The analysis, by accounting and consulting firm PwC, emphasized that its estimates are based on the anticipated capabilities of robotics and artificial intelligence, and that the pace and direction of technological progress are "uncertain."

It said that in the U.S., 38% of jobs could be at risk of automation, compared with 30% in Britain, 35% in Germany and 21% in Japan.

The main reason is not that the U.S. has more jobs in sectors that are universally ripe for automation, the report says; rather, it's that more U.S. jobs in certain sectors are potentially vulnerable than, say, British jobs in the same sectors.

For example, the report says the financial and insurance sector has much higher possibility of automation in the U.S. than in Britain. That's because, it says, American finance workers are less educated than British ones.