Giordino, who now works for Mutual of Omaha’s reverse mortgage division, described her role as “head cheerleader” for positive reverse mortgages research. Gregg Smith, CEO of One Reverse Mortgage, said the group is promoting “true academic research,” including work by professors with no industry ties.

In January, the American College cut its ties with the task force because the school, as a nonprofit institution, wasn’t comfortable being affiliated with an organization endorsing products, according to Vice President James N. Katsaounis. “A proper retirement portfolio is one that is well-balanced and diversified, which may or may not include reverse mortgages,” he said.

Mayer, the Columbia professor and reverse mortgage company CEO, said many older consumers could benefit from the loans because they can never owe more than their house is worth even if real estate prices plunge.

A former economist at the Federal Reserve of Boston with a Ph.D. from the Massachusetts Institute of Technology, Mayer joined the Columbia faculty in 2004 and currently co-­directs Columbia’s Paul Milstein Center for Real Estate. He wrote his first paper on reverse mortgages in 1994, when the FHA product was five years old.

In 2012, Mayer co-founded Longbridge, based in Mahwah, New Jersey, and in 2013 became CEO. He’s on the board of the National Reverse Mortgage Lenders Association. He said his company, which services 10,000 loans, hasn’t had a single completed foreclosure because of failure to pay property taxes or insurance.

While many colleges let professors engage in outside business activities, Gerald Epstein, a University of Massachusetts economics professor who’s studied academic conflicts of interest, said Columbia may need to scrutinize Mayer’s arrangement closely.

“They really should be careful when people have this kind of dual loyalty,” he said.

Columbia said it monitors Mayer’s employment as CEO of the mortgage company to ensure compliance with its policies. “Professor Mayer has demonstrated a commitment to openness and transparency by disclosing outside affiliations,” said Chris Cashman, a spokesman for the business school. Mayer has a “special appointment,” which reduces his salary and teaching load and also caps his hours at Longbridge, Cashman said.

Likewise, Boston College said it reviewed Professor Munnell’s investment in Mayer’s company, on whose board she served from 2012 through 2014. Munnell said another round of investors in 2016 bought out her $150,000 stake in Longbridge for an additional $4,000 in interest.

She said she now prefers another approach: States allowing seniors to defer property tax payments. The advantages include “no fee, no paperwork and no salespeople,” she said. In one way, she’s glad she exited her reverse mortgage investments.