As notable as the recent rise in state and local minimum wages has been to this effect, it has probably not been as important as the tightening labor market. In a tight labor market, firms have to compete more to hire and retain the workers they need, which among other things gives those workers more bargaining power to bid up their wages.

The Federal Reserve chair, Jerome Powell, has argued that reaching workers traditionally “left behind” is one of the most compelling reasons to sustain the expansion for as long as possible.

Still, this analysis suggests these minimum-wage increases are having a meaningful impact on wages, at least for the employed workers who benefit from them. For the bottom third, state and local minimum wage increases have probably been the difference between the wage growth just before the economic crisis and the wage growth that is now above that pace.

But that benefit also brings with it a cautionary note for policymakers.

Economists look to wages as one thermometer of how hot the economy is getting: Accelerating wages may eventually spill over into higher prices and signal an economy at capacity, though this hasn’t happened yet in this recovery.

But these continuing increases to state and local minimum wages — and any possible future action at the federal level — could skew wage data, making the American labor market look tighter than it actually is.

The recent rise in minimum wages, although not producing a giant effect, still might suggest overall wage growth is progressing about a year further along than the reality. For low-wage workers, whom policymakers are citing more often, the minimum wage effect can be worth closer to two years’ worth of wage acceleration.

The risk of misdiagnosing an overheating economy is one reason it’s important to be clear and precise about what role minimum wage increases have played in recent wage growth: They have been important, but they’re most likely not the biggest factor.