All the indicators suggest that UK gross domestic product is now growing again – after a lapse of four years in which it either fell or stagnated. And it has been doing so, up until now, without generating more inflation.

There are two key numbers that policy makers – and the British equivalent of US Federal Reserve watchers – need to know. The first is how fast the economy is actually growing. The second, which is far more difficult, is how much spare capacity there is in the economy.

The impression conveyed by the latest indicators is that GDP grew at an annualised rate of about 3 per cent– or more – in the third quarter of 2013, although we shall have to wait a couple of months for an official estimate. It would, however, be surprising if first impressions turned out to be all that wrong.

The problem about capacity is a more abstruse one. Capacity in the economist’s sense refers to the theoretical limit to the amount that an economy can produce at any given moment before inflation starts to rise as everything overheats. During recessions, economies tend to run below capacity. In a boom, they run above.

Radical critics of the coalition government’s so-called austerity policy like to point out that UK GDP is a good 15 per cent below the level it would have reached if growth had continued at its pre-2008 rate. There is, they say, therefore enormous unused capacity.

By way of reply, some of the government’s apologists say there is very little usable spare capacity after the ravages of the past few years. The economic damage done by the recession may have permanently lowered the level at which the economy can stably operate.

No one can be sure of the right answers. But there is a way of approaching them suggested by an English 18th century clergyman, the Reverend Thomas Bayes, in an essay first published in 1761 – two years after his death. This was at a time when the universities were moribund and the best way of doing academic work was often in the leisure of an ecclesiastical living. The question Bayes set himself was how to determine whether an event about which there is uncertainty actually happened.

To get the inquiry going, we need an estimate of the prior probability of it having happened. This might not be better than a rough guess – so long as it is honest. Bayes’ theorem deals with how the degree of confidence in an event or a theory rises as the evidence accumulates. If you are investigating a murder, the probability of someone’s guilt will rise if you find a motive, and then again if you discover the weapon in their glove box. Odds shift as evidence accumulates.

There is no need for this high-powered principle as far as the current UK growth rate is concerned. We shall soon find out whether annualised third-quarter growth was 3 per cent or more. There is not much case either for immediate stimulus or application of the brake.

But there is every need for Bayes in relation to the capacity question. If there is very little excess capacity the current upturn needs to be carefully watched to prevent the economy running up against the inflation barrier, say early next year. But if excess capacity is anything like 15 per cent, we can focus on keeping the upturn going.

We have the assurance of the Bank of England that, subject to certain conditions, monetary policy will not be tightened at least until unemployment drops from recent levels of 7.7 per cent to 7 per cent. But I do not find credible the bank’s projection that there is only a 50 per cent chance of that threshold being reached before the middle of 2016.

The underlying assumption must be that there is a great deal of capacity waiting to come into use, which does not quite conform to evidence on the ground. A picture of gradual economic expansion slowly eating up reserves of unused capacity may suit forecasters and policy makers. But that is not how things happen. It is much more likely either that expansion will eventually disappoint or that it will surge ahead very fast. The latter prospect will obviously not be harmful to the coalition – so we can expect Labour to warn of the vulnerability of any such expansion.

What can spoil the prospect of harmless party political games? Never take your eyes off sterling, which has so far held up. But veterans of past crises will know that this can change with great speed. The exchange rate is just a price that ought to be left to its own devices, but below a certain rate, panic sets in. Although Ed Balls, the shadow chancellor, understands these matters, it is not his job to give a pure economics lecture should things become unstuck.

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Letter in response to this column:

I foresee fewer probable birthdays / From Prof Wilfred Beckerman

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