ARE robots coming to steal our jobs? For those manning the tills at pizza restaurants, the answer seems to be yes. In late May Pizza Hut announced that by the end of the year a robot called Pepper would start taking orders and payment at some of its Asian restaurants, providing a “fun, frictionless user experience”.

There is plenty of research to suggest that restaurant workers are not the only ones at risk. One widely cited paper by Carl Frey and Michael Osborne at Oxford University found that as many as 47% of Americans work in jobs that will be highly susceptible to automation over the next two decades. But a new working paper by Melanie Arntz, Terry Gregory and Ulrich Zierahn of the Centre for European Economic Research paints a slightly brighter picture. The earlier study quizzed experts on the chance that a particular occupation could be automated, and then totted up the proportion of American workers in such jobs. But the newer study suggests that this method was too blunt.

Digging into more detailed data, the researchers find that many jobs involve bundles of tasks, only some of which machines can easily handle. Take clerks in book-keeping, accounting and auditing: the earlier study said the odds of computers supplanting them over the next 20 years were 98%. But the newer study finds that three-quarters of those jobs involve some group work or face-to-face interaction—tasks robot struggle with. Applying a similar analysis to all jobs, they find that only 9%, not 47%, are at high risk of automation.

Some caveats are in order: employers could restructure jobs to disentangle tasks that are more or less easy to automate. If that proves difficult, another possibility is that they simply forgo the human interaction now built into many occupations. A smile and some chit-chat once seemed an integral part of paying for groceries, until automated tills became commonplace. And finally, even if the 9% figure is closer to the truth, that still threatens the livelihood of millions. For the poorest quarter of the population, the proportion of jobs at risk rises to 26%, since more of them work in the sort of routine jobs most susceptible to automation.

Even so, the authors offer a few more reasons not to panic about robot-induced unemployment. Both studies look only at what is technically possible. If labour is cheap, businesses will have little reason to invest in fancy machines. Nissan, a car manufacturer, uses robots more intensively in Japan than in lower-wage India. For a robot army to be worrisome, it has to be worth someone’s while to build it.

Even if a wave of automation sweeps over the workforce, total employment may not fall. Innovation could lower prices and thus stimulate incomes indirectly, boosting demand for new jobs elsewhere. That is what happened in the past, at any rate: when automatic teller machines (ATMs) were introduced, the number of cashiers in America actually rose, since the device helped to cut costs, enabling banks to open new branches. From the Luddites to Keynes, many have worried needlessly about mass technological unemployment.

Even if things are different this time, then at least the transition is likely to be slow. The Boston Consulting Group forecasts that only 25% of cars sold in 2035 will have any self-driving features, for example. If the robots do steal our jobs, we should at least be able to see them coming.