THE news that average wages grew by 2.9% in December, the final full month of the Obama presidency, provides more evidence that America’s labour market is heating up. For some time, America has been creating plentiful jobs—2016 was the fifth consecutive year with more than 2m job gains. But wage growth has been weak enough to cast doubt on the labour market’s strength. A commonly cited reason for paltry pay rises was the number of 25- to 54-year-olds—dubbed “prime age” workers—who had stopped looking for work after the recession, and hence were no longer counted as unemployed. Wages, the argument went, would not pick up until they were encouraged back to work.

With the average pay-cheque now growing faster than at any time since 2009—when layoffs of low-paid workers were artificially boosting average wages—that argument is getting harder to make. In fact, 2.9% wage growth may be close to the limit of what the economy can produce without sparking inflation. Prime-age labour-market participation surged in the past year or so, and has now recovered about a third of its fall after the recession. Some of the remaining shortfall is almost certainly structural, rather than something stimulus, such as lower interest rates, can fix. After all, the participation of prime-age men has been falling since the 1960s, suggesting supply-side factors, such as the declining value of the skills of uneducated workers, are at work. And as the returns to schooling rise, you would naturally expect more people to choose to study rather than work.

Productivity growth, meanwhile, has been slow for a decade. That limits the potential for wage gains that do not spark inflation. Demographic forces are a further brake on how fast average wages can rise sustainably. The onset of the recession coincided with the first retirements of the baby-boom generation. As high-earners at the end of their careers have left the workforce, they have been replaced by low-earning younger folk. According to researchers at the San Francisco Fed, that has helped keep average pay rates down. That, too, suggests a lower speed-limit for wage growth than before the financial crisis, and hence that December’s wage growth indicates a labour market at close to full health.

That recovery is to be cheered. But the timing is frustrating for the outgoing president. If paychecks swell in 2017, Donald Trump will claim the credit, despite the fact that wage growth first began picking up in 2015 (see chart). During the campaign, Mr Trump cast doubt on official labour-market statistics, saying that they painted a rosy picture of the economy. Next year he will probably champion them.