I think that most researchers and commentators are too timid when predicting the rise of automation. People tend to look at how a human does a job and then ask: could a robot do that? But that's the wrong question. Instead of looking at "jobs", which are a social construct, look at the need that the human in the job is fulfilling and ask yourself if a robot could fill that need. When it happens, it's likely that the robot's "job" will look very little like the human "jobs" that were displaced.
Obvious example: Amazon has probably destroyed at least 100,000 retail jobs, but none of what Amazon's computer system does looks like the job of a retail clerk. A modern robot would be terrible at chatting with customers, stocking shelves, working a cash register, setting up displays, and pointing people to the restroom. If you were were to look at the job requirements of a retail clerk you might think, "this job is safe from robots!" And don't forget that Amazon has destroyed the white-collar jobs of store managers and owners as well.
Frey and Osborne focus on "engineering bottlenecks" in AI and robotics, and compare these stumbling points with the requirements of jobs in order to determine which are most and least likely to be vulnerable to automation. The biggest bottlenecks are perception and manipulation, creative intelligence, and social intelligence, all of which computers struggle mightily at (but Rosie the Robot excelled at, by the way). While the trend in recent decades has been towards a hollowing out of "middle-skill" jobs and an increase in low-paying service sector jobs and high-paying, highly educated jobs, Frey and Osborne expect that automation in the future will mainly substitute for "low-skill and low-wage" jobs.
So who, specifically, should be worried? They write:Our model predicts that most workers in transportation and logistics occupations, together with the bulk of office and administrative support workers, and labour in production occupations, are at risk. These findings are consistent with recent technological developments documented in the literature. More surprisingly, we find that a substantial share of employment in service occupations, where most US job growth has occurred over the past decades (Autor and Dorn, 2013), are highly susceptible to computerisation.
This may turn out to be correct, though I'd note two reservations I have. First, the model uses (in part) the notoriously unreliable subjective estimates of AI researchers to assign values to whether tasks can be automated or not, and second, it uses lists of job requirements, that the authors acknowledge are not written to assess whether a job can be easily automated. Indeed, job ads don't list things that are universal (or nearly so) across humans, such as rudimentary social intelligence, language understanding, and commonsense. As AI researcher Ernest Davis points out, there has been "only very limited progress" in equipping robots with commonsense reasoning skills.