TODAY Britain's Office of National Statistics released a new set of labour-market statistics. The numbers reinforce that what has become known as Britain's "productivity puzzle" has not gone away. The economy added roughly 450,000 new jobs in the year to November, sending employment to a new all-time high. But output has yet to recover its pre-crisis level. Correspondingly, output per hour—productivity—is below the pre-recession level and actually ticked down from the second quarter of last year to the third.

Britain's workers are ever less productive, and firms are snapping up ever more of them. That could only make sense in a world of falling wages. Nominal wages have grown steadily over the last decade, at a pace between 1-2% per year. But prices have risen much faster, leading to a steady erosion in real pay.

In a 2012 paper Bill Martin and Robert Rowthorn argued that falling real wages are the critical detail—the key to unlocking this puzzle. They suggest that wage moderation led directly to the labour-intensive nature of the British recovery in three ways. First, it kept firm income higher than it would have been, preventing some firms from going out of business. Second, it made labour hoarding more attractive. And third, at some margin, it led to some substitution of labour for capital in production, or some displacement of production from capital-intensive firms by labour-intensive firms.



The chain of causation here starts with falling wages. Because wages moderate, firms use more workers at lower productivity levels. Productivity is the dependent variable.

That the productivity of production might depend on, rather than determine, the wage is not an unknown concept in economics. A briefing in this week's print edition explores one example, provided by David Autor. The "task approach" to labour markets to which he has been a primary contributor provides a framework for thinking about when a job is done by labour rather than capital. The routine-ness of the task to be done matters; the more routine the job, the more vulnerable it is to automation. But relative costs are also important. Nissan produces similar cars in Japan and India. It uses much more robot labour in the Japanese plants than it does in India. If workers are cheap, firms are less likely to economise on them and productivity will be low.

This logic is at the heart of what Paul Romer called a "crazy explanation for [America's] productivity slowdown" in a paper designed to be provocative. And it is; Mr Romer essentially argues that what is disparagingly referred to as the "lump of labour fallacy" may accurately describe some labour-market dynamics. He's writing in 1987, I should mention, and attempting to explain the productivity slump that struck America in the early 1970s. He notes, "the data seem to be telling us that output responds much less to increases in the amount of labour supplied than a simple model...would suggest." Indeed, a given rise in the growth of the labour force (of say one percentage point) might be expected to generate a drop in labour productivity growth as large as 0.8 or 0.9 percentage points).

Why would that be? Well, if one supposes that a jump in labour-force growth leads to a corresponding decline in wage growth, then more labour would mean less reliance on labour-saving innovations. The effects could be quite long-lived if the labour-saving innovations in question might otherwise have generated knowledge spillovers leading to knock-on discoveries. That, he points out, is a story that is widely told about divergent productivity in capital-rich America and labour-rich Britain in the 19th and early 20th centuries: that the former developed more capital-intensive methods of production that led to a long-lived productivity edge. More workers mean lower wages and lower productivity.

One should ask why, in the general case, more workers would mean lower wages. One is tempted to look for the answer in demand and in the speed of market adjustment. Imagine an economy that is confronted by a wave of new entrants to the labour market (as the consequence, perhaps, of a baby boom some 20 years prior). If matching workers to jobs takes time, then a sharp rise in labour-force participation could lead to a backlog of job-seekers, otherwise known as unemployment. The demographic firehose creates a temporary labour glut, not unlike a garden-variety recession. This glut could become self-sustaining if it influenced expectations about growth in demand per worker: why scale up production of Camaros when these bums will never be able to afford them? The large and growing pool of unemployed workers would place downward pressure on nominal wages, and that, in turn, could trigger an eventual switch to lower productivity, labour-intensive methods.

Unless, that is, demand was booming. In that case, firms would snatch up workers even if they couldn't use them particularly productively. Nominal wages would rise, but prices would rise faster as demand outstripped the economy's ability to produce. The resulting drop in real wages squares the circle: more employment, low wages, low productivity. This, as it happens, is basically the story that Steve Waldman tells about America in the 1970s, noting:

I don't dispute that monetary contraction could have prevented the inflation of the 1970s. But under the demographic circumstances, the cost of monetary contraction in terms of unemployment and social stability would have been unacceptably high.

