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At the start of this month, we got the new government figures on U.S. workers’ wages before adjusting for inflation, and they looked pretty good – at least by the dismal standards of this historically weak American economic recovery. Yet if wages aren’t keeping up with prices, then it’s harder to argue convincingly that workers are gaining ground. And this morning we got the latest (government-generated) reminder that by this crucial measure, wage growth remains unimpressive.

According to the Labor Department’s latest report, American private sector wages after inflation were flat between April and May (whose numbers are still preliminary). That’s better than the (unrevised) 0.09 percent monthly dip in April, but it shouldn’t fall under anyone’s definition of “good.”

Year-on-year, real wages still aren’t killing it, either. The May annual advance was 1.42 percent. Between the previous Mays, it was 2.33 percent. From May, 2009 through May, 2014, inflation-adjusted private sector wages actually fell, so progress is being made once again. But its rate is already slowing; in January, real wages increased on-year by 2.09 percent.

And since the recovery technically began, in June, 2009, real private sector wages are up a total of 3.69 percent. That’s over a period of nearly seven years!

Manufacturing in May continued its recent trend of outperforming the rest of the private sector in wage growth both before and after inflation. The 0.09 percent sequential real rise was the slowest since December’s (which was only fractionally better). But year-on-year, manufacturing wages improved by 2.26 percent in May. That’s faster than both the 1.72 percent advance from May, 2014 to May, 2015, and than the January yearly increase of 2.07 percent.

In addition, these real wage increases are particularly welcome because manufacturing paychecks were shrinking in inflation-adjusted terms for so much of the recovery. Indeed, even with the recent spurt, they’re still up only 2.24 percent since the official June, 2009 recovery onset – much less than the private sector overall.

Moreover, manufacturing employment has been falling lately rather than rising. This development further reinforces the view that its recent wage strength stems largely from a practice of laying off less experienced (and lower-paid) employees, rather than from stronger worker bargaining power, and therefore a genuinely tighter labor market.

When the American economy as a whole, or manufacturing in particular, can foster historically adequate wage growth and hiring increases at the same time, the nation will be entitled to worry about wage inflation. But not one moment before.