Material progress has transformed human existence in the last two centuries, raising income and health to levels that would have been unimaginable to earlier generations. In the twentieth century, western societies became used to rates of economic growth which, in a generation, doubled standards of living. The notion of material progress is one of the most powerful and attractive ideas of the modern Western world.

For it to be delivered, economies need to grow year in year out. When they don't, or when growth disappoints, as happened in the 1930s and in the last eight years, belief in the idea of progress suffers. Today, many parents worry whether their children will be able to match their lifestyle, let alone exceed them. Economists worry that the world may have entered a prolonged period of low or no growth, of so-called secular stagnation.

One of the most influential advocates of this view is the US economist, Robert Gordon. His magisterial work, The Rise and Fall of American Growth, contrasts the innovation-driven blast of growth that transformed America in the century to 1970 with the more modest gains that have followed.

Gordon's book makes sobering reading for any techno-enthusiast. He argues that today's innovations are nowhere near as life changing as the five great inventions that fueled America's "Special Century" of growth between 1870 and 1970 – the internal combustion engine, urban sanitation, electricity, modern communication and chemicals and pharmaceuticals.

Gordon reminds us of what life was like before these innovations. In 1870 the average US family lived on less than £700 a year in today's money, virtually all of which was used for the necessities of shelter, food and clothing. In the late nineteenth century, before the invention of the domestic washing machine, housewives spent two days each week washing clothes. Before piped water, in 1885, a North Carolina housewife would walk an average of 148 miles a year to carry 35 tons of water. In urban areas in the late nineteenth century horses had created an environmental and health crisis. Their prodigious output of manure and urine was a health hazard and disposal of the stuff expensive and inadequate. In 1894 the Times predicted that by 1950 every street in London would be nine feet under manure. One recent study estimates that horse-related accidents in Chicago in 1916 killed seven times as many people as cars did in 1997 – in busy, confined areas horses are a far more unpredictable form of transport than the car.

The change from the 1870s was breakneck. Radio, the car and electricity created a connected society. By the late 1920s in the US there were nine cars for every ten households. Living standards were transformed, life expectancy soared. By 1940 most American homes were recognizably modern, with electricity, indoor plumbing, a gas cooker, fridge and telephone. As the US economist Paul Krugman has noted, "Life fundamentally improved between 1870 and 1940 in a way it hasn't since".

Gordon underlines this point by inviting readers to choose between owning one of today's ubiquitous technologies – the iPhone (or smartphones in general) – and one of the nineteenth century's great inventions, the flushing toilet. His point is that today's innovations are not changing lives, homes and work in the profound way that the technologies of America's Special Century did. Certainly some of the official data support this view. Productivity growth – a key measure of rising prosperity – has not performed as well since the 1970s in the US as it did in the period 1870 to 1970. And, as Gordon points out, there are others measures of progress, such as transport speeds, which have hardly improved in the last 50 years.

Gordon's arguments are weighty and important, but not conclusive.

Can we really be sure that technology has become less transformational? The last 300 years of technological change show that it takes more than a decade or two to realise the full value from a general purpose technology such as the internet. We have only begun to realise the productive potential of the latest innovations in robotics, medicine and genomics.

The official productivity and GDP data may underestimate the improvements in welfare brought about by new technology. Our system of economic measurement was created for a world of goods not services. The gains to consumers today from free email, web searching or mapping services are necessarily hard to capture in the official data. Businesses are increasingly investing in intangible, hard-to-measure assets such as brand, R&D, intellectual property and employee skills rather than in new factories and machines. More than 80% of the US S&P500's market capitalisation is accounted for by intangible assets, up from just 20% forty years ago.

There is a risk, too, in extrapolating recent trends into the indefinite future. Growth and productivity have slowed in recent years. But this may be cyclical, a product of the Global Financial Crisis, and not necessary the start of a new, slow-growth era. Productivity has slowed in the past in periods before revolutionary new technologies were fully applied. The period of electrification which started in the 1890s is one such episode.

The concept of secular stagnation was a product of the last prolonged period of economic weakness in the West, the Great Depression of the 1930s. In the late 1930s the US economist Alvin Hansen, foresaw a low or no growth future because all of the major drivers of growth, including technological innovation, had played out. That prophesy ushered in a half century of remarkable global growth.

But if material progress really has run its course the implications are immense. The modern ideal of progress over the generations would be at risk. It would be a profound societal change, a return to a pre-industrial Revolution world in which living standards are little changed over time. We could no longer rely on the up escalator of economic growth to meet growing needs for medical care, welfare and education. The choices we would face as a society would be far tougher.

As in so many other big debate in economics, it is too early to tell whether innovation has lost its ability to propel progress. But I am disinclined to bet against human creativity and ingenuity – or against economic growth.

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