Philip Hammond is copping flak for blaming the productivity slowdown on disabled workers. He said:

It is almost certainly the case that by increasing participation in the workforce, including far higher levels of participation by marginal groups and very high levels of engagement in the workforce, for example of disabled people – something we should be extremely proud of – may have had an impact on overall productivity measurements.

The problem with this is not that it’s offensive, but that it is mostly wrong.

The ONS estimates that since 2013 the number of disabled people in work has risen by over 20%, from 2.9m to 3.5m. This means they’ve increased from 9.7% of all workers to 10.8%.

What impact might this have had upon aggregate productivity?

Let’s say – for the sake of argument – that these additional 595,000 disabled workers are only one-third as productive as average workers.

Yes, I’m picking a number out of the air here. One the one hand, this is a very low estimate: you can work as well at a desk in a wheelchair as you can if you’ve got the use of your legs. But on the other hand, it might be that the extra disabled workers are unproductive and have been cajoled into work by the threat of benefit sanctions.

I don’t think, though that the gap can be very much greater than this. For this to be the case, one or both of two things would have to be true: that the able-bodied are massively productive; and/or that the newly-employed disabled are very unproductive. The former cannot be true because wages aren’t that high (unless you want to argue they are heavily exploited which I don’t think Hammond does). And the latter cannot be, because it would imply that employers have hired tens of thousands of people whose marginal product is below the minimum wage.

Let’s, then, run with that number just to get a Fermi estimate. If we do, then it implies that the additional disabled workers have reduced productivity by 1.2% over the last four years, or 0.3 percentage points per year.

During this time, total productivity has grown 0.35% per cent per year. That compares to average growth of 1.7% per cent per year in the 40 years. So there’s a productivity growth shortfall of 1.35 percentage points, of which increased employment of the disabled accounts for 0.3 percentage points. That’s just over one-fifth.

Which of course means that fourth-fifths is due to something else. We have countless candidates here (pdf): austerity, the legacy of the financial crisis in dampening animal spirits and investment; the slowdown in world trade which has slowed the rate of increase in the international division of labour; a slower rate of innovation, or a slower rate of diffusion of those innovations due to weak competition; and so on.

All these different explanations, though, have something in common: they attribute the productivity slowdown to either bad policy or to features of capitalism.

Which brings me to what is really wrong with Hammond’s claim. First, it reveals a lack of feel for numbers: any ball-park rough estimate attributes only a small fraction of the productivity slowdown to increased employment of the disabled. And secondly, it deflects blame for that slowdown away from where it really lies and onto our weakest and most vulnerable citizens.

The first fault is hard to forgive in a chancellor. The second is hard to forgive in a human being. And Hammond is supposed to be one of the more sensible members of this government.