CENTRAL banks have taken the brunt of supporting the global economy, ever since 2009, the last time that governments made any concerted attempt to indulge in a fiscal status. Low interest rates, quantitative easing, forward guidance and now negative rates have all been wheeled out.

But life for a central banker is more difficult than it used to be; the economic relationships that prevailed before the 2008 crisis may not hold good today. Take the relationship between unemployment and inflation, famously linked by the Phillips curve. As unemployment falls, inflation should start to rise as businesses compete for labour and wages go up. The relationship was the basis for the introduction of "forward guidance". In August 2013, Mark Carney, governor of the Bank of England, said that a fall in unemployment below 7% would be a necessary (but not sufficient) condition for tighter policy. UK unemployment has fallen to 5.1% but inflation is only 0.3% and there has been no need to tighten policy. 

The Federal Reserve had introduced forward guidance under Ben Bernanke way back in December 2012. That envisioned a US unemployment rate of 6.5% as a possible trigger; in fact, the first upward move in rates did not occur until December 2015, when the jobless rate had fallen all the way down to 5%. 

So what has been happening? The economic concept underlying the approach of the two central banks is that of the NAIRU; the non-accelerating inflation rate of unemployment. But it seems clear that the NAIRU is not a set figure; it varies from cycle to cycle. Paul Krugman has shown that the Fed's estimate of the NAIRU has trickled down as unemployment has fallen

It all depends on how much spare capacity there is in the labour market. The best measure might not be the unemployment rate, which measures those entitled to claim benefits, but the labour force participation rate, which calculates the proportion of those of working age who are in employment. In the US, that has fallen from a peak of 67% reached in 2000 to 62.9%. What is remarkable about the chart is that one would expect the labour force participation rate to rise as unemployment falls; until recently, the two have dropped in tandem. Would some of those people rejoin the labour market if wages were higher? It is hard to know; some may have been jobless for a time and thus may find it difficult to get jobs, others may have retired early. There is no "right" level of labour force participation that can be determined; the rate was below 60% for much of the 1950s and 1960s before more women joined the workforce..

So if you can't know how much slack there is in the labour market, are there other measures? Economists use the idea of the "output gap", the difference between the economy's actual output and its potential production. To figure this out, they need an idea off the tend rate of growth. But that is a slippery concept. It looks as if, in most developed countries, the trend rate of growth has fallen since 2008. In Britain, the Office for Budgetary Responsibility recently revised down its assumed rate of growth because of poor productivity.
The most significant forecast change we have made since November has been to revise down potential productivity growth. This is the amount of output the economy can produce sustainably per hour worked and is a key driver of its potential size. The data available in November showed a pick-up in productivity growth in mid-2015, consistent with our assumption that the receding financial crisis would exert less of a drag and that trend productivity growth would return to its pre-crisis average rate by the end of the forecast. But more recent data suggest that this was another false dawn. With the period of weak productivity growth post-crisis continuing to lengthen, we have placed more weight on that as a guide to future prospects – although this judgement remains highly uncertain. This in turn has prompted us to revise down our GDP growth forecasts by around 0.3 percentage points a year to an average of 2.1 per cent a year over the rest of the decade.
Why would productivity growth be weaker? This is a huge debate at the moment especially with the publication of Robert Gordon's "The Rise and Fall of Economic Growth" (reviewed here). Mr Gordon displays, in impressive detail, the transformational changes in America between 1870 and 1970 that brought vast improvements to both life expectancy and the quality of life; people have clean drinking water in their houses, for example, reducing the incidence of disease and the drudgery of clothes washing. The changes in the economy since 1970 have been remarkable in the sectors where they have occurred; information technology and communications. But they are nothing like as widespread as in the previous era.

Conversely, there has been no improvement in the real speed of road transport (congestion) or air transport (security checks) in the last 40 years. Vital household gadgets such as fridges, washing machines and central heating were all widespread before 1970.

Clearly, improvements in IT have the potential to improve productivity; we have seen it happen in areas such as distribution and retail. So why hasn't it happened in recent years?

One answer might be that wage growth has been so low; it is cheaper to employ workers than to invest in new technology. Another answer could be that modern economies are service- rather than manufacturing-dominated and it is simply harder to improve service productivity; a 10-minute haircut is not better (and probably worse) than an hour-long appointment. Perhaps the internet, with the instant distractions of e-mails, Twitter feeds and cat videos, actually reduces productivity for office workers.  Alternatively, we may simply be bad at measuring the improvement in service-sector productivity and later revisions may show that GDP is higher (and inflation lower) than we thought. We may discover this is the case in future, although it will need to be a big revision to explain the productivity slowdown.

In the meantime, central banks simply don't know the answer to these questions - how fast can the economy grow and, at what point will lower unemployment cause inflationary pressures? No wonder they sometimes seem adrift.