A common refrain among corporate and political leaders is that the U.S. needs more engineers, scientists and other workers with the kind of specialized expertise needed to boost economic growth. And that assessment plays a part in a range of public policy debates, from how to change the nation's immigration laws to how to energize job-creation.

But new federal data suggest that idea is largely a myth, and it raises questions for students who are planning their careers. Roughly three-quarters of people who have a bachelor's degree in science, technology, engineering and math -- or so-called STEM fields -- aren't working in those professions, the U.S. Census Bureau said Thursday.

Citing statistics from its most recent American Community Survey, the bureau found that only about half of engineering, computer, math and statistics majors in the U.S. had jobs in their chosen field. Science grads fared even worse: Just 26 percent of physical science majors and 15 percent of those with a diploma in biology, environmental studies or agriculture were in a STEM-related occupation.

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It's worth noting that unemployment among people with STEM degrees is considerably lower than for the general population of workers. As of 2012 (the latest year with available data), only 3.6 percent of college graduates between the ages of 25 and 64 were without a job, according to the Census Bureau, compared with 6.1 percent for the broader U.S. workforce.

Yet those grads aren't necessarily working in a STEM job, notes Liana Christin Landivar, a sociologist in the Census Bureau's industry and occupation statistics branch.

Hal Salzman, a professor of planning and public policy at Rutgers University, has calculated that twice as many STEM students graduate every year as are able to find jobs in their field. Some half a million grads with these degrees emerge from U.S. colleges and universities annually, and they must compete for roughly 180,000 job openings, he said in a 2013 article.

"Engineering has the highest rate at which graduates move into STEM occupations, but even here the supply is over 50 percent higher than the demand," he wrote. "[Information technology], the industry most vocal about its inability to find enough workers, hires only two-thirds of each year's graduating class of bachelor's degree computer scientists."

By comparison, at least three-quarters of college graduates in health fields find work in those disciplines.

The Chronicle of Higher Education, citing a National Academies report, concluded last year that an excess of university Ph.D. candidates has led to a glut of life scientists, lab workers and physical scientists.

Michael Teitelbaum, a senior research associate at Harvard Law School and former vice president of the Sloan Foundation, notes that over the last half-century U.S. policymakers have repeatedly sounded the alarm about a purported shortage of scientific talent.

After the Soviet Union launched the world's first man-made satellite, Sputnik, into space in 1957, the U.S. Defense Department and Atomic Energy Commission led efforts to produce more physicists. In 1983, under President Ronald Reagan, a blue-ribbon commission produced the report "A Nation at Risk," which warned of a "rising tide of mediocrity" in education and claimed that the country was falling behind in math, science and other areas. In more recent decades, concerns have also been raised about a shortfall in cancer researchers and in engineers.

After most of these episodes, employment in these fields temporarily boomed, only for jobs to eventually dry up.

"On the research side, the U.S. is still dominant," said Teitelbaum, author of a new book that explores whether the U.S. is falling behind other nations in producing scientists and engineers, in a recent presentation. "There's no evidence that it has fallen behind international competitors in science and engineering."

The broader picture is more complex, he added. Scientists and engineers at some degree levels find themselves strongly in demand, while there's a surfeit in other areas.