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There is a growing acknowledgement that inequality is one of the most pressing national issues. President Obama certainly feels that way. In his State of the Union Speech this past January, Obama focused his speech around the issue, framing the debate as a question about the future of America.

"Will we accept an economy where only a few of us do spectacularly well?" the President asked. "Or will we commit ourselves to an economy that generates rising incomes and chances for everyone who makes the effort?"

Obama made no secret of his own position, or that education was his preferred method of closing the gap between rich and poor. His address centered around a number of policies that would increase college access for lower-income Americans, including a $60 billion proposal to make community college free for all.

But is education really the solution to inequality that it's often presented as? A new paper from the Hamilton Project, co-authored by former Treasury Secretary and former Harvard University president Lawrence Summers, argues that the answer is no. Instead, the researchers assert, policymakers tend to conflate two separate issues: helping lower-income Americans become more financially secure and decreasing inequality overall.

Increased educational attainment across lower-income brackets would indeed result in higher income and more economic security for vulnerable groups, the paper finds. But so much income is concentrated among America's richest citizens that a modest increase in earnings at the bottom end of the income distribution will barely make a dent in overall inequality.

To reach this conclusion, Summers and his co-authors—Hamilton Project director Melissa Kearney and visiting fellow Brad Hershbein—created a simulation in which one out of every ten American men between the ages of 25 and 64 without a bachelor's degree suddenly graduated from college. (The simulation was restricted to men because less-skilled males have seen particularly steep drops in employment, earnings, and college attainment.)

"To be clear, this would be a tremendous accomplishment," the researchers note. Creating this many new graduates would be "only slightly less than the observed increase in the college share over the entire 34-year period of 1979 to 2013."

The authors then randomly assigned each of the newly credentialed Americans an income based on the earnings of actual graduates, and adjusted for the reduced premium a college degree would offer if more workers obtained one. The results show income in the bottom 25th percentile would increase from $6,100 to $8,720, and median income would increase from $34,000 to $37,060, while those with higher incomes were hardly affected.

Despite this significant surge in the earnings—the above increase would be "enough to nearly erase the decline in median earnings between 1979 and 2013, and cut the decline at the 25th percentile by one-third," according to the paper—inequality barely budged. Under the simulation's conditions, the Gini coefficient, a metric for measuring income inequality, declined from 0.57 to 0.55. For comparison, the Gini coefficient for the U.S. in 1979 was 0.43.

"Overall earnings inequality would hardly change—and would not come close to 1979 levels—if the share of working-age men with a college degree were to increase by even a sizable margin," add the authors.

Why does more education attainment have such a small effect? The researchers find that decreasing the portion of the population without a college degree primarily helps those in the bottom 25% of earnings, raising their wages relative to higher income groups. Meanwhile, this scenario would do little to decrease inequality in the top half of the earnings spectrum, where most of the nation's income disparity is contained.

The authors are clear to note that better access to higher education, whether it reduces inequality or not, is still an important goal. "Our nation should aim to increase the educational attainment and, more generally, the skills of less-educated and lower-income individuals because in the long-run, this is almost surely the most effective and direct way to increase their economic security, reduce poverty, and expand upward mobility," the paper concludes.

However, the group notes, fixing inequality and growing the salaries of the less-educated are not the same issue, and won't be solved by the same policies. "These are distinct, albeit interrelated challenges," the researchers explain, "and the public discourse would be much improved if it stopped conflating them."