The measure carries high stakes. If a school has more than 30 percent of its borrowers default on a loan for three consecutive years, or if its default rate rises above 40 percent in a single year, the Education Department could revoke an institution’s eligibility to participate in federal student aid programs. That would be a death sentence for most institutions.

The cohort default rate was written into law in the early 1990s amid concerns that colleges, mainly for-profit higher education institutions, were saddling students with debt and degrees with little value. Many experts and higher education leaders now acknowledge that it has outlived its usefulness.

The measure is a target in this year’s stalled effort by Congress to reauthorize the Higher Education Act. Senator Lamar Alexander of Tennessee, the chairman of the Senate Education Committee, “believes Congress can improve the way colleges and universities are held accountable,” a spokeswoman said. A reauthorization proposal from Mr. Alexander’s committee would shift to using the percentage of students actually repaying loans to measure the value of an institution’s degrees.

According to the G.A.O. report, the Education Department estimated that it would not recover more than 20 percent, or $4 billion, of defaulted loans. Based on the number of students turning to forbearance, auditors suggested that number is sure to rise. The percentage of students turning to forbearance as a long-term option, about 18 months, has doubled since 2009.

Those students were more likely to default on their loans after three years, as their loans swelled with interest. They faced long-term consequences such as bad credit ratings and barriers to securing employment and housing. Other repayment plans, such as income-driven repayment plans that allow loan forgiveness after 25 years, could be more beneficial, auditors said.

But it is in colleges’ best interest to push forbearance, auditors found. The loans are considered “in repayment,” and when forbearance extends for 18 months, it is nearly impossible for a student to default within three years of graduation.

The report was requested by House Democrats who ordered an inquiry into what they called a “shadowy industry” of debt management firms and the lack of oversight at the Education Department that has allowed them to flourish.