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Billions of taxpayer dollars go to college students who never end up with a diploma in their hands, a new report found.

Pell grants — which are given to low-income families and, unlike student loans, do not need to be paid back — are the costliest education initiative in the nation. But little official data exists on whether they are a good investment, according to the education watchdog Hechinger Report.

Education Department Undersecretary Ted Mitchell last month lauded Pell grants as "one of the key levers that we have" to increase college completion rates. But an analysis published Monday by Hechinger revealed that Pell recipient graduation rates are often considerably lower than the overall graduation rate — even six years after a student starts college.

"It may be that given the high failure rate of the program, it isn't a very good return on public investment."

To make matters worse, the government keeps no official tally of what proportion of those who receive the grants end up getting degrees — despite the fact that money spent on Pell grants has quadrupled since 2000.

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"There's two scandals here. We have spent over the last decade one quarter of a trillion dollars on Pell grants, and if you ask the federal government what percentage of those kids graduate from college, they can't tell you," said Richard Vedder, director of the non-profit Center for College Affordability and Productivity. "The second scandal is as far as we can estimate, that graduation rate is embarrassingly low."

Vedder has done research on Pell recipient graduation rates, which concluded that only about 40 percent Pell recipients graduate, significantly lower than the national average of about 60 percent.

"It's embarrassing to the Department of Education," he said. "It's even more embarrassing to some of the schools involved."

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Taxpayers paid $31.4 billion on Pell grants in fiscal year 2015, and since 2000, they have poured $300 billion into them, Hechinger reported.

"It's not surprising that Pell grant students graduate at most schools at a lower rate than the overall student body. We know that low-income students are less likely to get a college degree than their peers," Sarah Butrymowicz, Hechinger's data editor and author of the report, told NBC News.

This could be in part because students from a lower socioeconomic status may come into college less academically prepared, she said.

In her analysis, which was based on 82 of the largest private and public schools, Butrymowicz found that the more Pell students there are at a given institution, the lower the chance that they will graduate.

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According to Education Secretary Arne Duncan, more than 2 million students receive Pell grants. The grants are considered so successful that in July, the Department of Education announced it was starting a pilot program that makes prisoners eligible for them.

For the 2015-2016 school year, the maximum Pell grant award amount is $5,775. Last year, Congress ordered the Department of Education to compile Pell grant graduation rates; the report, released last November, only looked at 70 percent of Pell recipients, and didn't break down it down by college, citing lack of data, according to the Hechinger story.

"There's a concern about putting a burden on colleges because anytime you ask them to report something, that is a burden. The big problem is they should be doing it already, but some of them aren't," Butrymowicz said.

The government needs to push for all the data, Vedder said.

"These high non-graduation rates make me wonder whether we should have that many people receiving Pell grants. It may be that given the high failure rate of the program, it isn't a very good return on public investment, and maybe we should redo the program and downsize it some," he said.

The program might be better off if money was spent on researching attributes of grant recipients who succeeded, or if officials eliminated participating schools with low Pell graduation rates. Or Pell recipients could be monitored during college.

"Maybe a student that is below a 2.0 average two years into a Pell grant should lose their Pell grant. At least we cut our losses earlier than we do now," he said.

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The grants, which typically go to students in families whose incomes hover around the poverty line, fill an important need by opening doors for kids who may otherwise not get to go to college, Butrymowicz said.

"Pell grants are a good, important program for us to have, and there's a reason why they exist," she said. "We just need to know more about how it's working."