The Pew Research Center recently released a report comparing the wealth of young households with and without student debt. Unsurprisingly, young student debtor households have less wealth than similar households without student debt.

Such facts are often mobilized by those who argue that policies that reduce student debt would close the wealth gap. This is not the case.

Before explaining why, it's useful to go over the Pew statistics. College-educated households where the adults are under the age of 40, and have student debt, have a median net worth of $8,700. The same households without student debt have a median net worth of $64,700, which is $56,000 more. The households with student debt owed an average of $19,000, while those without student debt obviously carried none. Both types of households have the same income, which in 2010 was around $58,000.

One very quick way to get confused by these numbers is to compare the $19,000 student debt to the $56,000 wealth gap between these households. By noting that the wealth gap is bigger than the student debt amount, one can wrongly conclude that the wealth gap is not solely explained by the student debt and that therefore student debt is dragging down wealth in other ways as well. The problem with this conclusion is that the $19,000 figure refers to the student debt currently carried by these households, not the amount they had to begin with.

The initial debt amount of such households was almost certainly much higher than $19,000. If it was initially $56,000 higher than households that currently lack debt (a figure that is more plausible when you note that households can have two student debtors in them), then the student debt would explain the entire wealth gap. In fact, due to interest, the initial debt doesn't even need to have been that much higher to explain the full gap.

But details aside, it might seem obvious that getting rid of student debt would help close the gap. For instance, we could publicly fund college in such a way that nobody graduates burdened by student debt, which would ensure that the wealth variation between debtors and non-debtors doesn't exist.

But such a shallow analysis fails to grasp the deeper cause of the differential plight of these households: intergenerational wealth transfers. When parents pay for their kids' college education, and thereby allow them to graduate without debt, they are transferring wealth to them. Parents who do not have enough money cannot transfer as much wealth, which is why their kids start out less wealthy (i.e. in student debt).

Crucially, making college free does not alter the fact that wealthy parents have the ability to transfer more wealth to their kids than non-wealthy parents. Relieved from paying tuition, the wealthy parents would presumably transfer that wealth to their kids in other ways, recreating the very same wealth gap free college was meant to solve. For instance, a wealthy parent could take the $90,000 they'd save as a result of making the cost of attending a four-year public school totally free and plow it into a down payment on their kid's first home. Since less wealthy parents could not follow suit, the wealth gap — now represented in the form of home equity differences instead of student debt differences — would persist.

The only way to use college tuition policies to reduce a wealth gap caused by intergenerational wealth transfers is to charge rich families more money to go to college than non-rich families. Because such a policy drains more wealth from richer families, it cuts down on the amount of extra wealth they can transfer to their kids. But we already do precisely this. In 2011, the richest families paid about twice as much as the poorest families to attend four-year public universities.

Moving from our current price discrimination regime to a free college regime would likely make the wealth gap between college graduates worse. It would replace a system that operates in a way that mitigates intergenerational wealth transfer differences with one that does not mitigate such differences at all. There may be good reasons to make college free, but closing the wealth gap between households with and without student debt is not one of them.