Washington — Colleges that have complained that the U.S. Department of Education has been too strict in denying PLUS loans to their students now have a little better picture of the reason for those denials. And policy advocates who say the rules still allow overborrowing by students and families who may not be able to repay the loans may have some new talking points, too.

Data released by the department on Wednesday show that nearly 70 percent of all PLUS-loan applications initially rejected in the past two years were denied on the grounds that the borrower had other debts in collection or had settled a debt for less than the full amount. As result, rates of denial increased from the 2011-12 academic year by 13 to 15 percentage points in the following two years, depending on students’ sectors.

For example, in 2011-12, before the stiffer credit checks went into effect, the department denied 29 percent of PLUS-loan applications at public colleges, 23 percent at private colleges, and 35 percent at for-profit colleges. The next year, the denial rates for those sectors were 44 percent, 36 percent, and 49 percent, respectively. Some of the rejected loans were later approved through appeals.

The data “really reinforce that this is a big issue that really needs to be addressed,” said Cheryl L. Smith, senior vice president for public policy and government affairs at the United Negro College Fund.

The data were released just two days before federal negotiators are scheduled to meet to consider possible changes in the program. When they met for the first time, in February, several negotiators voiced annoyance at being asked to discuss proposals without adequate data on the PLUS-loan programs, which include loans for families of undergraduates and loans for graduate students.

Historically black colleges and other institutions particularly hard hit after the department started using stricter credit standards in 2011 said the new standards had been imposed with little advance notice and were too indiscriminate, depriving families of a last-chance option to finance their children’s education.

A report released this week by UNCF says denial rates for families of students at its member colleges were higher than the department’s averages, affecting two out of three loan applications. The report also says that the department’s efforts to streamline the loan-appeals process have “provided only marginal relief.”

Even with that assistance, the report says, the number of PLUS-loan borrowers at all historically black colleges and universities is still 32 percent lower than it was two years ago.

The data the department released also give a sense of the size and scope of the two loan programs.

The average Parent PLUS loan balance (including interest owed) for students at public four-year colleges is $19,941, and at private four-year colleges it is $27,443. Together those institutions account for 76 percent of some three million Parent PLUS borrowers and 85 percent of the more than $62-billion in Parent PLUS loan balances outstanding. Another 21 percent of borrowers and nearly 14 percent of the debt outstanding are associated with families of students at two-year and four-year for-profit colleges.

The average outstanding loan balance (including interest owed) on PLUS loans for graduate students at public four-year colleges is $27,021, and $47,023 for students at private colleges. Private colleges account for 57 percent of total Grad PLUS borrowers and nearly 65 percent of the loan balances outstanding.

PLUS loans for graduate students are used less frequently at for-profit colleges; those institutions accounted for less than 6 percent of Grad PLUS borrowers and less than 6 percent of the total loan balances outstanding. The average Grad PLUS loan balance at for-profit colleges is $40,556.

The department estimates about 912,000 borrowers now hold Grad PLUS loans, but notes that, as with the count of Parent PLUS borrowers, the total includes borrowers with more than one loan. According to its data, there are nearly six million Parent PLUS loans outstanding and more than 2.2 million Grad PLUS loans outstanding.