Democratic presidential candidates Elizabeth Warren and Julián Castro have introduced comprehensive plans to tackle the $1.5 trillion student debt load, pushing the party beyond its focus on free college to the equally controversial idea of loan forgiveness.

The proposals share similarities and have some stark differences, but both operate with the understanding that investments in grant funding and public higher education would mitigate the need to borrow. The loan forgiveness plans reveal ideological differences in how the candidates perceive the burden of student debt.

So how do the plans compare? Let’s start with the basics.

Warren’s pitch: The senator from Massachusetts is proposing the cancellation of up to $50,000 in student debt for people with annual incomes of less than $100,000. For borrowers with higher incomes, debt forgiveness would decline by $1 for every $3 in income above $100,000. That means a person with a household income of $160,000 would get no more than $30,000 of their debt forgiven. The plan is capped for households pulling in more than $250,000, but would reach about 95 percent of Americans with outstanding education debt.

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Castro’s pitch: The former San Antonio mayor and housing secretary under President Barack Obama would offer partial loan forgiveness for people who receive public assistance benefits for three years within a five-year period. That would include borrowers enrolled in Supplemental Nutrition Assistance Program, Supplemental Security Income, Temporary Assistance for Needy Families or Medicaid.

The proposal did not go into detail about how forgiveness would be calculated, but Castro’s campaign said it would be determined by income, family circumstance and other factors still being fleshed out.

Who benefits: An array of think pieces and editorials have criticized Warren’s plan for delivering the largest share of relief to upper-middle-class families.

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Nearly 40 percent of all annual savings from the relief plan would go to borrowers making between $68,000 and $111,000 a year, according to an analysis by Adam Looney at the Brookings Institution, a think tank. And more than a quarter of the annual benefit would go to those earning even more money.

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Considering that people with higher incomes tend to have more education, it makes sense they would also have a disproportionate share of education debt, especially if they pursued advanced degrees. Thirty-four percent of all outstanding student debt is held by people in the top income quartile, while only 12 percent is held by people in the bottom quartile, according to the Urban Institute, a think tank.

Still, an analysis from experts at Arizona State University, Brandeis University and the University of Tennessee found that more than 85 percent of families in the bottom 40 percent of the income distribution would have their debt canceled under Warren’s proposal.

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The plan would wipe out student debt for about 90 percent of borrowers with an associate degree or less, but provide the same level of forgiveness to only a quarter of people with a professional degree or doctorate.

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“Warren’s plan is about broad-base cancellation of debt for a lot of people and would eliminate a lot of debt,” said Mark Huelsman, associate director of policy and research at Demos, a liberal think tank. “It comes from a belief system of whether student debt is good or bad.”

Castro’s plan received far less attention than Warren’s, so there is a dearth of analysis. Using data from the 2016 Survey of Consumer Finances, the Urban Institute estimates that about 16 percent of households with college debt receive benefits from public assistance programs. That number is likely to be higher because some people enrolled in the programs may not report their participation in the survey, according to the institute.

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Sawyer Hackett, a spokesman for the Castro campaign, said the policy is aimed at borrowers who owe less than $10,000 but account for two-thirds of student loan defaults. Often, these are borrowers who never completed their degree, but wound up with debt they have no ability to repay.

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“If you are someone who took out loans for college and are in need of food assistance . . . you are very likely to be delinquent or default on your loans,” Huelsman said. “Targeting loan forgiveness at those for whom student debt is really just not a good investment is smart. There are definitely some good equity implications in that.”

Tying debt forgiveness to public assistance is a distinctive feature of Castro’s plan, but not the only way the candidate seeks to disrupt federal loan repayment.

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Castro would require borrowers to pay nothing until their income exceeds 250 percent of the federal poverty line, or about $31,225 for an individual in 2019. Once borrowers reach the repayment threshold, their monthly bills would not exceed 10 percent of their qualified income — the amount left after that $31,225 is subtracted from adjusted gross income. After 20 years of payments, including months when the payment is zero, the borrower would have the remaining balance forgiven.

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“If you’re concerned about people who are really struggling, forgiveness gets you some of the way but maybe you also have to think about the way the repayment system works,” said Matthew Chingos, vice president of education data and policy at Urban Institute.

Castro’s proposal would essentially reform income-driven repayment in a way that would make the forgiveness portion more generous. Existing plans allow borrowers to pay nothing if they lack discretionary income, meaning they lack any earnings above 150 percent of the federal poverty line ($18,735 for a single person). By raising the repayment threshold to 250 percent, Castro’s plan could result in the federal government forgiving more debt.

Borrowers would also be spared the tax hit that accompanies existing income-driven plans because Castro would no longer treat loan balances that are forgiven as taxable income, and neither would Warren.

“Warren’s plan is much more detailed in the backward facing component of what do we do about the current debt,” Chingos said. “The Castro plan is more detailed in the forward looking piece.”

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