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One of the study’s coauthors, Boston Fed senior economist Paul S. Willen, said the government would be better off giving the money directly to struggling borrowers to help them with their payments, rather than to lenders that are averse to working out the troubled loans.

“Loan modification is not profitable for lenders,’’ Willen said. “If it were profitable, they would go out and hire staff.’’

US Representative Barney Frank, head of the House Financial Services Committee, said the study results may provide answers about why so few struggling homeowners have been able to get help.

Frank, a Newton Democrat, said he is holding a hearing Thursday on his proposal to provide government loans to homeowners who have lost their jobs and can’t qualify for loan modifications and other help because they don’t have income.

“The problem is worse than we thought,’’ Frank said. “The failure to do these modifications means the whole situation stays bad longer.’’

The Fed’s study found that only 3 percent of seriously delinquent borrowers – those more than 60 days behind – had their loans modified to lower monthly payments; about 5.5 percent received loan modifications that did not result in lower payments.

The study focused on 665,410 loans that were originated between 2005 and 2007 and subsequently became seriously delinquent. It also followed about 150,000 borrowers for six months after they received help, through the end of 2008.

The lenders may have compelling reasons not to find new borrowers to help, according to the study. For example, up to 45 percent of borrowers who did receive some kind of help on their loans ended up in arrears again, the study found. Conversely, about 30 percent of delinquent borrowers are able to fix their problems without help from their lenders.

“A lot of people you give assistance to would default either way or won’t default either way,’’ Willen said. “They are trying to maximize profits, and at this point maximizing profits does not mean modifying loans.’’

Officials from Hope Now, the private-sector alliance of mortgage servicers and investors, were unavailable for comment yesterday.

US Treasury officials declined to comment on the Fed study, but noted in a statement that more than 240,000 homeowners have received loan modifications this year under the president’s program. Moreover, federal regulators said the pace of loan modifications has been increasing steadily since last year. CLICK THE LINK BELOW FOR THE CONTINUATION OF THIS STORY AT THE BOSTON GLOBE.