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Despite the sudden recent spate of handwringing (or crocodile tears?) that’s broken out lately over the (long overdue) discovery that American wages continue to go essentially nowhere, almost no one seems to have noticed that the Bureau of Labor Statistics just came out with its first set of inflation-adjusted wage numbers for December. They’re especially interesting because they show how tricky it gets to judge wage trends, and by extension how tight or loose the labor market really is, when inflation is significantly weakening.

Most observers seem to assume that crashing oil prices will, among other things, have the effect of pushing up inflation-adjusted wages for the time being because the cheaper oil will wind up putting more money in workers’ pockets. And if you believe, like me, that inflation-adjusted (also called “real” or “constant dollar”) wages are the best measure of a workers’ real worth, then it’s clear that’s a positive.

At the same time, this kind of real wage growth shouldn’t be misinterpreted as a sign that the American employment scene is looking much brighter – especially since we could still be just at the beginning of a period of unusually low inflation. For the data show no signs that employers are loosening their wallets because the workers they need are becoming so incredibly hard to find.

Here’s how we know this. The new Labor Department data show that in the last few months, inflation-adjusted wages have shown some signs of acceleration. After essentially flat-lining on a month-to-month basis from November, 2013 through July, real wages rose by 0.58 percent in August. They languished in September and October, but ticked back up by 0.58 percent in November, and by another 0.10 percent in December. (The last two readings are still preliminary.)

Here’s what happened to actual wages, without adjusting for inflation. These wages – which tell us what employers are actually paying – were weak for the first half of 2014, but generally stronger than real wages (which is of course to be expected). But August’s 0.58 percent inflation-adjusted wage increase was greater than the 0.33 percent pre-inflation increase.

In September and October, the more conventional relationship returned, but when the oil price drop gained momentum, real wages began outperforming again. In November, when they increased by 0.58 percent, nominal wages rose by only 0.24 percent. In December, when the real wage increase slowed to 0.10 percent, nominal wages actually fell. That 0.20 percent decrease was the first such monthly decline since July, 2013.

You can see the same pattern in recent year-on-year real and nominal wage changes, but in this case, it shows up as a narrowing of the gap between the increases. Here’s what I mean. From August, 2013 to August, 2014, pre-inflation wages rose by 2.12 percent, but inflation-adjusted wages were up only 0.49 percent. By December, the year-on-year pre-inflation wage gain had slowed to 1.65 percent. But the real wage gain had risen to 0.97 percent.

So clearly, American businesses lately haven’t been writing bigger paychecks for workers because they’re getting anxious about retaining them or finding new ones. Instead, it mainly appears that they haven’t adjusted yet to the latest bout of renewed price weakness. If most employers are confident that price trends will normalize sooner rather than later, they may resume the pattern that’s prevailed during the recovery of handing out very modest nominal and real wage increases. If they foresee continued or even greater price weakness, they’re could well start a period of nominal wage cuts, especially if price stagnation or even deflation starts hurting sales and profits.

As opposed to this conjecture, however, it’s clear that the signs seen to date of stronger real wage growth really are something of a statistical artifice (at least as a sign of fundamental labor market health), and that American workers are still a long way from being out of the woods.