The share of people not making payments on their federal student loans within three years of leaving college is at the lowest level in seven years, the Education Department said Wednesday.

About 10.1 percent of borrowers who began repayment Oct. 1, 2015, defaulted by Sept. 30, 2018, a 6.5 percent decline from the prior cycle. More than 4.5 million people from 6,130 schools began repaying their federal student loans in October 2015. Of those, 458,687 defaulted.

“We are glad to see that the cohort default rate continues to decline,” Angela Morabito, a spokeswoman for the department, said in an email. “The Department is committed to ensuring borrowers are equipped with the information, tools, and resources they need to make informed decisions.”

Cohort default rates, as the three-year metric is known, are used to determine whether colleges are eligible to receive federal student aid. The Education Department can levy sanctions on schools with default rates of about 30 percent for three consecutive years, or 40 percent for a year.

This year, 13 for-profit schools, one public college and one private university hit those thresholds. The colleges, most of which are cosmetology or barber schools, must all appeal to the department if they want students to be able to take out federal loans and receive federal grants.

Bennett Career Institute in the District is the only school within the Washington area under threat of losing access to the federal student aid program. According to the Education Department, colleges in the District had borrower default rates of 8.2 percent; Maryland, 9.3 percent; and Virginia, 9.8 percent.

Across the country, public colleges and universities, which educate a majority of students, recorded the most significant change as default rates fell from 10.3 percent to 9.6 percent. At private nonprofit colleges, the default rate slid from 7.1 percent to 6.6 percent. Defaults at for-profit colleges were down from 15.6 percent to 15.2 percent, but the sector still has the highest three-year rate.

The number of borrowers entering repayment who attended community colleges or for-profit institutions has significantly declined over the years, which experts say reflects a decrease in enrollment.

The design and use of cohort default rates have long been a point of contention among higher education experts. Some say schools can manipulate the metric by encouraging students suffering financial hardship to postpone payments through forbearance or deferment. A 2015 report from the Education Department said cohort default rates were “susceptible to gaming behavior by institutions,” yet the agency never took action.

“These numbers are at best an artificial picture,” said Ben Miller, senior director for postsecondary education at the Center for American Progress, a liberal think tank. “Many schools hire outside companies or employ individuals who will engage in tactics that will keep borrowers out of default while not necessarily helping them with their long-term repayment.”

There are about 1 million people defaulting every year, though half as many show up in the cohort default rate, Miller said. The numbers only capture a slice of total defaults on federal student loans at a given time. A more comprehensive look at the federal government’s portfolio reveals that millions of people had not made a payment on about $177.8 billion in federal student loans for at least nine months as of March, a nearly 10 percent increase over the same period a year earlier.

Some critics of the cohort default rate say the Education Department should track the share of students at an institution who are able to pay down their loans, a measure that would be more difficult for schools to manipulate. If a student’s loan balance fails to decline after a period of entering repayment, it would count against the college.

But with so many people enrolled in income-driven repayment plans, that could become complicated. Because monthly payments in those plans are tied to earnings, some borrowers may have high balances for years until they begin making more money.