WONKISH, as they say.

Economic puzzles have been in no short supply in recent decades. New ones keep appearing without waiting for old ones to be solved. The productivity puzzle that began in the 1970s persists, thanks to the apparent fizzle in productivity growth since the internet boomlet of 1996-2004—and despite what looks to many like an ongoing acceleration in technological discovery. The British economy has developed its own acute version of the productivity puzzle; over the course of the financial crisis and recovery productivity collapsed, shielding the economy from labour-market carnage. There are puzzles of wage stagnation and falling labour-force participation. There are savings glut puzzles and secular stagnation puzzles. The common thread linking the puzzles is that they almost always mean trouble of one sort or another.

Many stories have been presented to explain some of these phenomena (and others, as well, like rising inequality and the striking emergence of jobless recoveries). But not much effort has been made to tie these stories together into a broader narrative of what is happening to (primarily) rich economies and what might usefully be done about it. The nearest thing to an attempt is the secular stagnation narrative that, while not originating with him, has been popularised in recent months by Larry Summers. In this post I hope to tighten up and extend the arguments in Mr Summers’s story in pursuit of a broader theory of troubles.

Since this post is long and not exactly bursting with colour, I'll go ahead and share the gist of the story in hopes of enticing you to read on: because we rely on market wages to allocate purchasing power we have resisted technology-driven reductions in employment, and because we have resisted that decline in work we have trapped ourselves in a world of self-limiting productivity growth. Enticed? Good.

The immediate motivation for the argument presented here is work done on the diverging fortunes of the British and American economies over the past six years. A recent Free exchange column explored the case. Two rich economies, relatively similar in structure, reacted very differently to the global financial shock of late 2008. In America output sank sharply but then rebounded to new highs. Employment, by contrast, fell dramatically and has recovered much more slowly; it has yet to regain the pre-crisis peak. In Britain the trends were reversed; employment is setting new highs while output suffered an L-shaped recovery.

The key difference appears to be rates of inflation. Higher inflation in Britain reduced real wages. That, in turn, allowed firms to meet a given level of demand by using more workers less intensively—at lower productivities. In America, by contrast, lower inflation meant that real wages rose over the course of the recession and recovery. Some research results suggests that firms respond to sticky real wages by wringing more output out of existing workers—raising productivity. Firms meet a given level of demand using fewer workers more intensively, resulting in a jobless recovery.

One possible takeaway from this divergence is that productivity is often endogenous to the real wage. Confronted with high real wages, firms reorganise production, invest in training and capital, and take other steps to boost productivity and economise on labour. When real wages are falling, by contrast, the incentive to economise is reduced and productivity lags.

In two related blogposts I aimed to generalise this result a bit and apply it to some key economic trends of the past generation. Such as:

Since the early 1980s, labour markets have polarised or “hollowed out”.

Work published in 2006 by David Autor, Lawrence Katz, and Melissa Kearney argued that employment and wage growth in America have “polarised” in recent decades, a conclusion that has been reinforced by subsequent research. Employment in high- and low-skill positions has risen substantially relative to middle-skill jobs. The resulting employment distribution generates a distribution of wages that is similarly polarised and more unequal than that which prevailed prior to this period.

Polarisation is mostly attributable to elimination of “routine” tasks by trade and technology.

Daron Acemoglu and Mr Autor pioneered a “task approach” to labour markets. Tasks can be completed by either labour or capital. The more routine a task is, the more susceptible it is to automation. But whether or not a task is automated depends upon the relative supply—and the real wage—of workers of various skill levels. Subsequent work has shown that automation and trade are responsible for displacement of routine tasks previously done by middle-skill workers, in both manufacturing and clerical or service activities, leading to polarisation of local and national labour markets.

Since the early 1980s, polarisation has occurred almost entirely during recessions.

Examining patterns of polarisation in America, Nir Jaimovich and Henry Siu find that displacement of routine work is not a gradual process but occurs almost entirely during recessions. Since the mid-1980s, roughly 92% of job loss in middle-skill, routine jobs has taken place during or within a year of recessions (as dated by the National Bureau of Economic Research). This pattern is linked to the phenomenon of “jobless recoveries”, which followed the recessions of 1990-1, 2001, and 2007-9 but not earlier downturns.

The jobless recoveries of the past generation have been characterised by a change in the cyclical behaviour of productivity.

Prior to the mid-1980s both output and productivity growth tended to fall relative to trend in recessions and rise relative to trend in expansions. Beginning with the recovery from the 1981-2 recession, however, the behaviour of productivity flipped. It has since risen relative to trend in recessions and fallen relative to trend in expansions.

Productivity-rich recessions, and jobless recoveries, are a product of sticky wages.

Mark Bils, Yongsung Chang, and Sun-Bin Kim find that sticky wages push firms to wring more output from existing employees when confronted by a decline in demand. Productivity therefore rises during recessions—rising most in industries where wage rigidity is most binding—reducing the incentive to take on new workers despite relative wage flexibility among the unemployed.

