Can an economy’s gross domestic product (GDP) per person continue to grow forever? Or does there come a time when growth dissipates and the economy converges to a constant level of income per person, so that living standards no longer progress from generation to generation?

These are at present but academic questions in fast-growing emerging economies such as India, which is expected to grow anywhere between 7% and 8% during the current and coming fiscal years. But it is fast becoming an existential debate in advanced economies such as the US, Canada and countries in western Europe. These economies were growing on average at about 2% before the great financial crisis of 2008-10, and have barely grown since then.

One set of theories, those associated with the “secular stagnation" hypothesis that I explored in an earlier column, are relatively optimistic. According to this view, whose chief proponent is Harvard economist Lawrence Summers, the growth slowdown is principally due to insufficient aggregate demand. The correct remedy, therefore, is a return to Keynesian-style fiscal policy of a type that was largely abandoned during the so-called Great Moderation which preceded the crisis, when the consensus emerged that monetary policy alone could fine-tune the macroeconomy.

The much more pessimistic view, as articulated by Northwestern University economist Robert Gordon in a recent much-discussed and controversial book, The Rise and Fall of American Growth, is that the principal cause of the recent growth slowdown in the US emanates from the supply side, and is likely to be persistent. In other words, the US and other advanced economies should get used to slow or no growth in per capita income as being the new normal.

Before probing the arguments that Gordon offers, let us first establish that this is no mere arcane academic debate. In the long run, rising living standards are driven, as a matter both of economics and basic statistics, by sustained growth in per capita income, not by periodic bursts of growth that quickly fizzle out. There is a mathematical formula, the rule of 72, which tells us that the number of years it takes for something to double is approximately 72 divided by the growth rate expressed as a percentage.

Thus, an economy growing at a steady 2% income per capita per year will double income per person in about 35 or 36 years, or a little more than a generation. That was the experience of the advanced economies, in particular the US, for a century or so starting in the late 19th century. Roughly speaking, it means that, each generation, the average American was about twice as well off as their parents during this golden century of growth.

Compare that to the red-hot 10% growth rate that fast-growing economies in East Asia and then China experienced for a generation or more. In such an economy, income per person doubles not every generation, but about every seven or eight years. Thus, income would double, quadruple or grow even more within a given individual’s working lifetime. This has been the lived experience of recent generations in China and, to a lesser extent, in India.

But now imagine that the annual growth rate of per capita income is only 0.5% on average per year, as has been the case in the US and other advanced economies in recent years. In such a situation, it will take close to a century and a half for the average person’s income to double; in other words, all except the very long-lived will not see a doubling of living standards in their lifetime.

Finally, if the growth rate of per capita income is zero, then income per person will be constant—progress, at least as measured by growth in income per person, will have ceased. In the language of classical economists such as David Ricardo, we would then be in a “stationary state".

Indeed, for much of history, as Gordon himself observes, economies were essentially stationary, and most people, therefore, would have expected a steady income level, rather than growing income, to be the norm.

It is only in the past century and a half or so that it came to be believed that steady growth was the norm, in the advanced economies at least. It is telling that a no-growth stationary state would be routinely described in this more recent period as “stagnation" of income, implying, therefore, that growth was the norm and stagnation was not.

As a matter of economics, and this is the key to understanding Gordon’s analysis, sustained growth in income per person must necessarily be driven by growth in productivity: roughly, how much output a given quantum of inputs—capital, land, labour and so forth—can generate. In the long run, output per person will grow approximately at the rate of growth of productivity.

In the absence of productivity growth, the existence of diminishing returns to capital will ensure that economic growth will necessarily dissipate over time, until an economy converges to a stable level of income per person. In jargon, this is a “steady state" in which all inputs along with output grow at the same rate, so that the proportion between any two inputs remains the same, and that output grows at the same rate as the inputs. For instance, if population is growing at 2%, then capital and output will also grow at 2%, and output per person will be constant.

