There's now broad agreement among politicians that inequality of income is a serious problem in the United States, but there's little consensus on what to do about it.

A simple thought experiment may rule out one potential solution: Helping more people go to college.

Getting a college degree is valuable, according to calculations by a group of economists including former Treasury Secretary Larry Summers. If more people went to college, they'd be much better off. It's just hard to imagine how helping more high school graduates to earn college degrees could substantially undo the massive increase in inequality of the past several decades, which is largely a result of skyrocketing earnings among the very rich. Indeed, the wealthiest 1 percent of Americans now claim nearly as large a share of national income as they did on the eve of the Great Depression.

"I am all for improving education," Summers told Wonkblog earlier this month. "But to suggest that improving education is the solution to inequality is, I think, an evasion."

Summers and his collaborators, the Upjohn Institute's Brad Hershbein and Melissa S. Kearney of the University of Maryland, calculated what would happen if they could wave their magic wands and give a college education to about 6.8 million American men who don't already have one. Relatively speaking, that's an enormous increase -- about the same proportion as the increase in the overall share of the population with a college degree since 1979.

Everyone would be better off, not just those lucky men. Annual earnings at the first quartile -- those Americans making less than three quarters of the rest of the population -- would increase by about 43 percent. Median earnings -- what the typical worker makes -- would increase by 9 percent, or about $3,020 a year.

These improvements are small compared to the overall level of inequality in the economy as a whole, however. A common measure of the disparity between rich and poor called the Gini coefficient would only decline slightly, from 0.57 in 2013 to 0.55. (The figure was 0.43 in 1979.)

You might think that adding millions of college degrees would dramatically reshape the U.S. economy. Yet earnings for people with college degrees have declined since the turn of the millennium.

Federal Reserve Bank of New York.

Meanwhile, salaries for highly compensated workers, particularly corporate executives, have been rising. Given these larger trends, even heroic efforts to improve educational attainment can only achieve so much.

And it's important to note that Hershbein, Kearney and Summers don't try to provide a clear explanation of how to get so many people through college.

Talking about levels of income in the abstract without considering specific policies can sometimes lead commentators astray. David Brooks made this mistake in a recent column on Hillary Rodham Clinton, the former secretary of state and a likely Democratic presidential candidate. Citing economist David Autor, Brooks argued that education was more important to inequality than the overall concentration of wealth:

If we could magically confiscate and redistribute the above-average income gains that have gone to the top 1 percent since 1979, that would produce $7,000 more per household per year for the bottom 99 percent. But if we could close the gap so that high-school-educated people had the skills of college-educated people, that would increase household income by $28,000 per year.

The problem, of course, is that closing the gap between those with college degrees and high school diplomas would take just as much magic. If it were possible, it would probably require the kind of redistributive policies that would reduce overall inequality anyway. Expanding Pell grants would be one approach. Another would be redesigning tax credits for college savings so they encourage poor parents to send their children to college, instead of benefiting middle-class and wealthier families who likely would send their children to college anyway.

That's an idea the Obama administration proposed and then quickly abandoned earlier this year in response to intense criticism. The episode just goes to show that the kind of redistributive policies that might have a chance of helping more people go to college are going to be politically sensitive, whether politicians describe them as an education reform or addressing inequality of income.

Hershbein, Kearney and Summers argue that making sure the poor and less educated have opportunities to find work that pays well is a worthy goal, but that people shouldn't necessarily conflate it with the broader aim of a more equitable distribution of wealth.