Taken together, these observations imply that in the presence of moderate inflation, real wages will be more flexible and productivity will flip back to falling, rather than rising, amid weak demand. That brings us back to the motivating example of the Britain versus America comparison, where that implication seems to have verified.

If one were feeling a bit daring, one could draw further lessons from this, however. These facts describe a particular relationship between technological change and macroeconomic policy. Low inflation in the era after the Volcker recessions significantly reduced the flexibility of real wages. As a result, employers faced pressure to raise employee productivity at times of weak demand, in order to reduce the effective real wage of existing workers. Often enough, that meant reorganisation and/or higher capital intensity, contributing to structural changes in the American economy.

One might then reason that both productivity and employment respond to real wages. The real wage can determine the capital- or labour- intensity, and the productivity, of an economy’s output. To be slightly more precise: maximum achievable productivity places an upper limit on wages, but how close to achievable productivity an economy operates depends on wages.

Though somewhat heretical, this is not a ridiculous assertion on its face. Other things equal, a relative increase in the price of one factor of production should lead to less use of that factor. In 1987 Paul Romer speculated that a surge in labour-force growth in the 1970s (thanks to rising labour-force participation among baby boomers and women more generally) could generate a decline in real wages. That, in turn, could discourage labour-saving innovation and, to the extent that such innovations would have produced spillover benefits, to productivity growth across the economy as a whole.

Contrasts drawn between patterns of industrialisation in Britain (or Europe generally) and America often feature real wage differences as part of the story. As Moses Abramovitz and Paul David put it:

[T]he early sparse settlement of America’s virgin lands and its abundant forest resources made American wages relatively high and local labor supplies inelastic. And high wages in turn encouraged the development of the era’s capital-intensive mechanical technologies.

And certainly relative factor abundance and relative factor prices are relied upon in analysing the factor-intensity of production across countries and resulting trade patterns. Mr Autor notes that Nissan, when producing its cars in Japan, relies upon a much more capital-intensive process than when making similar models in low-wage India.

So, consider a story. This may or may not describe reality, but hopefully readers will find it a useful possibility to think through.

The key dynamic in this story is steady improvement in technological progress. There is a universe of tasks, and output is generated by combining various tasks from that universe. Technological progress is the process of reducing the cost of using capital to complete tasks. As technology improves, an ever larger share of the universe of tasks becomes potentially automatable, in that the cost of using capital to complete a task falls below typical labour costs to complete the task.

Rising incomes, in this story, are a result of substitution of capital for labour: of raising the ratio of capital to labour across the economy and in doing so boosting the level of output per worker. In the early stages of technological advance, technological progress need not reduce overall labour demand, and might well raise it, since the share of all tasks that can be completed by capital is low. Some substitution of capital for labour raises incomes. That raises consumer demand, which in turn leads producers to draw on a broader range of tasks. Because there are so many more non-automatable tasks than automatable ones, technological advance raises labour demand.

Note that this story assumes that there is a finite number of different tasks, all of which are theoretically automatable. At sufficiently high levels of technological progress, in other words, there is nothing a human can do that a machine can't.

Human labour is necessary in order to do required tasks that aren't yet automatable. At a very low level of technological progress that's basically everything. At a very high level of technological progress that's basically nothing. But the process of substitution is uneven. Easy-to-automate tasks tend to involve mildly challenging but routine work done by middle-skill labour. Automation begins from the middle and works outward, because difficult-to-automate tasks fall into two categories: those that must be done by highly skilled workers (like inventing iPhones) and those that are manually challenging (like navigating and cleaning a cluttered office).

So, imagine that the labour force exists along a skill continuum. As technology improves, opportunities to substitute capital for labour grow. Periodically there is reorganisation and some workers are displaced. Workers above some skill threshold are reallocated to a new high-skill task. Workers below that skill threshold are reallocated into competition for low-skill jobs. Technological advance will tend to raise that threshold while educational attainment will tend to lower it (so that a larger share of the labour force, when displaced, is reallocated into relatively high-skill work rather than into competition for low-skill jobs).

But: the real wage varies with labour supply at various skill levels. When many workers are shunted into competition for low-skill jobs, the real wage at which low-skill work is done falls. That, in turn, makes further automation of low-skill work less attractive. Technological advance can become self-limiting. Substitution of capital for labour raises productivity growth but displaces workers and places downward pressure on wages. That, in turn, tends to slow productivity growth by reducing the incentive for further substitution of capital for labour. Note that rapid increases in educational attainment could help attenuate this effect, by slowing the growth in the glut of workers competing for low-skill work. But rapid increases in educational attainment are no longer nearly as cheap or easy to come by as was the case in the 19th and early 20th centuries.

The broader takeaway, however, is that apparent rapid progress in technological capabilities is not at all inconsistent with lacklustre productivity growth.

