The information sector, which includes Internet, data processing, and telecommunications firms, has gained 3,000 jobs from its prerecession peak. And professional and business services, which include many research, scientific, and information technology positions, have 11,800 more jobs than before the recession.

In any economy undergoing such labor market turmoil and shifts, said Northeastern University economist Alan Clayton-Matthews, it is simply unrealistic to expect tens of thousands of people trained for one occupation to suddenly retrain for an entirely different one.

“You can’t be roofing houses one day and breaking down molecules in a laboratory the next,” he said. “It’s not an easy switch for people.”