In its September update on the state of the housing market, analysts at Freddie Mac point to the strong growth in multifamily rental construction as the key bright spot in the sector. While single-family construction is "slowly chugging along," according to the report, construction of buildings with at least five apartments recently hit the highest monthly construction pace since the beginning of 2006.

Almost all these new buildings are for rentals, not condos. Over the past four quarters, Freddie Mac points out, all the growth in net household formations has been among renters. The decline in homeownership rates has been primarily concentrated among younger households. For example, for those 35 years and younger, their homeownership rate has fallen from 43.6 percent to 35.9 percent over the past decade.

"The apartment market has been vibrant, reflecting the desire of many Millennials to live in an urban setting and retain locational flexibility. Unfortunately, if they’re looking to live in the larger cities, that’s where rents are rising the fastest, especially in the West or Northeast regions of the United States, places like Los Angeles and New York City. In the South region, areas like Miami and the Washington-Baltimore metro have seen real rents exceed the U.S. average. But in the Midwest, only the Chicago metro area has outstripped the U.S. average," Frank Nothaft, Freddie Mac vice president and chief economist, said in a statement.

The movement of younger Americans into rental has caused absorption rates to spike and pushed vacancies to record lows, the report said. The latest absorption rates for unsubsidized, unfurnished newly built apartments have been at the fastest pace in a decade: The Census Bureau reported that the latest three-month and six-month absorption rates had risen to 64 percent and 83 percent, respectively. Thus, demand is there to absorb the new supply.

The increased number of tenant households has pushed vacancy rates down to the lowest level since 2000, and on average, inflation-adjusted rents in the U.S. have returned to their prior peak levels of 14 years ago.