Recent advances—everything from driverless cars to computers that can read human facial expressions—have pushed experts like Mr. Brynjolfsson to look anew at the changes automation will bring to the labor force as robots wiggle their way into higher reaches of the workplace. They wonder if automation technology is near a tipping point, when machines finally master traits that have kept human workers irreplaceable.

“It’s gotten easier to substitute machines for many kinds of labor. We should be able to have a lot more wealth with less labor,” Mr. Brynjolfsson said. “But it could happen that there are people who want to work but can’t.”