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Even in a strong national economy, half of older Americans living alone and nearly one-quarter of older couples struggle to afford basic necessities, according to a report that lists Massachusetts as a leading state for “elder economic insecurity.”

Massachusetts tops all states in the share of single people over 65 whose income doesn’t cover living expenses such as food, housing, health care, and transportation. More than six in10 here fall short, according to the elder economic security standard index released Tuesday by the Gerontology Institute at the University of Massachusetts Boston.

The state ranks third, after Vermont and New York, in economic insecurity for seniors in two-person households. Nearly 30 percent in Massachusetts fall below the index.

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“It really comes down to the cost of living, particularly the cost of housing and health care,” said UMass Boston gerontology professor Jan Mutchler, director of the institute’s Center for Social and Demographic Research on Aging, which has tracked data on income and living costs for older adults over the past decade. “Some of the same things that make Massachusetts a good place for younger people to get jobs are also driving up the cost of housing for seniors.”

About 300,000 seniors in Massachusetts are considered economically insecure — and about 10 million seniors across the country, according to the UMass Boston index. The cost of living for older adults in Massachusetts ranges from $26,220 to $39,408 a year for a single person and from $38,424 to $51,612 for a couple, depending on whether they rent, own a house that’s been paid off, or own a house on which they’re paying a mortgage, the index calculates.

In Massachusetts, a hub for higher education and well-paying industries, the findings from the report belie the popular image of prosperous retirees with disposable income.

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“The perception of seniors in Massachusetts is they’re comfortable economically, they’re well-off, and they’re looking for leisure activities,” said Carolyn Villers, executive director of the Massachusetts Senior Action Council, a statewide advocacy group based in Quincy. “The reality is the vast majority of seniors here are focused on meeting basic needs.”

One such senior is Sarah Blakeney, 92, who lives in a Milton apartment and depends largely on her modest Social Security check to cover her rent, food, health insurance, and other expenses. “My rent just went up, and I had dental work,” she said. “Thank God I have people from my church who help me out, or I wouldn’t be able to afford everything.”

Mutchler’s research, conducted with doctorate students Yang Li and Nidya Velasco Roldan, compares income data from the US Census with the Elder index, a county-by-county measure of the income needed by older adults to maintain their independence and meet their living costs while remaining in their homes. The data do not include financial help from families or government supports, such as food stamps, Medicaid, and housing subsidies. Many of the states ranking highest in elder economic insecurity were in the Northeast, where living costs have surged as economies have grown, or in the South, where lower incomes make it harder for seniors to make ends meet even with a lower cost of living. A breakout for Boston, where costs are higher than Massachusetts or the nation as a whole, found that nearly three out of four older adults living alone lack the income to cover necessary expenses.

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Researchers found many seniors fall into an “economic security gap” where their incomes — which include Social Security and, for some, wages, savings, and pensions — are too high to qualify for public benefits but too low to achieve economic stability. Those who can’t get family help sometimes resort to skimping on food or medicine, Mutchler said.

“We hear a lot about people making all kinds of adjustments,” she said. “They can’t avoid paying their rent, but they keep their heat down in the winter or don’t turn on their air conditioning in the summer. Some of them don’t eat as well as they should, or don’t take the medication they need, or don’t go to the doctor when they should.”

The high levels of senior economic insecurity documented in the UMass Boston report should spur policy makers to find ways to create more affordable housing, help older adults pay for rising medical costs, and provide relief from soaring property taxes, said Villers.

Villers said the waiting list for affordable senior apartments is seven or eight years in some Massachusetts cities and towns, while some seniors spend 20 to 30 percent of their monthly income on health insurance premiums. In response to rising health costs, the Baker administration recently expanded access to a Medicare savings program that allows high-cost states to set income eligibility requirements above the federal minimum.

Boston officials, for their part, have adopted a plan to add 2,000 low-income housing units to the 12,800 already available in the city.

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“We’ve gone into high gear to build more subsidized housing for seniors,” said Sheila Dillon, the city’s chief of housing and director of neighborhood development. “We’re looking for new sites and new opportunities to build.”

Both the state government and the city of Boston, where about 31,000 older residents fall below the UMass Boston economic security standard, have taken other steps to improve elder economic security as part of the “age-friendly” initiatives rolled out in recent years.

But they, along with other cities and states across the country, continue to grapple with high costs that fall hardest on their oldest residents, according to the UMass Boston report.

It recommended, among other things, efforts to protect Social Security benefits, which account for at least 90 percent of the income for more than half the older adults who can’t afford essential living expenses. It also proposed keeping older employees in the labor force longer at a time when many businesses and other organizations are finding it difficult to attract workers.

“A lot of [baby] boomers are crossing that retirement threshold and aren’t really prepared for the costs they’re going to face,” Mutchler said.

Robert Weisman can be reached at robert.weisman@globe.com. Follow him on Twitter @GlobeRobW.