Stephen Roach, former chief economist of Morgan Stanley, has been puzzled by what he calls the "productivity paradox". "Over the past five years," he notes,"from 2010 to 2014, annual US productivity growth has fallen to an average of 0.9%. It actually fell at a 2.6% annual rate in the two most recent quarters (in late 2014 and early 2015). Barring a major data revision, America's productivity renaissance seems to have run into serious trouble."

The graph of Year-on-Year growth of Nonfarm Business Sector: Real Output Per Hour of All Persons illustrates what he says.

Roach is not the only person to comment on this. Others include Gavyn Davies and Jon Hilsenrath.

But if you look at the right parameters there is no puzzle or paradox. The numbers are perfectly logical as we shall now see.

As economics textbooks never tire of telling you, a worker with a backhoe can dig more mud than a worker with a shovel. The backhoe of course costs much more than a shovel, which is to say that if you want productivity you need to make capital investments. And capital investment is exactly what has been lacking in the US economy since 2007, as the graph of real net private investment to real GDP shows.

If you consider an investment of 5% of GDP the minimum required to get the economy chugging properly, then the shortfall in investment since 2007 amounts to a total of 17.5%.

When unemployment is high and the labour participation rate low, low investment does not matter so much, because there is enough capital per worker to go around. Consider, for example, a factory with 10 employees and 10 CNC lathes. When the recession began the factory let one worker go. So it could cannibalise one lathe to provide spare parts for the other nine. Or it could use two lathes to provide spare parts for the other and run the eight lathes for nine shifts a week instead of eight.

But as workers are rehired this leeway vanishes. Meanwhile, the machines that have been flogged cry for maintenance or replacement. Naturally productivity per worker falls. The fall in productivity is actually a sign that the economy is returning to normal.

Roach quotes Robert Solow's comment in 1987 that "you can see the computer age everywhere except in the productivity statistics." He then goes on to add: "The productivity paradox seemed to be resolved in the 1990s, when America experienced a spectacular productivity renaissance. Average annual productivity growth in the country's nonfarm business sector accelerated to 2.5% from 1991 to 2007, from the 1.5% trend in the preceding 15 years. The benefits of the Internet Age had finally materialized. Concern about the paradox all but vanished."

But when you look at the graph of real net private investment to real GDP you realize that the high productivity simply reflected investment that ran above the normal rate for a long time.