The relative importance of education and skills to the rise in U.S. economic inequality is a widely debated issue. One of the questions at the core of this debate is how much would an increase in the supply of college-educated workers reduce income inequality? Earlier this week, David Leonhardt of The New York Times wrote a column arguing policy should strongly promote college as a universal aspiration just as the United States promoted universal high school during the 20th century.

In making his argument, Leonhardt cites two studies that look at the impact of completing college on the earnings of students who just got into four-year degree institutions. For many states, such as Florida and Georgia, students who receive a score over a certain level are offered a spot in state universities. The two studies, one by Joshua Goodman of Harvard University with Michael Hurwitz and Jonathan Smith of the College Board, and the other by Seth Zimmerman (soon to be of the University of Chicago) looks at the impact of college by comparing students that just crossed the threshold to similar students who scored just under the threshold.

By comparing these students, the researchers can see the impact of a college degree on a so-called “marginal student.” The effects found in the research are quite large. In the paper by Zimmerman, the marginal student who does attend a college degree earns 22 percent more than a marginal student who doesn’t by their late 20s.

This sparks a very important question: Would this marginal effect be as large further down the income spectrum? In other words, these very well done papers estimate the effect at one specific margin, but don’t tell us what the return would be if we move further into the pool of non-four year graduates. There might be factors as to why these potential students might look at college and consider not attending.

Consider that the gains only accrue to students who actually finish their degree. In a response to Leonhardt’s piece, Jared Bernstein of the Center on Budget and Policy Priorities points out the importance of the “completion margin” when it comes to college promotion efforts. When Leonhardt and others talk about boosting college enrollment, they’re talking about getting more students into college. But there should be, as Bernstein points out, a focus on completion as well. For many students, the major problem is an inability to actually complete a four-year degree and could be a concern for potential entrants.

Closing this “completion margin” would be progressive in its effect. Completion rates are far higher for students coming from families higher up the income ladder. Students at the bottom are far more likely to drop out of college. Yet Goodman, Hurwitz, and Smith find that attending a four-year public school actually increased the completion rate for low-income students. So increasing completion isn’t just about fixing rates within schools, but also about shifting students to school with better rates.

At the same time, some of the advantages that college graduates have over other workers in the labor market might be diminishing. Take, for example, the consequences of recessions. Research by Joseph Altonji and Lisa Kahn of Yale University and Jamin Speer of the University of Memphis finds that college graduates are seeing larger negative effects from graduating into the last two recessions than in previous decades. These effects are still not as large as the consequences felt by other workers in the labor force. In other words, college-educated workers are starting to experience the labor market more like the majority of workers. At the same time, there’s evidence that the demand for cognitive skills, which college graduates are trained to provide, is on the decline. This shift could result in a decline in the college wage premium.

But there would still be a return. And the research from Altonji, Kahn, and Speer shows that the advantages appear to be declining, but they haven’t disappeared yet. Education does have a positive effect on incomes. And the research cited by Leonhardt is evidence that more young workers in the United States could be better off if they attend and complete college. Compared to other advanced economies, the United States has stagnated in terms of the share of the adult population that has a higher-education degree. Other advanced economies have done a better job at getting younger workers postsecondary education, according to data from the Organisation for Economic Co-operation and Development.

The question is just how large the return would be. Achieving higher levels of education is not the singular silver bullet to reducing income inequality. But it certainly should be part of the overall solution. Anyone who wants to response to high levels of income inequality and puts all or the majority of the burden of reduction of education will be sorely disappointed. Higher education should be promoted for many reasons. But as a solution to income inequality, it is just one (and possibly minor) tool in our toolbox.