You misspelled "the taxpayers". Student loans are almost exclusively federal affairs these days.

As this WSJ piece from December on the matter of the GAO estimating $108 billion in writedowns (probably a low figure, as they admit their accounting on the matter is crap) puts it:

"To help pay for ObamaCare, Democrats simultaneously federalized the student loan market and projected fictitious savings, all while adding more than $1.2 trillion to the federal balance sheet... then cited the government “savings” to peddle the fallacy that the feds make money off student loans—a pretext they then used to sweeten debt forgiveness plans that have helped keep default rates artificially low."

http://www.wsj.com/articles/obamas-giant-student-loan-con-14...

Things may be changing, but the recovery rates on defaulted student loans used to be 120%, meaning that the government was collecting an additional 20¢ on each dollar in default. This is in comparison to programs like SBA that have recovery rates around 50%. When you factor in an already high interest rate, this state of affairs is profitable.

Do you have a source for that? A 120% recovery on defaulted loans seems insane.

I'm not sure what year I read that, or what article it was in, but after some cursory searching, in 2014, the recovery rate was 103-111%. Recovery rates are much higher in student loans because they cannot be discharged. So 120% is certainly not out of the question some years.

https://www2.ed.gov/about/overview/budget/budget14/justifica...

In FY 2016: 100-112% https://www2.ed.gov/about/overview/budget/budget16/justifica...