Distributional issues are key in this narrative. If we assume that purchasing power is allocated via market wages, then the task facing central banks immediately becomes impossible. If they try to maintain low and stable inflation, then competition for low-skill work will place downward pressure on the wages of low-skill workers, but wages will be too rigid to provide employment for all willing workers. The result is a stagnant real wage for all but those at the high end of the income spectrum and a growing number of frustrated workers pushed out of the labour force due to lack of work. Productivity growth will follow a middle path. It will be lower than it could be, because society will still be trying to employ everyone by reducing the real wage of less skilled workers until they are competitive at tasks machines could reasonably do. Indeed, efforts to employ everyone by reducing their real wage will retard cost declines in industries, like health care or education, that should be subject to rapid displacement of workers by capital, thereby leaving real wages for workers not immediately at risk of displacement lower than they could be. But productivity will be higher than it would be in a high inflation scenario.

But in general, the benefits of growth will flow to high-income workers and owners of capital. Since they have low propensities to spend, central banks will find it difficult to generate adequate demand, except by nurturing unsustainable borrowing by workers with stagnant incomes. Central banks cannot have adequate demand and low inflation.

On the other hand, if central banks are willing and able to raise inflation rates, then real wages will be more flexible, and firms will be more willing to use labour to do tasks that could reasonably, or even easily, be automated. In this scenario the central bank succeeds in generating adequate demand; because low real wages encourage less substitution of capital for labour, a higher share of income flows to labour, to workers with a high propensity to spend. But adequate demand is incompatible with a low rate of inflation. It may also be unsustainable, since many central banks will interpret the high inflation necessary to boost employment as evidence the economy is running at capacity.

But of course, the economy isn't running at capacity; it's running farther below capacity than in the inadequate demand case, because firms are using capital much less intensively than they could. (One question central banks may face is how to generate higher inflation given excess capacity; the British case points to one tried and true method: depreciation.) Nonetheless, the concept of full employment becomes divorced from the concept of maximum sustainable output growth. The central bank is forced to choose between two undesirable outcomes.

A corollary to this would seem to be that full employment is no longer compatible with full utilisation of capital. The "great savings glut" story may indeed be a tale of insufficient investment opportunity. The return on capital is low because the return on labour is low: because society is allowing the market to become glutted with labour, none of the potential high-return capital investments are economical. The global savings glut might well be thought of as a global labour glut.

What might a potential solution look like? Fiscal expansion could help, but the gain from fiscal policy is likely to be limited unless it is structured to try and reduce labour supply. That's right, reduce labour supply.

The most attractive options to accomplish this are probably those which seek to voluntarily reduce the number of hours of "full-time" work. John Maynard Keynes was right; a 15-hour work week should be sufficient to provide a worker with a "full-time" income. But this will require subsidies from the state; in the form of wage top-ups, perhaps, or a universal basic income.

Why are subsidies necessary now when they weren't a century ago, when rising productivity was allowing workers to work less but still earn a good living via a market wage? You could say that technological progress was labour-augmenting then and has since become labour-substituting, but that's not quite right. Technological progress is always capital-augmenting, but when it augments capital in tasks that are complementary to those done by labour, it looks labour-augmenting. As the share of tasks completed by labour falls, any given technological change is more likely to appear to be labour-substituting, since the share of workers that could potentially benefit from the change as a result of working on complementary tasks keeps dropping.

We don't want to force workers out of the labour force. Because some labour is still necessary, forcing the wrong workers out will reduce growth relative to potential. And if a worker who no longer needs to do low-wage work to support himself wishes to keep doing it anyway, it would probably be utility reducing to force him to stop.

A minimum wage looks less unattractive in this world, in part because we know employment effects will be minimised by firms' efforts to raise productivity, and in part because what employment effects there are could boost the economy by reducing labour supply labour demand. But a minimum wage will not do anything to allocate purchasing power to those pushed out of the labour force, and so it would certainly need to be paired with other redistributionary policies.

Redistribution at the scale described above would be very difficult to engineer. Society would face two main challenges (among a pile of others). First, if the tax code were going to raise enough money to support non-workers from a dwindling pool of people earning high market incomes, then the tax code would need to become much more efficient. Otherwise, taxpayers would face intense pressure to reduce their tax burden in any way possible and would generally succeed: enough, anyway, to break the system. The second challenge is related; however efficient the tax code, the social conflict arising from an effort to reorganise society in this fashion would probably be intense and unpleasant.

The upside to managing the transition would be enormous, however. What we are talking about here is a world which is much, much richer. Everyone should be able to enjoy much higher incomes while doing much less work. The endpoint would not be a socialist paradise, necessarily. But it might seem a bit like one, in the way that a 19th century worker putting in 70 hours per week in an attempt to earn enough to keep his family from starving might view a world in which people are able to live in extraordinary comfort (by comparison) working just 40 hours per week as something like heaven.

Getting from 19th century misery to 20th century prosperity took a lot of social and governmental reform and investment. It is unreasonable to think that similarly grand shifts would not be necessary now. It is also unreasonable to expect that this transition should require qualitatively similar reforms to those which did the trick in the 20th century.

If, that is, all of the above is something more than so much nonsense.