For years, Boys Town sent as many as half of its graduating class — usually 90 to 100 students total — into the military, which provided needed structure and career opportunities. A few years ago, those numbers plummeted, the result of a smaller, increasingly selective military. Last year, just one student made the cut. In 2013, zero.

In his search for solutions, Jeff Peterson, the senior director of home campus operations, found that many high schools were reorienting toward producing skilled workers.

The public school system in nearby Grand Island built the $5 million Career Pathways Institute, an old warehouse now outfitted for instruction in welding, general construction, information technology and manufacturing. It was started after complaints about a lack of skilled labor for farm machinery manufacturer Case IH and other businesses.

Mr. Peterson heard similar needs. One contractor said he was “going nuts” because his workers could not identify a square; meanwhile, skilled laborers could earn a premium. “I talked to our roofing guy, talked to our construction guys. We met with union folks and trade groups,” he said. “They said the same thing: ‘If a kid can frame, he’ll start out at $3 or $4 higher than a general laborer.’”

Mr. Peterson’s discoveries follow the findings of a 2011 report by the Harvard Graduate School of Education recommending technical training as a way to solve a growing crisis of unemployed or underemployed young people.