Amid all the fear of robots taking human jobs, skeptical voices have been asking: Where are these robots? Machine-learning systems — commonly marketed as artificial intelligence, but really closer to fancy statistical algorithms — are beating humans at games, improving search algorithms and transforming industry in countless small ways. But so far, the machine-learning boom hasn't done anything to reverse the slump in productivity growth.

Now, it's possible that productivity gains are just being mismeasured. But the slowdown seems to be worldwide, including in developing countries. That's inconsistent with the theories about sweeping robotization. As economist Larry Summers has pointed out, a robot boom would raise both productivity and business investment, as companies rushed to install the new machine-learning systems. That hasn't happened.

In a new paper, economists Erik Brynjolfsson, Daniel Rock and Chad Syverson have an answer: Wait. It's coming.