These executives’ frustrations are reflected in the results of a new study by McKinsey & Co. that shows that only 42% of employers believe new graduates in the workforce are adequately prepared by their colleges or other pre-employment training programs.

Recent graduates know they’re ill trained: The same study finds that 45% of youth think they’re prepared for their jobs.

Schools and training centers, however, have a much rosier view. Nearly three-quarters of education providers tell McKinsey their graduates are ready to roll. “We call it parallel universes,” study co-author Diana Farrell says of the disparity in perception among employers, students, and schools.

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And the perception gap is global. Farrell and her team surveyed people in nine countries (and looked at programs in 25 nations) and found huge differences between how employers and schools view graduates’ skills. The chasm was biggest in Germany, where 83% of educators think students are prepared and only 43% of employers are happy with the quality of incoming young hires.

Farrell notes that colleges and universities tout the successes of their incoming students–test scores, academic achievement, acceptance rates, and the like–but rarely spend the same amount of energy sharing data about job placement and success rates of graduates. Where, she asks, is the ranking of  colleges (a la the US News & World Report Best Colleges lists) based on outcomes? “We think focusing on what’s happening to kids on the way out is a big opportunity.”

She and the authors of the report, “Education to Employment, Designing a System that Works,” call for countries to create the role of “integrator”–a government appointee or someone designated by a public-private partnership, to make sure employers, educators, and students are getting what they need out of the system. “When someone is looking at the data from all three of these angles, they  will see gaps and can drive change.”

Executives, consultants and, yes, educators, have been calling for reforms to make education more employer friendly. That may sound unappealing to fans (and beneficiaries) of liberal arts studies or less structured programs, but schools may face little choice: The world could face a labor shortage of some 40 million high-skills workers in 2030, according to a different McKinsey study.

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The McKinsey study doesn’t single out educators. Employers, too, have a role to play in ensuring employee preparedness. About a third of employers say they are getting the workers they need, in part because they are engaged in the training process, communicating directly with schools and students to develop course work or to the let institutions know what skills new hires need.

So to all those executives who fret about worker shortages and lack of qualified labor, perhaps part of the solution lies in proactively working with schools and training programs to make sure students are graduating with the right set of skills.