For the wonkish: these are standard implications of textbook growth theory, both the so-called optimal growth theory of mathematician Frank Ramsey, in which households optimally choose the path of consumption over time, as well as the more Keynesian-style model of Nobel Prize-winning economist Robert Solow, in which, following Keynes, it is assumed that households save a constant and fixed share of income every period.

The essence of Gordon’s claim is that the century from 1870 to 1970, which he calls a “golden century", was special and unrepeatable, especially for the US.

This is so, he argues, because of the many one-time-only inventions of the period, which dramatically boosted productivity, and allowed a century of unbroken growth. The epochal technological revolutions of this period included electricity, telephone, radio, television, automobile, aeroplane, modern plumbing and on and on, right up to the modern computer.

An average person’s life in the US in 1970 was unrecognizably different for the better than his or her great-grandparent’s life in 1870.

Gordon’s further claim is that the innovations that have followed in the 40-odd years since then have not been as dramatic, or as important in terms of productivity, as those that preceded them. He has in mind, in particular, the array of innovations that together constitute information technology and communications, which relate to the Internet, modern computers, smartphones, cloud computing and the like.

Thus, for example, the Gordon thesis suggests that the impact of the mobile phone on productivity is much lower than that of the landline phone that preceded it.

Naturally, Gordon’s thesis has aroused much controversy. Other well-known economists have entered the fray and pushed back against his claims, as is well summarized by economist Tyler Cowen reviewing the book in the influential journal Foreign Affairs. Cowen himself is one of the critics and the piece well assembles the major criticisms.

Most of the criticisms rely on two basic counterarguments. First, some scholars argue that the current downturn in productivity, on which Gordon is correct, is temporary. Thus, potentially game-changing new technologies currently in the works, such as artificial intelligence, three-dimensional printing, driverless cars and so forth, once their potential is fully realized, would lead to another sustained spurt or two of productivity growth, which if properly harnessed could potentially power US economic growth well into the current century.

The second counterargument is that an era of rapid technological progress is never foreseen. Thus, an observer making a linear extrapolation of future productivity growth in the US in the 1860s, before the spate of new innovations burst on to the scene, could credibly have predicted that the 20th century would be one of zero or slow economic growth. Yet, the reality completely upended such a reasonable and sober forecast.

Gordon dismisses such critics as “techno-optimists". And they, in turn, could dismiss him as a “techno-pessimist". While Gordon’s view would have been the mainstream position up until the middle of the 19th century, a century and a half of very rapid growth in the advanced economies has schooled many folk into believing that technological innovation, and the economic growth that comes with it, should be the norm, not the exception.

The reason that economics cannot settle the debate is that, despite its own many innovations, neither economics nor the social sciences more generally have any real theory of the ultimate source of technological innovation. Indeed, in neoclassical growth theory, productivity growth was simply assumed to occur at some exogenously given rate, like manna dropping from heaven.

The so-called endogenous growth theories that emerged in the 1990s, pioneered by economists such as Paul Romer and Nobel Prize-winning economist Robert Lucas, attempted to drill down into the sources of productivity growth, and gave us a better grasp on how productivity is shaped by incentives, government policy and so forth. But even the most sophisticated theory of economic growth is ultimately forced to leave as a black box the wellsprings of human creativity that generate technological innovations in the first place.

That is why, ultimately, economics cannot tell you whether you ought to be on the side of Gordon or his critics, for it depends on whether you are an optimist or a pessimist.

The good news also is that India and other emerging economies have a long time to go before they need to worry about these advanced economy problems. Even with the best of enabling economic policies in place, India has many more decades of rapid growth ahead of us before we get anywhere close to the technological frontier and confront the spectre of no growth.

Unless, of course, something unexpectedly stops us in our tracks. But, on this score, I for one am an optimist.

Economics Express runs weekly, and features interesting reads from the world of economics and finance.

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