Building permits for new construction of houses in New Jersey have reached their highest levels in six years. Still, a brand-new home remains an elusive goal for many millennials in the state.

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In 2013, more than 24,000 new housing construction units got the green light in New Jersey. Economic analyst Patrick O'Keefe of CohnReznick in Roseland said that's a marked increase.

"Housing authorizations were up over 35 percent in New Jersey," O'Keefe said.

O'Keefe reports that the majority of these, about 53 percent, were for multifamily rentals. He predicts that trend will continue.

"We will see historically high levels of multifamily construction for the remainder of this decade," O'Keefe said, "and well into the next decade."

Many millennials, according to O'Keefe, lack the means to afford even a down payment on a new home in the pricey New Jersey market. So, the idea of going the multifamily route should linger for a long time.

As for the increased construction activity, O'Keefe said that is due in large part to an improving jobs market and a quickening economy. He said it's good news for those engaged in construction enterprises, as well as their supporting subcontractors.