Mr Waldman brings with him another important piece of the puzzle: wage rigidities. Because wages were rigid, the adjustment needed to put everyone in the demographic bulge to work would have been long and painful. Only inflation, which quickly and effectively eroded the real wages of much of the labour force, was able to spare the American economy years of prolonged, high unemployment. Now we have another link in the chain: high inflation gets you flexible real wages, flexible real wages fall amid a demand shock, lower real wages allow for lower productivity work, which in turn allows for less employment variability in recessions. The inflationary nature of recessions in the 1970s—and in Britain in the 2000s—potentially prevented disastrously high unemployment.

Which takes us to the next question: what happens when the central bank makes it its business to keep inflation low and stable? This week a new NBER working paper came across the wire. Here is the abstract:

We consider a matching model of employment with wages that are flexible for new hires, but sticky within matches. We depart from standard treatments of sticky wages by allowing effort to respond to the wage being too high or low. Shimer (2004) and others have illustrated that employment in the Mortensen-Pissarides model does not depend on the degree of wage flexibility in existing matches. But this is not true in our model. If wages of matched workers are stuck too high in a recession, then firms will require more effort, lowering the value of additional labor and reducing new hiring.

If wages for existing workers are sticky then firms will respond to plunging demand by firing lots of workers. But they may also seek to wring more production out of existing staff so as to lower the effective real wage. They will, in other words, come up with ways to boost worker productivity. Maybe they will try to wring more effort out of the staff. Maybe they will invest in labour-augmenting capital equipment. Or, maybe they will take the opportunity to reorganise production in productivity-enhancing ways. The dynamic is similar to that which appears to minimise the employment effect of minimum wages; rather than simply sacking workers firms often find ways to boost effort and productivity.

The paper's authors, Mark Bils, Yongsung Chang, and Sun-Bin Kim, find that in industries with stickier wages productivity is more countercyclical, rising above trend in downturns and below in booms. What's more, they note that countercyclical productivity shifts have been a feature of American business cycles, but only for the last 25 years.

They point to research from the Kansas City Fed, produced by Willem Van Zandweghe, who examines the cyclicality of productivity beginning around 1950. Prior to the mid-1980s productivity was very pro-cyclical, falling in recessions and rising in recoveries. But this pattern began to shift in the recovery from Paul Volcker's disinflationary recessions of the early 1980s. Thereafter productivity became sharply countercyclical, contributing to the "jobless recoveries" of the Great Moderation era.

Mr Van Zandweghe considers several possible explanations for the change. He rejects supply shock incidence as a cause; supply shocks don't look much different before and after 1984. Instead he argues that structural changes in the labour market are the culprit. From the mid-1980s firms may have found it easier to hire and fire workers, perhaps because of shifts toward more flexible contractual arrangements. And firms may also have found it cheaper and easier to substitute capital for labour thanks to improving information technology.

Those stories are perfectly reasonable. But they are also perfectly consistent with a world in which very low inflation has made wage rigidities substantially more binding, forcing firms to fire or boost productivity.

It also seems relevant that labour share has fallen since the early 1980s, according to recent research by Loukas Karabarbounis and Brent Neiman—who credit the falling cost of investment goods relative to labour, which has eased substitution of capital for labour. Looking at their data for individual countries it becomes clear that in America the drop in labour share has come from large declines in recessions and early in recoveries, which are not quite offset by gains in late recoveries.

Over the long run, technology sets potential productivities, which govern the wages workers can earn. But relative prices may influence choices between available technologies, and those choices can have long-run effects if they send economies off on different innovation trajectories. Wages and productivity determine each other.

It may be reading too much into recent experience, but one could also argue that under certain constraints the lump of labour fallacy is no fallacy at all. Low inflation rates and cheaper, more powerful technology seem to exacerbate the condition. Maybe Britain's productivity puzzle is less a puzzle than a clue to why labour markets have worked so strangely over the past generation.