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Might growth be ending? This is a heretical question. Yet an expert on productivity, Robert Gordon of Northwestern university, has raised it in a provocative paper. In this, he challenges the conventional view of economists that "economic growth . . . will continue indefinitely."

Yet unlimited growth is a heroic assumption. For most of history, next to no measurable growth in output per person occurred. What growth did occur came from rising population. Then, in the middle of the 18th century, something began to stir. Output per head in the world's most productive economies - the U.K. until around 1900 and the U.S., thereafter - began to accelerate. Growth in productivity reached a peak in the two and a half decades after the Second World War. Thereafter growth decelerated again, despite an upward blip between 1996 and 2004. In 2011 - according to the Conference Board's database - U.S. output per hour was a third lower than it would have been if the 1950-72 trend had continued. Prof. Gordon goes further. He argues that productivity growth might continue to decelerate over the next century, reaching negligible levels.

The future is unknowable. But the past is revealing. The core of Prof. Gordon's argument is that growth is driven by the discovery and subsequent exploitation of specific technologies and - above all - by "general purpose technologies", which transform life in ways both deep and broad.

The implementation of a range of general purpose technologies discovered in the late 19th century drove the mid-20th century productivity explosion, Prof. Gordon argues. These included electricity, the internal combustion engine, domestic running water and sewerage, communications (radio and telephone), chemicals and petroleum. These constitute "the second industrial revolution". The first, between 1750 and 1830, started in the U.K.. That was the age of steam, which culminated with the railway. Today, we are living in a third, already some 50 years old: the age of information, whose leading technologies are the computer, the semiconductor and the internet.

Prof. Gordon argues, to my mind persuasively, that in its impact on the economy and society, the second industrial revolution was far more profound than the first or the third. Motor power replaced animal power, across the board, removing animal waste from the roads and revolutionizing speed. Running water replaced the manual hauling of water and domestic waste. Oil and gas replaced the hauling of coal and wood. Electric lights replaced candles. Electric appliances revolutionised communications, entertainment and, above all, domestic labour. Society industrialized and urbanized. Life expectancy soared. Prof. Gordon notes that "little known is the fact that the annual rate of improvement in life expectancy in the first half of the 20th century was three times as fast as in the last half." The second industrial revolution transformed far more than productivity. The lives of Americans, Europeans and, later on, Japanese, were changed utterly.

Many of these changes were one-offs. The speed of travel went from the horse to the jet plane. Then, some fifty years ago, it stuck. Urbanization is a one-off. So, too, is the collapse in child mortality and the tripling of life expectancy. So, too, is control over domestic temperatures. So, too, is liberation of women from domestic drudgery.

By such standards, today's information age is full of sound and fury signifying little. Many of the labour-saving benefits of computers occurred decades ago. There was an upsurge in productivity growth in the 1990s. But the effect petered out.

In the 2000s, the impact of the information revolution has come largely via enthralling entertainment and communication devices. How important is this? Prof. Gordon proposes a thought-experiment. You may keep either the brilliant devices invented since 2002 or running water and inside lavatories. I will throw in Facebook. Does that make you change your mind? I thought not. I would not keep everything invented since 1970 if the alternative were losing running water.

What we are now living through is an intense, but narrow, set of innovations in one important area of technology. Does it matter? Yes. We can, after all, see that a decade or two from now every human being will have access to all of the world's information. But the view that overall innovation is now slower than a century ago is compelling.

What does this analysis tell us? First, the U.S. remains the global productivity frontier. If the rate of advance of the frontier has slowed, catch-up should now be easier. Second, catch-up could still drive global growth at a high rate for a long time (resources permitting). After all, the average gross domestic product per head of developing countries is still only a seventh of that of the U.S. (at purchasing power parity). Third, growth is not just a product of incentives. It depends even more on opportunities. Rapid increases in productivity at the frontier are possible only if the right innovations occur. Transport and energy technologies have barely changed in half a century. Lower taxes are not going to change this.

Prof. Gordon notes further obstacles to rising standards of living for ordinary Americans. These include: the reversal of the demographic dividend that came from the baby boomers and movement of women into the labour force; the levelling-off of educational attainment; and obstacles to the living standards of the bottom 99 per cent. These hurdles include globalization, rising resource costs and high fiscal deficits and private debts. In brief, he expects the rise in the real disposable incomes of those outside the elite to slow to a crawl. Indeed, it appears to have already done so. Similar developments are occurrring in other high-income countries.

For almost two centuries, today's high-income countries enjoyed waves of innovation that made them both far more prosperous than before and far more powerful than everybody else. This was the world of the American dream and American exceptionalism. Now innovation is slow and economic catch-up fast. The elites of the high-income countries quite like this new world. The rest of their population like it vastly less. Get used to this. It will not change.

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