In New York City , where luxury apartments have been going up at a fast clip since the recession , landlords are increasing both amenities and concessions. The share of rentals with landlord concessions set a new record at the start of this year. Over 30 percent of New York landlords offered concessions, with the heaviest use within 2-bedroom apartments, according to Jonathan Miller, of Miller Samuel, who provides monthly reports for real estate broker Douglas Elliman.

"There are lots of available units at just-completed projects," according to Jay Denton, vice president of RealPage's Axiometrics business group. "Also, top-tier existing projects are losing performance momentum for the first time in this market cycle. Some renters from established luxury projects are opting for the newest deliveries in order to take advantage of rent discounts often offered during the initial lease-up process."

Demand for rental apartments fell short of new supply by about 100,000 units nationwide, according to RealPage, a real estate analytics firm. Apartment occupancy is still high, but it is softening a bit, dropping to 94.5 percent in the first quarter of this year, compared to 95.1 percent at the end of 2016. Occupancy has been falling for the past six months.

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Most of the concessions are monetary — a month or two of free rent — but others are more creative.

"What we're seeing more of now is discounted deposits in addition to free months of rent. You only have to put down $500 or $1,000 deposit. It impacts what people are looking at, and that sweetens the deal for a lot of people," said Gabby Warshawer, director of research for CityRealty.com, a New York City real estate listings and analytics company. "There are also stray offerings for gift cards — a $1,000 MasterCard gift card when you sign the lease or, in some cases, free access to the building's amenities package."

While concessions are hitting the luxury end, rent growth is still relatively strong moving down the rent scale. Pricing is strongest in the middle-market, so-called Class B properties, which tend to be older buildings or rentals in the close-in suburbs.

"Top-tier projects in neighborhoods with the most construction are struggling to push rents at all. In many metros, that's especially true in the urban core. However, Class A product rent growth is still substantial in desirable suburbs adding comparatively modest new supply," said RealPage's Denton.

Rents and rent growth obviously vary market to market, as with all things real estate, and Sacramento, California, now tops the charts, with rents up 9.8 percent annually. Seattle, Washington, and San Bernardino, California, are not far behind. Rent growth is about half that in Charlotte, North Carolina, Denver, Colorado, Minneapolis, Minnesota, and Tampa, Florida.

The real estate investment trusts (REITs) behind multifamily apartments are responding accordingly. Top markets for REIT returns include Phoenix, Arizona, Tampa, Florida, and Oakland, California. Below average trends can be found in New York City, Philadelphia, and Boston, according to Gaurav Mehta, a multifamily REIT analyst at Cantor Fitzgerald.

"We continue to expect the largest supply increases in New York, the strongest job growth in Orlando and the highest rent growth in Seattle," said Mehta, who expects supply to peak this year with the largest increases in New York, Nashville, Charlotte, Austin, and Seattle.

Analysts at RealPage say demand should grow through this year, as increasing job growth supports more household formation. Both economics and demographics favor more demand for rentals. Supply, however, is also growing and demand is unlikely to meet it. There are currently over 581,000 apartment units under construction with scheduled deliveries climbing to an average 102,000 units per quarter, compared to 82,000 finished per quarter in late 2016 and early 2017.

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