Which is the most realistic production function – the Cobb-Douglas or Leontief? This sounds like an abstruse question. But it is key to assessing one increasingly common explanation for the fall in productivity or - what is the same thing – the resilience of employment in the face of the fall in output since the start of the recession in 2008.
Sir Samuel Brittan says: "Falling real wages have priced workers into jobs, or least enabled them to stay in employment." And Paul Gregg says: "In the current environment it is easier, cheaper and less risky to hire to meet demand rather than invest."
The truth of this theory rests upon the nature of production functions. In Cobb-Douglas functions, labour and capital are easily substitutable and so if labour becomes cheap relative to capital, firms will hire more of it, thus increasing the labour-capital ratio and - ceteris paribus - depressing labour productivity. However, there's another sort of production function - the Leontief. In this, there's no substitutability between capital and labour. A given number of machines require a given number of workers to operate them. The capital-labour ratio is then fixed, until new machines are installed.
The Gregg-Brittan theory requires there to be many Cobb-Douglas functions, with high levels of substitutability. But are there? Say you want to build more car engines. Do you really hire more men to make them by hand? Or don't you need more precision tools too? The only way you can raise output by raising the labour-capital ratio is to put on an extra shift – which is quite an investment. If you're a retailer, do you think "I can't afford to open another store, so I'll employ more checkout assistants"? Or do you just have you existing staff work harder?
The answers to these questions will vary from firm to firm, and according to the size of the change in demand. My suspicion, though, is that technical limits to the degree of substitutability limit how far lower real wages can keep staff in work.
Let's do some sums. Between 2008Q1 and 2012Q2 real GDP fell 4.8 per cent. If productivity had grown at its rate of the previous 20 years (2.2 per cent a year), then we'd expect that total hours worked would have fallen 17.5 per cent. In fact, they fell only 1.5 per cent. Labour demand, then, is 16 per cent higher than it "should" be. Can lower real wages explain this?
Since 2008Q1, these have risen 6.1 per cent in nominal terms. But the GDP deflator has risen 9.4 per cent, so real wages have dropped 3.3 per cent. To raise labour demand by 16 per cent requires a price elasticity of demand of 4.8 (16 divided by 3.3). This is surely far too high.
One reason I say this is simple precedent. In the early 00s, real wages rose quite sharply. If capital and labour are substitutable, this should have led firms to economize on staff and so raise labour productivity. But productivity trended down. If you want to go back further, real wages fell in the late 70s - but we didn't get the productivity stagnation then that we have now.
Granted, lower real wages might explain some of the productivity fall; production functions aren't entirely Leontief-type. But I doubt they can explain a lot of it. So what can? Here are three possibilities:
■ Banks have been more loath to foreclose on struggling firms in this recession than they were in earlier ones. This means low-productivity "zombie firms" have kept going, which has dragged down average productivity.
■ A high productivity sector has shrunk, thus reducing GDP per worker. I'm thinking here not of financial services but of North Sea production. Oil and gas output fell 40 per cent between 2008Q1 and 2012Q2.
■ Firms have hoarded labour. This gives us another sense in which workers might have priced themselves into jobs. The lower are real wages, the cheaper it is to retain otherwise unproductive staff in the hope of an upturn in demand. The option value of retaining staff is greater, the lower is their cost.
I don't say all this to offer definitive explanations. I'm merely suggesting that the productivity puzzle is a deep one.