(NY TIMES) David Goodman, October 11, 2017 — The four-story building sits on a quiet street in Brooklyn, across from a church and an arts school. Eight apartments, front and back, two on each floor.

The building, near the boundary of Clinton Hill and Bedford-Stuyvesant, has gone through incarnations as a rental, then a tenant-run cooperative, then a rental again. The most recent change brought a handful of new tenants, lured not by a landlord seeking to profit off the neighborhood’s gentrification, but by the promise of affordability.

The building is a small part of what Mayor Bill de Blasio has called the most ambitious affordable housing plan in the city’s history. Its eight apartments are counted toward Mr. de Blasio’s goal of preserving or creating 200,000 units of housing in which rents are regulated by 2024.

For much of his first term in office, Mr. de Blasio, a Democrat, has made affordable housing a centerpiece of his agenda — highlighting it in his State of the City addresses and calling it the No. 1 issue on the minds of New Yorkers. In July, he heralded a numeric accomplishment: 77,651 units financed so far.

Not everyone is impressed by the numbers. Angry dissent over his rezoning plans has met Mr. de Blasio at recent town halls. And black and Latino religious congregations have a permit for a 5,000-person protest at the gates of City Hall next week to pressure the mayor to build more housing for the poorest New Yorkers.

Indeed, the effect of the mayor’s plan on the city’s real estate market has thus far been subtle. The vast majority of these affordable units are existing apartments, not new construction — a strategy born of design and necessity.

Gone are the vast swaths of publicly owned land and blighted or abandoned private apartments that the city took over in the 1970s and ’80s, and that served as the fuel for Mayor Edward I. Koch’s effort to create more than 150,000 units of affordable housing.

Mr. de Blasio is instead trying a multipronged approach. The city has chosen several neighborhoods for rezoning, creating a requirement, known as mandatory inclusionary housing, that would allow for taller buildings and more density, as long as any new housing built included affordable units.

The mayor, like his predecessor, Michael R. Bloomberg, is also trying to harness the energy of the private market to compel developers and landlords to keep apartment rents below the market rate for the long term.

For the past three years, the city’s Department of Housing Preservation and Development said, it has used some combination of city money, public incentives and private loans to spur deals with private developers and nonprofits to rehabilitate buildings, build new ones and subsidize apartment rents. In each case, the city imposes a regulatory agreement, and it says it controls who lives in the apartments, based on income in most cases.

The bulk of the mayor’s plan is focused on what housing experts call preservation, a designation that could mean, as in the case of at least 7,500 units so far, something as simple as a new financing agreement to keep apartment rent below market levels.

Yet City Hall officials could not say how much they were increasing the stock of such rent-regulated and income-tested units because, a mayoral spokeswoman said, they do not track the number of preservation units that they are bringing under city regulation for the first time.

Officials said they could not build new public housing even if they wanted to because of a 1998 amendment to federal housing law that fixed the total amount of public housing eligible for federal subsidies according to the number of existing units. In New York City, the limit is set at just above 180,000 apartments.

“When all these advocates run around and say, ‘Why isn’t the City of New York building housing?’ It doesn’t exist. There’s no such thing,†said Alicia Glen, the deputy mayor for housing and development. “It’s all about, to what extent can you use the resources of the private sector, and the resources the public sector has, to put together the best deals you can possibly do.â€

The city held lotteries for 5,310 apartments last year, more than twice as many as four years before, but not enough to transform the housing market. Tens of thousands of residents apply and must meet income thresholds, with far more applications coming in for the lowest-rent apartments than for those aimed at middle-income New Yorkers.

Overall, rents in the city appear to be flattening amid a broad boom in market-rate apartment construction, housing experts observed. But prices are still escalating in some neighborhoods.

Those in fast-gentrifying neighborhoods still fear displacement, and many remain skeptical of Mr. de Blasio’s plans, opposing individual developments and pushing local officials to beat back rezoning proposals.

Only two of the 15 large-scale neighborhood rezonings pledged by the de Blasio administration have been completed amid such resistance. The second rezoning, in Far Rockaway, was approved by the City Council last month. (The rezoning of East Midtown, approved in August, was aimed at spurring commercial real estate development.)

“So far, in the rezoned area, there has been zero units built to date,†said Rafael L. Espinal Jr., a city councilman who represents an area in East New York that was rezoned last year. “If you were to speak to some residents, they would say they have seen an uptick in the number of speculators knocking on their doors, trying to buy their properties.â€

Indeed, development backed by the de Blasio administration has been an issue in some elections this year, including a Council race in Central Brooklyn. In that district, opposition has stalled a plan to encourage the creation of a recreation space and affordable housing by allowing condominium development on city-owned land at the Bedford Union Armory.

