Aditya Chakrabortty says UK manufacturing is in "demise". Tim Worstall says it ain't. Who's right?

It depends.

My chart shows manufacturing output since 1970. This shows that Tim is right in the sense that output is higher now than it was at any time before 1988. We're producing more now than we were in the 1960s or 70s, even though manufacturing jobs have halved since then.

However, in another sense Aditya is right. Output has actually fallen slightly since the late 80s; it's actually done even worse than agriculture in this time. This is not merely because we're comparing different points of the economic "cycle." At its low-point in 2009Q3, output was exactly the same as it was in at the low-point of the 1991 recession.

But of course, any comparison of two points is subject to sampling error. Maybe we've had some good luck in recent years, in which case the data overstates the fate of maufacturing. Or maybe we've had some bad, in which case it understates manufacturing's health.

We can measure this by estimating the standard error of trend growth rates. This tells us that in the last 25 years, trend growth has been zero per cent per year, with a standard error of 0.66 percentage points. So maybe Tim's right, maybe Aditya is.

Over the last 50 years, manufacturing output has grown by 0.7% per year, with a standard error of 0.6%. This means that although Tim is probably right over this period, there's a roughly 7-1 chance that Aditya is.

The point here is a simple one, but more familiar to scientists than partisans - that in noisy data even basic inferences are tricky.

Does this matter? I'm not sure. On the one hand, I'm not sure there's much to mourn in the decline of manufacturing jobs; very many of these were tedious, noisy and dangerous.

But on the other hand, perhaps we should worry about relative weakness in the production of internationally tradeable goods. Our large trade deficit is accompanied by a big general external deficit. And this could well be something to worry about, either because (when accompanied by high unemployment) it is a sign of a mismatch between demand and supply, or because it's a sign that domestic debt is rising.