‘It is one thing to imagine such a future . . . It is another to have confidence that it is approaching’

Are we nearing a dramatic moment in economic history? Before humans developed agriculture, the world population — and thus the world economy — doubled in size roughly every 250,000 years. After acquiring the power of agriculture, the world economy doubled in size roughly every 900 years. After the industrial revolution, growth accelerated again, and since the second world war the world economy has been doubling in size roughly every 15 years. These numbers have been collated by Robin Hanson, an economist at George Mason University in Virginia; they are based on educated guesses by various economic historians.

If another step change of a similar scale were to happen, the world economy would double in size between now and Christmas. That is hard to imagine but, before the industrial revolution happened, it too would have been hard to imagine. And a small band of believers, not short on imagination, look forward to an economic “singularity”. Hanson is one of them, and the computer scientist Ray Kurzweil, author of The Singularity Is Near, is perhaps the most famous.

The singularity would be a point at which, rather than humans developing new technologies, the new technologies developed themselves. They would do so at a rate far beyond our comprehension. After the singularity, our civilisation would be in the hands of cyborgs, or brains uploaded into the cloud, or genetically enhanced superbeings, or something else able to make itself smarter at a tremendous rate. The future economy might consist of rapid interactions between artificial intelligences. The idea that it might double in size every few weeks no longer seems quite so unimaginable.

But it is one thing to imagine such a future. It is another thing to have confidence that it is approaching. Many economists point out that productivity growth has been sluggish for a long time, which hardly seems to be a precursor to a transformative economic take-off. Growth in advanced economies, far from accelerating, seems to require extraordinary stimulus to prevent it from stopping altogether. Other economists are more bullish, reminding us of a basic fact about the rapid exponential growth in computing power: if it continues, then by definition growth in the future will dwarf growth in the past.

Recently, the economist William Nordhaus published a research paper that aims to adjudicate on this debate. Nordhaus proposes a series of tests that we could use to spot an imminent singularity, looking for evidence that either the productive forces of the economy, or the goods that we enjoy consuming, are being transformed by computing.

Nordhaus’s first test is on the demand side. Is it likely that singularity-prone products such as games, films and computers will eventually absorb most of our spending?

So far, the answer seems to be no. The proportion of spending on such products is falling because their price is collapsing. If this trend continues, limitless digital goods will be the intricate icing on a stodgy economic cake. Our economy will move at the pace of the slowest sectors, and we will be chained to productivity improvements in mundane products such as food, shelter and transportation. After all, we cannot eat smartphone apps.

Perhaps, instead, computing will revolutionise how we produce these mundane products. An obvious second test, then, is to ask whether US productivity is accelerating. It isn’t.

Other tests look at the importance of investment goods in the economy. If the singularity is approaching, one might expect them to become very cheap and to dominate economic output. Are the average prices of investment goods — which include computers and software but also buildings and machinery — falling relative to wages at an accelerating rate? The answer, again, is no. What about the stock of capital relative to US economic output — is it rapidly rising? No.

So far there is not much sign of a singularity in the data. But a couple of tests do point in that direction. For example, the share of US national income accruing to capital rather than labour is increasing, albeit at a modest pace. That is what one might expect as the robots march into human affairs. And within the capital stock, the share of information assets such as software and intellectual property is increasing, although it is still only 6 or 7 per cent of the total. Nordhaus argues that these two tests suggest a singularity is many decades away; his other tests all point in the wrong direction entirely.

At this point the pro-singularity crowd might complain that conventional economic statistics do a poor job of measuring some of the new products and services. A mobile phone, for example, comes bundled with dozens of free products — a flashlight, satnav, an alarm clock and much more.

All this Nordhaus acknowledges — he is, it so happens, one of the world’s leading authorities on measuring the value of goods that conventional statistics miss. He ponders various back-of-the-envelope measures — for example, the amount of time that people spend consuming digital goods such as email. But none of these efforts suggests anything transformative yet.

Perhaps this is complacency. In the movies, the robot takeover tends to be rather sudden. Perhaps cyborgs have kidnapped the real Nordhaus and are using his name to spread disinformation. It is more likely, though, that the singularity is not near.

Written for and first published at ft.com.