WHEN you have excluded the impossible, observed Sherlock Holmes (the old one, that is), whatever remains, however unlikely, must be the truth.
The mystery of the growth in employment is one worthy of the great detective. Nothing could have been more unlikely than the recovery being led by jobs. Unemployment, said the economics textbooks, is a "lagging indicator", meaning it is one of the last things to improve when an economy starts growing after recession.
Once again, the textbooks are being torn up. Last week, I found myself at an address by Tim Harford, author of the runaway best-seller 'The Undercover Economist', a book that put the price of a cappuccino at the heart of micro-economics.
He was talking about the remarkable career of Bill Phillips, originator of the 'Phillips Curve', one of the best-known gizmos in economics. Published in 1958, it showed a clear connection between unemployment and inflation. The higher the one, the lower the other.
Inflation was good for jobs, it seemed. That held out the glorious prospect that there was a certain level of inflation that would provide full employment and there would be no need to let prices rise faster than that.
Well, perhaps not full employment. Later work developed NAIRU, "the non-inflationary rate of unemployment", below which, the monetarist economists said, it was better not to go. That textbook too requires revision.
The 1970s oil crisis showed that high inflation and high unemployment could go together. The 2000s boom showed that low inflation and low unemployment could also go together.
Many analysts and central bankers thought this 'Great Moderation' proved they had finally cracked the long-standing problem. Except that it turned out to be a marriage made in hell.
The fascinating thing about Mr Harford's talk was that Bill Phillips didn't really trust his curve. A self-taught engineer from rural New Zealand who took to economics and built a water-powered model of the UK economy (that won him a professorship), he did not believe in perpetual motion machines.
He would have liked more time to study the data but it looked too much like a perpetual motion machine for others to let him keep it under wraps.
Now the crash has produced a new, intriguing version of the curve. The different employment experiences of the UK and US economies appear to point to another connection, one between employment and "real" wages – wages after allowing for inflation.
With actual wages fairly static, real weekly earnings have fallen by a massive 8pc on average.
In the US, real wages are up 2pc. Growth is much better, with real output per worker 7pc higher than in 2007, while in the UK it is down by almost 4pc.
But look along the other axis of the curve – employment. The extraordinary thing is that UK employment is 2pc higher than in 2008, while the US still has 1pc fewer jobs than it did then.
Economists do not like the fall in productivity represented by less output per worker because it reduces overall incomes, but most people would choose jobs first, especially in these circumstances.
All very curious. This is the opposite of a traditional Phillips curve. For a bit of fun, I thought I would look at the equivalent Irish figures. Our employment experience has been quite different from either the British or the American, which is hardly surprising, given the depth of the crash.
Employment began growing only in 2012 – three years later than in the other two economies . But it then put on quite a spurt, adding 58,000 jobs last year, which is a 3pc increase. However, employment is still 12pc below 2008, which makes the US shortfall seem puny and the British experience quite remarkable.
In both those countries, wages rose by just over 1.5pc a year. But British inflation, at 3pc a year, was twice the US figure, giving rise to that difference in real wages.
Ireland is different again. Hourly earnings fell by more than 2pc since 2008, while prices rose by just 1pc. Real earnings are therefore down 3pc, which is about half the UK fall but five percentage points greater than the US figure.
Research quoted in last week's 'Economist' magazine found that in financial crashes, because actual wages tend not to fall, jobs recover only if inflation is high enough to make real wages decline. In Ireland, wages did fall, so perhaps that does have something to do with the unexpected increase in jobs, even though inflation was very subdued.
Or perhaps not. Ireland is different in lots of ways. In a recent note, Davy Research argued that the "productivity puzzle" – employment increasing while output is weak, as in the UK – could be explained just by the "patent cliff", where the value of pharmaceutical production plummets as drugs come off patent.
The implication is that the economy is doing better than the headline figures suggest. Davy analysts think it may grow by 3pc this year and are considering an increase in their 1.5pc forecast for personal spending growth. Trends like those would explain a good deal of the jobs puzzle.
The Central Statistics Office surveys found that employment increases are pretty reliable, but the estimates for different sectors are much more uncertain. Analysts think the large increases in the agricultural sector are a statistical quirk but that means other sectors are doing better than the figures say.
One of these may be construction, where rapid growth would not be surprising, coming off what is not a phenomenally low base. Finance Minister Michael Noonan indicated last week that his mind is moving in that direction.
The much-maligned – even if justly maligned – building industry now has the potential to provide badly needed jobs while still remaining a relatively small sector by past standards.
Mr Noonan also expressed concern about wage demands and the threatened strike by the shock troops of the trade union movement, the TEEU. One does not have to believe in fancy new curves of real wages and unemployment to think that trying to restore the fall in real incomes while unemployment is over 12pc is bad timing.
Trade unions do not think that. They argue that higher wages will generate jobs from the extra spending of that income.
It would be great if it were true but, just as with Bill Phillips, it seems too much like a perpetual motion machine to be entirely convincing.