It took barely a month for the bubble of optimism that formed over the American economy at the start of the year to deflate. Job growth slowed sharply in December, and stayed weak in January, suggesting more than bad weather was to blame.

The unemployment rate, though, tells a much cheerier story: it dropped to 6.6% in January from 7% in November. Indeed, it could soon hit the Federal Reserve’s 6.5% threshold at which it may consider raising interest rates.

The jobless number has been sending a strangely upbeat message about America’s recovery for some years now. Yet the Fed and other researchers have downplayed its significance, linking the rate less to buoyant demand for labour than to stagnant supply, as discouraged workers stop hunting for jobs. On February 11th Janet Yellen, in her inaugural appearance before Congress as chairman of the Fed, called the recovery in the labour market “far from complete” and averred that she would consider “more than the unemployment rate” in deciding when to declare it healed.

Listen to the numbers

Even so, recent research suggests the unemployment rate is saying something important. It’s just that the message is a depressing one: America’s labour supply may be permanently stunted. If so that would mean that the economy is operating closer to potential—using all available capital and labour—than generally thought, and that there is less downward pressure on inflation than the Fed has assumed.

Figuring out the gap between actual and potential output is tricky because potential, always hard to discern, is more uncertain than usual. In a recent report Lewis Alexander of Nomura Securities, a bank, calculated the output gap using three different labour market indicators (see chart). The proportion of people with jobs plunged from 63% of the population in late 2007 to below 59% in 2009. It has barely budged since, suggesting the output gap has not closed at all. The unemployment rate, in contrast, is 1.1 percentage points above its estimated “natural rate” of 5.5%, suggesting most of the output gap has disappeared. Finally, if one looks just at those who have been unemployed for less than six months, the output gap appears to have closed completely.

Deciding which measure to use involves determining why so many people have left the labour force. The labour participation rate (measuring those in work or looking for it) is down to 63% from 66% in 2007. The Congressional Budget Office (CBO) attributes just a third of that decrease to discouraged workers who have temporarily stopped looking for jobs. The remainder it ascribes to demographics, as ageing baby boomers retire early, or to people who have gone jobless for so long they have permanently given up looking. This is one reason the CBO has sharply revised down its estimate of America’s potential, and with it, the size of the output gap, which it now puts at a little over 4% of GDP. Had its estimates of the economy’s potential not shrunk since 2008, that gap would be 10% of GDP.

So if the unemployment rate is understating the output gap, it is not by much. Indeed, for the Fed’s purposes, it may even be overstating the gap. That’s because the longer someone is unemployed, the less attention they get from recruiters and the less vigorously they hunt for work. As a result they are not much of a curb on wages.

In 2005 Ricardo Llaudes of the European Central Bank found that short-term unemployment predicted inflation in European economies better than total unemployment. This was less true for America, where short-term and long-term unemployment have tended to move together. But the two have recently parted ways, with long-term unemployment declining much more slowly.

Several researchers from the Federal Reserve Bank of New York recently re-examined the relationship and found that short-term unemployment better explained why wage growth has not fallen further. To be sure, inflation itself has fallen to a little over 1%, well below the Fed’s 2% target. But a report accompanying Ms Yellen’s testimony attributed some of that to falling commodity prices and a stronger dollar. It noted that growth in wages has been weak but that unit labour costs, which adjust wages for productivity, are growing at about the same rate as before the recession.

This doesn’t mean the Fed has to raise interest rates now, given how low inflation is. But if inflation moves up, “this debate becomes front and centre, right away,” says Mr Alexander.

The Fed could, of course, let inflation rise above its target in hopes of getting unemployment down further. Ms Yellen played a central role in the adoption of a strategy that allows for that. But it may be fighting a losing battle. Unpublished research by Alan Krueger of Princeton University finds that in 2010 about 18% of the long-term unemployed quit the workforce each month. That has since risen to 24%. Meanwhile, the rate at which they find work has edged down to 10% per month. The work they find is often transitory or part-time. Thus, with each passing month, more of the unemployed are drifting to the fringes of the labour market than re-entering it. More monetary and fiscal stimulus may have saved them a few years ago, but are of much less help now.

Policymakers will need to put more effort into making the long-term unemployed once again employable. Barack Obama recently persuaded several hundred companies to pledge not to discriminate against them. Unfortunately that will probably not be nearly enough.