The number of jobs lost to more efficient machines is only part of the problem...In the past, new industries hired far more people than those they put out of business. But this is not true of many of today’s new industries.”

This sentiment, from Time magazine, dates from the early weeks of John Kennedy’s presidency. Yet it would slot nicely into many a contemporary political speech. Like any self-respecting remorseless killer robot from the future, our techno-anxiety just keeps coming back.

Arnold Schwarzenegger’s Terminator was science fiction — but so, too, is the idea that robots and software algorithms are guzzling jobs faster than they can be created. There is an astonishing mismatch between our fear of automation and the reality so far.

How can this be? The highways of Silicon Valley are sprinkled with self-driving cars. Visit the cinema, the supermarket or the bank and the most prominent staff you will see are the security guards, who are presumably there to prevent you stealing valuable machines. Your computer once contented itself with correcting your spelling; now it will translate your prose into Mandarin. Given all this, surely the robots must have stolen a job or two by now?

Of course, the answer is that automation has been destroying particular jobs in particular industries for a long time, which is why most westerners who weave clothes or cultivate and harvest crops by hand do so for fun. In the past that process made us richer.

The worry now is that, with computers making jobs redundant faster than we can generate new ones, the result is widespread unemployment, leaving a privileged class of robot-owning rentiers and highly paid workers with robot-compatible skills.

This idea is superficially plausible: we are surrounded by cheap, powerful computers; many people have lost their jobs in the past decade; and inequality has risen in the past 30 years.

But the theory can be put to a very simple test: how fast is productivity growing? The usual measure of productivity is output per hour worked — by a human. Robots can produce economic output without any hours of human labour at all, so a sudden onslaught of robot workers should cause a sudden acceleration in productivity.

Instead, productivity has been disappointing. In the US, labour productivity growth averaged an impressive 2.8 per cent per year from 1948 to 1973. The result was mass affluence rather than mass joblessness. Productivity then slumped for a generation and perked up in the late 1990s but has now sagged again. The picture is little better in the UK, where labour productivity is notoriously low compared with the other G7 leading economies, and it has been falling further behind since 2007.

Taking a 40-year perspective, the impact of this long productivity malaise on typical workers in rich countries is greater than that of the rise in inequality, or of the financial crisis of 2008. In an age peppered with economic disappointments, the worst has been the stubborn failure of the robots to take our jobs. Then why is so much commentary dedicated to the opposite view? Some of this is a simple error: it has been a tough decade, economically speaking, and it is easy to blame robots for woes that should be laid at the door of others, such as bankers, austerity enthusiasts and eurozone politicians.

It is also true that robotics is making impressive strides. Gill Pratt, a robotics expert, recently described a “Cambrian explosion” for robotics in the Journal of Economic Perspectives. While robots have done little to cause mass unemployment in the recent past, that may change in future.

Automation has also undoubtedly changed the shape of the job market — economist David Autor, writing in the same journal, documents a rise in demand for low-skilled jobs and highly skilled jobs, and a hollowing out of jobs in the middle. There are signs that the hollow is moving further and further up the spectrum of skills. The robots may not be taking our jobs, but they are certainly shuffling them around.

Yet Mr Autor also points to striking statistic: private investment in computers and software in the US has been falling almost continuously for 15 years. That is hard to square with the story of a robotic job-ocalypse. Surely we should expect to see a surge in IT investment as all those machines are installed?

Instead, in the wake of the great recession, managers have noted an ample supply of cheap human labour and have done without the machines for now. Perhaps there is some vast underground dormitory somewhere, all steel and sparks and dormant androids. In a corner, a chromium-plated robo-hack is tapping away at a column lamenting the fact that the humans have taken all the robots’ jobs.