For all the jobs that machines can now do — whether performing surgery, driving cars or serving food — they still lack one distinctly human trait. They have no social skills.

Yet skills like cooperation, empathy and flexibility have become increasingly vital in modern-day work. Occupations that require strong social skills have grown much more than others since 1980, according to new research. And the only occupations that have shown consistent wage growth since 2000 require both cognitive and social skills.

The findings help explain a mystery that has been puzzling economists: the slowdown in the growth even of high-skill jobs. The jobs hit hardest seem to be those that don’t require social skills, throughout the wage spectrum.

“As I’m speaking with you, I need to think about what’s going on in your head — ‘Is she bored? Am I giving her too much information?’ — and I have to adjust my behavior all the time,” said David Deming, associate professor of education and economics at Harvard University and author of a new study. “That’s a really hard thing to program, so it’s growing as a share of jobs.”