“The community put the line in the sand: no luxury condominiums,†said Councilwoman Laurie A. Cumbo, who prevailed in a tough re-election fight in the Democratic primary in which the project was a central issue.

Some nonprofit housing developers and advocates for low-income residents have charged that the administration is improperly focused on meeting numerical goals rather than on creating more apartments for the poorest New Yorkers.

“If under Bloomberg they had offered what they’re offering now, people would have been happy,†said Benjamin Dulchin, the executive director of the Association for Neighborhood and Housing Development, a nonprofit. “But by this point, people are fed up and want real answers. That’s the dilemma they’re in.â€

The mayor responded, earlier this year, by adding $1.9 billion in city money to increase the number of units in the plan for households earning less than $40,000. Some in the city’s poorest areas want him to go further.

“We’re definitely going to push the envelope,†said the Rev. David K. Brawley, who represents an East New York congregation, the St. Paul Community Baptist Church, and has complained about Mr. de Blasio’s affordable housing plan. He is helping to lead the protest next week.

Mr. de Blasio has put the total capital cost of the housing plan at $41 billion, almost twice as much as was spent on affordable housing during the Bloomberg administration. That includes public and private funding, with the city’s portion amounting to about a quarter of the total. So far, the de Blasio administration has spent more than $2.2 billion in city money on the housing plan out of about $18.5 billion in total financing.

For those who work in the field of affordable housing, the de Blasio approach has been a reasonable one, given the limitations of the times.

“For this city to survive, there is an absolute need for as much affordable housing as can be created,†said Marc Jahr, a top housing development official under Mr. Bloomberg. “What makes New York City unique is the immense commitment of city capital to its effort. There is no comparable commitment anywhere in the nation than what this administration or the prior administration have undertaken.â€

The largest concentrations of units created or preserved so far by Mr. de Blasio are in three areas: the South Bronx, Harlem and in Stuyvesant Town in Manhattan, where a city-orchestrated deal with developers helped keep 5,000 units under rent regulation, in exchange for tax breaks.

But projects are scattered and can be found in unexpected places, often hidden in plain sight.

No city signs mark 365 Bond Street in the Gowanus section of Brooklyn, where young men and women glide past a 24-hour concierge in a fashionably appointed lobby — and 86 of the 429 apartments have been set aside for low-income New Yorkers. A new tower of steel and glass at the far west end of 42nd Street in Manhattan has 1,175 apartments, two pools and an indoor basketball court; less apparent are the 20 percent of its units reserved for families making $51,000 or less.

Even some of the New Yorkers who had recently moved into these newly constructed apartments were unaware that their homes were part of a scattered but growing archipelago of new buildings supported by city money.

“I love this apartment, I’m not going to lie,†said Melody Richey, 38, whose first-floor apartment in a rapidly gentrifying section of East Williamsburg gleamed with the crisp edges of new construction. She had no idea the unit — which she received through a placement by a nonprofit — had anything to do with Mr. de Blasio or the city. She beamed as she showed off the new appliances, the two bedrooms and a wide bathroom door that could accommodate her wheelchair. Her old apartment, in Flatbush, had an elevator that often broke down.

At the Clinton Hill building, Valerie Roberts, 61, also had no idea that her fourth-floor apartment, where she has lived for decades, counted as affordable under the mayor’s plan.

She and her husband, Reginald Spies, said their modest three-bedroom home on Madison Street did not feel affordable to them. The rent had increased steadily — “every year, it goes up,†he said — and at $1,271 was about three times what they said they had once paid in co-op maintenance years before.

The building is among those that the city has targeted for preservation, buildings that had been part of a decades-old program intended to create tenant-run cooperatives, like the one Ms. Roberts’s apartment was part of. The cooperative arrangements often ended because the owners fell far behind on their city water and tax payments, leading the city to foreclose and transfer ownership to a third party. In practice, that meant a private or nonprofit developer. There are currently several dozen such cooperatives facing foreclosure by the city, with some tenant-owners actively fighting to keep ownership.

The housing plan is more readily apparent under the rumbling No. 3 subway line in East New York, outside of the rezoned area, and in parts of the South Bronx. “Housing New York†banners adorn active construction sites. Residents in new buildings praise their surroundings, which, in bigger buildings, include common spaces for daytime classes with children as well as playgrounds and plate-glass storefronts.

Yet not everyone is convinced of the plan’s efficacy.

“At the end of de Blasio’s second term, we’ll ask two questions: Will he have built the 80 percent of the 200,000 units?†said Mr. Dulchin, the housing advocate. “But the other question is, Will the city be more affordable? And a lot of communities are not convinced of that.â€