The White House last week announced a new proposal that would make two years of community college available free of charge to students who meet a series of requirements. The new plan is one of the several President Obama will discuss in his State of the Union address next week. In pitching the plan, the president cites higher education as vital for the future success of U.S. workers and the overall economy. And given that higher education is often cited as a key tool to reduce economic inequality, the new community college free-tuition proposal seems likely to reduce record levels of inequality.

But does this last claim hold up? Is higher education still that important? Research increasingly shows that boosting education levels might not live up to the hype.

In setting the stage for Obama’s new proposal at The Upshot, economist Justin Wolfers compares the expansion of free higher education to the “high school movement” of the early 20th century. This movement dramatically increased the supply of educated workers in the U.S. economy and helped give it a boost. The increased access to college after World War II also boosted the education level of the workforce. But Wolfers notes that since the late 1970s, the growth in the supply of educated workers has stalled.

The Obama community college proposals could help reverse this trend. The decades-long stagnation in the supply of highly educated workers is cited by some economists as a major cause of rising inequality. They argue that skill-biased technological change—a change in technology that resulted in an increased demand for skilled workers—caused the demand for skilled workers to grow faster than the supply of workers to fill those jobs. The resulting large wage premium for college educated workers increased income inequality.

Intuitively, then, increasing the supply of educated workers should reduce inequality as it would increase wages among a broader supply of more educated workers. But that assumes the demand for educated workers will continue to rise. Problem is, recent research finds that the demand for skilled labor appears to be on the decline.

Research by economists Paul Beaudry and David A. Green at the University of British Columbia and Benjamin M. Sand at York University finds that the demand for skills and cognitive tasks has been on the decline since 2000. David Autor of the Massachusetts Institute of Technology, one of the key developers of the theory of skill-biased technological change, finds a similar trend. In previous research, he found that job growth across the skill spectrum was U-shaped—lots of jobs at the low- and high-end. But in a paper presented at the Federal Reserve’s economic policy symposium in Jackson Hole, Wyoming this past August, Autor finds the pattern in the 2000s was more of a downward ramp: lots of growth at the bottom and not much elsewhere.

If the demand for skills is on the decline then the wage premium for college educated workers and income inequality should decline. This trend would accelerate if there were an increase in the supply of college-educated workers at the college level.  But that reduction in inequality would result in declining wages for better educated workers. Not exactly the rising tide that policymakers and economists often envision when trumpeting the benefits of education. Either skill-biased technological change story only held true for a certain time or the hypothesis was flawed to begin at its conception.

Now this is not to say that education is irrelevant or undesirable. A more educated workforce is likely to be more productive, leading to faster economic growth. And, securing a college education has other economic and non-economic benefits. For example, a college degree may act as a shield against dropping out of the labor force as the economy becomes a “cruel game of musical chairs.” But the sad reality is that higher levels of college education, once thought of as the best tool to reduce inequality, may no longer live up to the hype.