In the day job, I say that if productivity hadn't fallen since the end of 2007, there would now be three million fewer people in work. This is just a simple mathematical claim. But it raises the question: what would have happened if productivity had kept growing at its pre-2007 rate? Would we really now have almost six million unemployed, or would there have been some offsetting mechanism to create jobs?

One obvious possibility is that if productivity had kept growing, we would have seen more quantitative easing. This is because inflation would have been much lower, partly because firms' labour costs would have been lower as they sacked more workers, and partly because higher unemployment would have depressed consumer spending.

But it's unlikely that QE alone would have created so many jobs. The Bank estimates (pdf) that the first ''200bn of QE raised GDP by 1.5-2%. This suggests that, to create three million jobs - a rise in employment of 12% - we'd have needed almost ''1.4 trillion of QE. That would have required the Bank to have bought every gilt in existence, and then some. Which is a big ask*.

Another possibility is that fiscal policy would have been looser, which would have created jobs. But again, this is unlikely. Higher unemployment might well have raised the deficit relative to what it would otherwise have been, causing the government to (wrongly) fear it was too big.

It's unlikely, therefore, that policy responses to higher unemployment would have been sufficient. But are there any endogenous responses to higher productivity and unemployment that would have tended to create jobs?

You might think that the very fact that workers are more productive in this alternative universe would cause firms to hire more of them. But things aren't so simple. Firms only hire if they anticipate sufficient demand for the additional output. And where would this demand come from? The tendency for higher unemploymentwould depress consumer spending. On the other hand, it's likely that business investment would be higher - not least because a world of growing productivity is a world in which there are more investment opportunities and easier access to finance. But as business investment is only 8.3% of GDP, it's unlikely that it would be so much higher as to create three million jobs.

Another possibility is that the tendency towards higher unemployment would have depressed wages even more, and this would have encouraged job creation. I suspect, though, that this would have been only a small benefit given that the price-elasticity of demand for labour, for given aggregate demand, is quite low; we know this because the minimum wage did not destroy that many jobs.

Another possibility is that sterling would have fallen more than it did. But again, this is little help given the low price elasticity of demand for exports - we didn't get an export boom after sterling fell 20% in late 2008 - and their relatively low labour content.

My conclusion here is simple. It's very easy to imagine that, if productivity hadn't fallen, we would have much higher unemployment now.

Such a situation, though, would probably be even worse than the one we're in. Not only would we have the human misery of greater joblessness, but we'd also quite possibly have serious political unrest.

Which brings me to a paradox. There is no question that, in the long-run, higher productivity is a huge blessing; it's this, and pretty much this alone, that makes us rich. But in the short-run, it is not such a good thing. I'm not at all sure how to reconcile these.

* A larger obstacle is that it would have required nominal corporate borrowing costs to fall below zero.