Earnings inequality in America has increased since 1979 — that much we know. But why and what to do about it is murky — in part because we’re not all talking about the same group of people when we talk about inequality.

“Many of us are talking past each other in public,” said Melissa Kearney, a senior fellow at the Brookings Institution and professor at the University of Maryland. She’s also the director of the Hamilton Project, which just released a new paper cutting through some of inequality’s monolithism by making an important distinction between what’s going on above and below the median wage distribution.

There are really two separate, but often conflated, issues at play in America’s inequality story. The first is that Americans at the bottom end of the distribution face poor employment prospects and don’t earn enough money. That’s different from the second issue of overall inequality, which is largely driven by outsized earnings at the top of the distribution.

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The takeaway? Increased educational attainment can help address the first problem, but not the second.

Using Current Population Survey data, Kearney, along with Hamilton co-author Brad Hershbein and former Treasury Secretary Larry Summers, simulated what the earnings distribution would look like if one out of every 10 men (between the ages of 25-64) who did not have a bachelor’s degree got one. In other words, they inflated the share of the population with a bachelor’s degree from about 32 percent to 39 percent, then looked at how that affects inequality. (They justify their exclusion of women, the predominant low-wage workers, by pointing to low-skilled men’s sharp decreases in employment and college attendance in the recent past.)

The first take-away from their research is that higher education is still worth it. The college wage premium may have stagnated, Kearney said, but if men without bachelor’s degrees got them, their average earnings and employment prospects would increase. If college attainment elevated those workers, inequality in the bottom half of the earnings distribution would fall too. (Remember, though, this is a data simulation; it doesn’t take into account whether low-skilled men have the money or institutional support to complete a four-year degree in reality.)

It’s easy to count that first conclusion as validation of skills-based-technological change. According to this structural interpretation of the labor market, Americans are unemployed and low-wage workers don’t earn enough because they don’t have the skills employers demand. (That’s different from plain-old skills-mismatch, which is a more cyclical problem.) If American workers can’t keep up with technology, the obvious remedy would be to bring them up to speed.

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That perspective was on full display at a February Hamilton Project forum and related paper — a kind of antecedent to this paper — called “The Future of Work in the Age of the Machine.” (Read our coverage of the event.) In today’s “second machine age,” robots not only replace manual workers; they’re coming after white-collar workers, too, which would seem to increase the education premium.

But the authors’ second conclusion is far more depressing than knowing that a bunch of automated giants are after your job: increasing educational attainment really doesn’t reduce overall earnings inequality.

Actually, no one thought it would, Kearney said. That’s because high overall inequality is a reflection of what’s going on at the top of the earnings distribution. Fragmentations between the 90th and 99th percentiles, for example, have nothing to do with differences in educational attainment, so boosting the share of the population receiving bachelor’s degrees is a moot point.

The chart below shows the Gini and Theil coefficients, where 0 represents the most equitable distribution of earnings and 1 represents the most unequal. Note that the simulation (in both indices) doesn’t do much to return inequality to its 1979 levels.

So improving education can help address one inequality problem, but certainly not all of the problem. In fact, at Hamilton’s February forum, Summers said — now somewhat famously — that skills training is “an evasion” of the problem. In Summers’ view, what’s in short supply today is work, not workers.

Likewise, this recovery’s lousy productivity growth has convinced some economists, like the Center for Economic and Policy Research’s Dean Baker, that robots aren’t taking our jobs the way we’ve heard they are, calling into question the cry for more skills and training as a blanket solution.

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It’s worth noting, though, that training could mean many different things. Encouraging low-wage workers to complete vocational apprenticeships, for example, could have a different effect from pushing them to take on debt to study for a four-year degree.

But regardless, that’s still the lower end of the earnings distribution we’re talking about. It will take stronger policy prescriptions than higher educational attainment, the authors write, to tackle the changes at the upper end of the earnings scale.

Just what it’ll take though, is a matter of debate depending on why you believe earnings accrue toward the top. “It’s not immediately obvious, even to me,” what’s going on, Kearney said. Get ready for a whole lot more talking past each other.