“For now, it seems to me that both sides are circling each other wearily,” Nyhan says. “I have always felt that Harvard has a lot of opportunities to help Boston.”

Two weeks ago, Menino called on Harvard and a few other wealthy tax-exempt institutions to increase their voluntary payments in-lieu-of taxes (PILOT) to help fill city coffers.

Last fall, Harvard agreed to pay another of its newer host cities, Watertown, at least $3.8 million annually—a figure which, Harvard officials say, significantly raises the bar for Harvard’s PILOT in Boston and elsewhere.

“We enunciated a principle with respect to PILOT payments in the context of the Watertown deal, and we’re certainly prepared to implement that principle,” Summers said in an interview last month.

Harvard currently pays Boston about $1.6 million in voluntary payments.

Menino says that his call for Harvard in particular to make higher payments was a warning to the University as they seek zoning permissions for their new property in Allston—“I will insist [PILOT] be part of the negotiations,” Menino told The Globe.

But officials at Harvard are quick to point to current philanthropic activities, such as its highly-touted Boston after-school program and its contributions to an Allston-Brighton affordable housing fund. And Mary Power, Harvard’s senior director of community relations, also underscores that the University’s contributions do not come solely in the form of cash.

“It’s implicit that Harvard’s development helps the city’s economy,” she says.

Power points to a recent study funded by Harvard and seven other local universities that demonstrates how the academic research institutions provide vital economic support, even in times of recession.

Grogan, who oversaw the beginning of the impact study, says that the study’s demonstration of universities’ economic value is a valuable political tool for institutions like Harvard.

“It’s a way to increase their stature, and to increase the level of cooperation they will get from the political world, the business world, and surrounding communities,” says Grogan, who as former vice president for government and community relations, knows the territory well.

He warns that an old-fashioned approach to wealthy universities needs to be abandoned for more reciprocal relationships.

“It’s a mistake for cities to think of these universities as cash machines,” he says.

Grogan, the author of Comeback Cities, believes that better partnerships between universities, communities, and businesses can help Boston’s economy.

He hopes such a paradigm could replace the “extraction model,” in which cities simply take from universities.