Job seekers meet with recruiters during the Quad Cities career fair in Moline, Illinois, last year. (Daniel Acker/Bloomberg News)

How many times have you heard that Americans’ wages have stagnated? Countless commentators (including me) have repeated this complaint. Naturally, politicians of both parties — Hillary Clinton and Donald Trump — deplore it. It’s conventional wisdom that wage stagnation has contributed to the sluggish recovery and the downcast attitudes of millions.

But what if it’s not true?

A new study from the Federal Reserve Bank of San Francisco suggests just that. It concludes that widely cited figures showing stagnation are mostly a statistical fluke. Workers continuously employed in full-time jobs received wage increases higher than inflation from 2002 to 2015. Last year, the gain was a 3.5 percent increase after inflation, up from 1.2 percent in 2010.

Typically, the median wage — the wage exactly in the middle of all wages — is cited as evidence of stagnation. Indeed, the Fed study confirms this. Median wage increases have fluctuated around 2 percent, unadjusted for inflation. But the median wage is misleading, the report argues, because it’s heavily driven by demographic changes: an influx of young and part-time workers whose relatively low wages drag down the median; and the retirement of baby-boom workers whose relatively higher pay no longer lifts up the median.

“Exiting workers with higher wage levels are [being] replaced by entrants to full-time employment who earn less than the median wage,” says the study, which was done by economists Mary Daly and Benjamin Pyle of the San Francisco Fed and Bart Hobijn of Arizona State University. The result is that all workers, as judged by the median wage, seem to be treading water when many workers are actually receiving modest increases.

If corroborated, the study resolves a major mystery. Economic theory suggests that, as the recovery proceeded and labor markets tightened, wage increases should have accelerated as employers had to pay more to retain and attract workers. Yet annual gains in the median wage seemed stuck. Now, we know that the likely explanation is that demographic forces have obscured real wage gains for millions.

The implications are significant. For starters, the study urges de-emphasizing the median wage as an indicator of labor market conditions; relying on the wage changes for full-time workers would be more accurate. Indirectly, the study exerts pressure on the Fed to raise interest rates, because labor markets are tighter than indicated by the median wage (though even it has recently risen more rapidly).

The larger implication is that the study compromises the prevailing economic narrative, which emphasizes the stagnation of wages and living standards. Clearly, millions of households — especially the recently unemployed — have suffered large losses, and the gains of many others are underwhelming. But the impression that most people in the middle class are slipping backward seems overwrought. The anxiety about the future is real, but its causes must be more complicated than commonly thought.

Read more from Robert Samuelson's archive.

Read more on this topic:

Harold Meyerson: Why salaries don’t rise

Robert J. Samuelson: What’s behind wage stagnation?