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Missing middle: Big houses, small apartments — where’s the home in between?

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As the shortage of housing becomes an increasingly critical issue in the Greater Boston region, new data is highlighting how families with children face a particularly uphill climb in finding homes that meet their size and income needs.

Houses, condos, and apartments with three or more bedrooms make up 59 percent of the housing stock, but fewer than half of those units are occupied by households with children, according to an analysis by the Metropolitan Area Planning Council.

The data found that over-55 households occupy about 45 percent of large units, with over-70 households occupying nearly 15 percent.

“Many communities haven’t been building housing fast enough to meet demands,” said Tim Reardon, MAPC data services director. “And a lot of the homes that do exist are being occupied by empty-nesters and seniors living alone. So there is family housing that exists but it’s not available or on the market for the families who need it.”

Reardon said larger units are not available to families in part because many communities have zoning rules that prevent or discourage developers from creating the one and two-bedroom units — particularly rental apartments — that might attract empty-nesters.

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“Those seniors who would like to downsize to something smaller don’t have many options in many of these suburban communities,” he said.

Foxborough planning director Paige Duncan knows firsthand the challenges facing empty-nesters looking to downsize. The 51-year-old Franklin resident and single mother of two had planned to purchase a smaller home when her youngest child heads to college next fall.

“But it dawned on me that if I sell my house for $500,000, I’d walk away with $200,000,” she said, referring to her net proceeds after paying off the mortgage. “But any home I bought would cost more than that. So I have no place to go — I’m going to have to stay in my house.”

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The MAPC analysis also points to how cost-burdened many families with children are with their existing housing; more than 30 percent pay over 30 percent of their income on housing and one in seven over 50 percent. More than 20,000 live in overcrowded units.

Moreover, there are limited options for families unable to purchase a home. Rental units make up just 13 percent of existing three-plus bedroom units in the Greater Boston region, effectively excluding families from communities where “the purchase of a single family home is the price of admission,” the MAPC said.

Three-bedroom-plus rentals are a “rare commodity” in Chelsea and Revere; and when available “they are generally out of reach for the vast majority of families in our communities,” said Rafael Mares, executive director of The Neighborhood Developers, a nonprofit that builds affordable housing in the two cities.

“So families share apartments . . . resulting in overcrowding,” he said by e-mail. “Other families pay more than they can afford, requiring them to sacrifice other basic needs, such as food. Some families have to do both. We see many families who have a social network, children in school, and jobs in or near Chelsea and Revere, being displaced and pushed out of our communities by the housing market.”

The MAPC issued a report in February examining the housing challenges of child-rearing families in Boston and 13 surrounding communities. The new analysis, prepared at the Globe’s request, expands upon that urban core study to encompass data from 155 cities and towns in the Greater Boston region, excluding Boston and Cambridge.

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The resulting data provides a window into the housing difficulties families face, even in far-flung suburbs.

Reardon said larger units are much more common in the extended area than in the urban core — where only 38 percent of units have three or more bedrooms — but a greater share of the units in the extended region are occupied by over-55 households.

Rental units also claim a much greater proportion of housing in the urban core, though many of them are occupied by roommate households.

The data reveals some geographic variations within the extended region. The area north of Boston, for example, has the highest percentage of families that are housing cost-burdened, while three-bedroom-plus units are relatively more plentiful in MetroWest.

Reardon said adopting zoning changes to allow more multifamily housing and expanding the use of accessory — or in-law units — are two ways municipalities could help ease the housing crunch for both young families and empty-nesters.

He said local adoption of such changes would be boosted if state lawmakers approve pending legislation lowering the threshold to pass most zoning changes from the existing two-thirds majority to a simple majority. From 2016 to 2019 in the region studied, 19 zoning changes that under the new law would require only majority votes failed after receiving majority but not two-thirds votes.

Karina Milchman, MAPC’s chief of housing and neighborhood development, said addressing community fears that new family housing will overburden local schools is also a key to getting new units built.

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“You hear over and over again in communities that ‘our schools are at capacity . . . and we simply can’t have more families,’’’ she said. In some cases those concerns are valid, she said, but more often than not they are misplaced, citing a 2017 MAPC report that found no meaningful link between housing production and enrollment growth.

Susan Connelly, director of community assistance and strategic partnerships for the Massachusetts Housing Partnership, also disputed the idea that rising enrollment is to blame for escalating school costs, saying the real cause is increasing health and retirement costs.

Connelly thinks housing options for families are limited because the state’s locally controlled zoning system is out of step with market demand.

“Local officials and developers who respond to local concerns say ‘We will create housing that does not attract families,’ and the way communities push 55-plus restrictions is part of that,” she said.

As an example, she said last year a 1,300-square-foot Lexington home on an 8,000-square-foot lot was demolished and replaced with a 3,500-square-foot house.

“That could have been three or four town houses,” she said.

James Freas, Natick’s director of community and economic development, sees a connection between the lack of housing opportunities for families raising children and the fact that midrange density housing is rarely being built anymore in New England.

“If you look at what is being built around the region it’s single-family, duplexes, and big projects,” he said, noting that under local zoning rules those are the only ones that work financially for developers. “Missing are the middle housing opportunities that are often really well suited for family housing,” such as three- and four-family homes.

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“What we are seeing built in the suburbs are massive homes,” Duncan said, noting that local density limits and high land costs give developers no incentives to build anything else. Foxborough, for example, has 1-acre zoning and plots of that size cost about $275,000.

She said the town is considering removing the restriction on non-relatives occupying accessory units while it works on a long-term plan to meet its housing needs.

Finding a three-bedroom unit in Salem is “extremely difficult,” said Tom Daniel, the city’s director of planning and community development, a problem he said is closely connected to the lack of downsizing options for older residents.

He said the tight market in the city for one-level living units makes it difficult for even those seniors with ample resources. And for seniors of more limited means, the challenge is even greater because few of those units are affordable.

The City Council is weighing a proposal to allow non-relatives to occupy accessory units in Salem — a similar proposal died in December when it fell short of a two-thirds vote. Also before the council is a proposed ordinance requiring affordable units in multifamily projects.

The council last year approved another zoning proposal — after it initially failed to earn a two-thirds vote — allowing for developers to pursue plans to convert two former Catholic schools and the city’s former senior center into multifamily housing.

Framingham Mayor Yvonne M. Spicer said the city faces a pressing need for more housing to accommodate its growing population, so she welcomes the 900 new rental units that three new developments are bringing to the downtown.

But concerned about the need to maintain the city’s diversity, Spicer is exploring how the city might encourage developers to include more three-bedroom units affordable to families with children — few of the new downtown units are that size — as well as moderately priced “workforce housing” and units for seniors and veterans.

“We have to make our cities and towns accessible to all,” she said.

Jennifer Constable, Rockland’s assistant town administrator and a Hull selectwoman, sees affordability as a key issue in meeting the housing needs of child-raising families and older adults.

“In Hull and Rockland, the availability of homes is so sparse and the competition for them is very competitive, pricing out a lot of family households,” she said.

Middle-income families not qualifying for subsidies face a particular squeeze finding suitably priced housing, said Constable, who believes expanding opportunities for accessory apartments, and more programs to help in financing homes, could help.

Like many communities, Hull and Rockland have aging populations, and for that reason Constable said both want to attract child-rearing families to town — not keep them away.

“What makes a community is the diversity of the population,” she said.

To view the analysis, go to mapc.ma/largeunits.

John Laidler can be reached at laidler@globe.com.