The fear that automation in the form of robots or artificial intelligence is going to destroy jobs is widespread. But it can be difficult to gauge just how serious to take the threat. Different reports offer different estimations of how many jobs will be lost, while politicians and economists argue that technology creates as many jobs as it destroys, maintaining an equilibrium in employment over the long run.

But is this really true? A new study from the National Bureau of Economic Research aims to add some solid numbers to the debate, looking at the historical effects of robots on employment in the US. Economists Daron Acemoglu and Pascual Restrepo studied the US labor market between 1990 and 2007, looking at employment rates in different areas and industries while controlling for the influence of factors like increased imports from China and the offshoring of jobs.

They found that each new robot added to the workforce meant the loss of between 3 and 5.6 jobs in the local commuting area. Meanwhile, for each new robot added per 1,000 workers, wages in the surrounding area would fall between 0.25 and 0.5 percent.

These figures may seem relatively small given some of the apocalyptic rhetoric we hear about automation and jobs, but the study’s definition of a robot is likely more restrictive than most people use. Acemoglu and Restrepo went by the definition of an “industrial robot” as outlined by the International Organization for Standardization, or ISO. These are bots that are “automatically controlled, reprogrammable [and] multipurpose.” Under this definition, something simple like a conveyor belt is not a robot, neither is software like Microsoft Word.

It’s also important to remember that these job and wage losses are not distributed evenly among the population. Although the introduction of industrial robots leads to “negative effects [for] essentially all occupations,” some jobs are — expectedly — more fragile than others. Acemoglu and Restrepo write: “Predictably, the major categories experiencing substantial declines are routine manual occupations, blue-collar workers, operators and assembly workers, and machinists and transport workers.” The only jobs not affected were managerial ones.

Looking at this study, though, the million-dollar question is: what happens next? Are these trends going to hold, or will they get worse?

Acemoglu and Restrepo note that because there are relatively few industrial robots in the US, the number of jobs lost to them so far has been limited. (They estimate between 360,00 and 670,000 jobs — a decline in employment to population ratio of between a 0.18 and 0.34 percentage points.) “However, if the spread of robots proceeds as expected by experts over the next two decades, the future aggregate implications of the spread of robots could be much more sizable.”

The spread of industrial robots is one thing; the spread of industrial robots augmented with AI, and of new innovations like self-driving cars (and trucks) is another. Last week, US treasury secretary Steven Mnuchin said that he wasn’t worried about the effects of AI and automation on employment. “Quite frankly, I'm optimistic. I mean, that's what creates productivity,” said Mnuchin. That may be true, but this evidence suggests employment still suffers all the same.