I say this because between the mid-90s and 2010 there was a very strong relationship between the core inflation rate (which excludes food and energy) and the unemployment rate 12 months earlier. High unemployment led to low inflation, and low unemployment to high inflation. That's just as the textbook Phillips curve predicts. In fact, two-thirds of the variation in inflation between 1997 and 2010 could be explained solely by the unemployment rate 12 months previously.
However, inflation has recently been higher than this relationship would predict. A year ago, unemployment was 9.1 per cent. The 1997-2010 relationship predicts that this means core inflation should now be just 0.9 per cent. In fact, it's 2.1 per cent. There's a less than one in a thousand probability that this is due to mere chance.
The trade-off between inflation and unemployment has therefore worsened. This matters much more for UK investors than you might think. There has for years been a strong correlation (0.81 since 1988) between the dividend yield on the All-Share index and US inflation and unemployment, with rises in either being associated with a higher yield. This means that a 'bad' Phillips curve - high inflation for a given rate of unemployment - is bad for equity valuations. A big reason why shares are quite lowly priced now, therefore, lies in what's happening in the US labour market.
If share prices are to rise, the trade-off between US unemployment and inflation must improve. Which poses the question: why has it deteriorated?
It's not obviously because the Fed's easy money policies have raised inflation. In theory, loose monetary policy raises inflation by increased aggregate demand - but this should reduce unemployment. Monetary policy, in the short term at least, moves us along the Phillips curve. It doesn't move the curve itself. Which is what has happened.
A more theoretically acceptable possible explanation for this is that the US has suffered an adverse supply shock. If it becomes more expensive for companies to expand production, we'd expect both weak demand for labour and higher inflation, which is what we've got.
But it's not obvious what the adverse supply shock is. There are several suspects, but all have some kind of alibi, for example:
■ A fall in labour productivity. This has stagnated in the last year. But only in the last year. Since the recession began in early 2008, output per worker in the non-farm business sector has risen 7.6 per cent.
■ Rising commodity prices. However, the US coped well with these for much of the 2000s, so why should the much smaller rises we've had recently be so calamitous?
■ A lack of credit. If banks become more reluctant to finance companies' expansion, we'd expect to see less hiring and higher inflation as companies raise prices in the confidence their rivals won't be able to expand and undercut them. But this supply shock is being reversed. Having fallen by 25.1 per cent in the two years to October 2010, lending to industrial and commercial companies has risen 14.2 per cent in the last 12 months.
■ The effective labour supply has declined, in part because increased eligibility for unemployment insurance has reduced the incentives of the unemployed to find work. Although the University of Chicago's Casey Mulligan has proposed this idea, many other economists are contemptuous of it.
With the obvious supply shocks so questionable, there might be another explanation for the worse unemployment-inflation trade-off. To see it, look at what's happened to job openings, or vacancies. In June, there were 3.8m of these, equivalent to 2.7 per cent of total employment. This rate is lower than it was in the good times - consistent with the fall in demand for labour. But it's not hugely lower; at its peak in June 2007 the opening rate was 3.3 per cent.
This suggests that the unemployment rate is higher than you'd expect from looking at the vacancy rate. Between 2001 (when the data began) and December 2010, there was a huge correlation (minus 0.88) between the opening rate and unemployment. Had this relationship continued, the unemployment rate now would be around 6 per cent. But it's two percentage points higher than that. This means the Beveridge curve - the relationship between unemployment and vacancies has worsened.
One reason for this is that there's a mismatch between the unemployed and labour demand. Unemployed building workers, for example, cannot quickly retrain as IT workers. Such a mismatch can cause unemployment to be high while inflation is around average. Economists at the New York Fed estimate that a worsening mismatch can explain around 1.2 percentage points of the rise in unemployment since 2006. That's only a small part of the total increase. But it's quite a large part of the rise in unemployment consistent with inflation being around 2 per cent.
But here's the thing. A worse mismatch is quite common after a recession. In the mid-70s, 1983-84 and in the early 90s inflation was higher than you'd expect from looking at lagged unemployment. This is consistent with the Phillips and Beveridge curves worsening. It's also consistent with the fact that recessions don't just reduce aggregate demand, but also jumble up the patterns of supply and demand by hurting some industries more than others and so creating a coexistence of unemployment and vacancies for which some unemployed are unsuited.
And here's the good news. Such mismatches tend to be temporary. In the late 70s, mid-80s and mid-90s, both unemployment and inflation fell as the degree of mismatch declined; this can happen either as hard-hit industries recover or as workers relocate to healthier sectors. Timothy Taylor, an economist at Macalester College in St Paul, Minnesota, says: "Whoever is elected president in November 2012 will look like an economic policy genius by early in 2014. It won't be so much because of any policies enacted during that time, but just a matter of the slow economic adjustment of the Beveridge curve."
This could be fantastic news for shares, because a fall in unemployment at a given level of inflation is traditionally associated with higher equity valuations. The post-1988 relationship between the All-Share dividend yield and US unemployment suggests that a one percentage point fall in US unemployment would be associated with a rise in share prices of over 8 per cent. And this is only the valuation effect. It's before considering any increase in dividends resulting from the economic growth that's associated with falling joblessness.
In this sense, the apparently abstruse question of the fate of the US Beveridge curve matters a lot for UK investors. And - unless politicians foul things up by failing to draw back from the 'fiscal cliff' - it might just give us a reason for optimism.
