact size of the this shadow market, but it's size-able. 
If you travel through out the valley you will see many signs for homes for sale but many of these are for "sale or lease" while others are for lease; a large portion of these homes have been available for a long time while other owners are dropping the rent in order to at least cover some of the mortgage and support an unsaleable product.

Single family homes compete with higher end apartments in the $1,000 plus rate, while condos and condo conversions and reversions compete with the smaller apartment complexes where rents are below $1,000.

This shadow market will keep rental growth to a minimum in the Phoenix MSA, it will increase vacancy as well.  You can see this now with a lot of for rent signs were in the last few years there were just a few if any.  The housing market has a ways to go before we go through this excess home inventory.

The Greater Phoenix market is in a good position to get through it quickly.  We have strong job growth and population growth.  Both of which are above the national median.  It's the job growth which will drive population growth and demand for housing. 

For owners of smaller multifamily properties I would advise to hold on until the market improves, unless you can get a better returns by selling. 
For investors interested in increasing their apartment holdings or even first time investors, this is the time to buy.  There are many good properties, some of which are in excellent locations.  Savvy investors will do well with carefully picked properties.  Call me if you would like to discuss your Phoenix real estate plans.