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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.

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Often, when a very versatile new technology comes along, it takes a while before businesses figure out how to use it effectively. Electricity, as economist Paul David has documented, is a classic example. Simply adding electric power to factories made them a bit better, but the real gains came when companies figured out that changing the configuration of factories would allow electricity to dramatically speed production.

Machine learning, Mr. Brynjolfsson et al. say, will be much the same. Because it's such a general-purpose technology, companies will eventually find whole new ways of doing business that are built around it. On the production side, they'll move beyond obvious things such as driverless cars, and create new gadgets and services that we can only dream of. And machine learning will also lead to other new technologies, just as computer technology and the internet led to machine learning.

If Mr. Brynjolfsson et al. are right, then those who have dismissed the rise-of-the-robots story are in for a nasty shock. That phenomenon could just be getting started. On one hand, that would make the economy even more fantastically productive than it is today. But it could also lead to the widespread displacement of human labour that many fear.

During the Industrial Revolution, there was deep anxiety that new technologies would make human labour obsolete, sending wages, employment and living standards crashing. Instead, the opposite happened – humans learned to do much more productive tasks by co-operating with machines instead of competing with them. A weaver displaced by power looms could now oversee a team of workers operating the very machines that put them out of business. The shift took a long time, and it wasn't painless, but eventually most workers got much richer.

Techno-optimists like to recall the misplaced fear of industrialization when arguing that machine learning will be a good thing for human workers. But there's no reason history has to repeat itself. It might be the case that people simply have two kinds of skills – physical and cognitive. In the Industrial Revolution, technology replaced many human physical skills, but we learned to use our brains to complement the dumb machines. But now, if machine learning replaces human cognitive skills, what skills will humans have left that machines lack?

Some say that social skills will be the next frontier – humans will complement machines by dealing with other humans, through marketing, management and so forth, with machines doing all the technical thinking. But what if machine learning also manages to replicate humans' ability to interact with each other? Already, bots have become hugely influential on social media. There seems every reason to believe that the cold pseudo-intelligences now being developed by software engineers will eventually be able to simulate a human in a wide variety of interpersonal interactions.

So if Mr. Brynjolfsson et al. are right, the scary robots takeover could still be rushing toward us. But there's also a chance that they're wrong. The productivity boom from machine learning, even if it comes, could be short-lived.

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The computer and internet revolutions provide a precedent. In 1987, famed economist Robert Solow quipped that "you can see the computer age everywhere but in the productivity statistics." Eventually the statistics caught up – in the late 1990s and early 2000s, information-technology adoption pushed productivity growth back to levels not seen since the mid-20th century. Companies made themselves more efficient by replacing paper records and communications systems with electronic ones. They created new consumer products – video games, smart phones and social networks. And they began developing whole new business models based around the internet – outsourcing, supply chains, just-in-time product development and the gig economy.

In other words, all the developments that Mr. Brynjolfsson et al. foresee for machine learning happened with computers and the internet. But in terms of productivity, the boom only lasted about a decade.

So no one, even the smartest economists, really knows what's going to happen now that machine learning has burst upon the scene. It could be the replacement and devaluation of most human labour. It could be only a tiny blip in a long process of technological stagnation. Or it could be the beginning of a new age of widespread human affluence. Only time will tell.

Noah Smith is a Bloomberg View columnist. He was an assistant professor of finance at Stony Brook University, and he blogs at Noahpinion.

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