It was widely reported yesterday that the word “patient” was dropped from the Federal Reserve statement on monetary policy. But too much focus on this one word might lead one to miss the forest through the trees.

Yes, the Fed no longer is committed to official “patience.” In practice that’s their way of saying we could raise rates at any time in coming meetings without giving you (and by “you,” I mean “markets”) any more warning. This has been widely (and reasonably) interpreted to mean that such a rate increase is coming soon.

Such a rate increase would be a mistake. The labor market is clearly improving, with unemployment falling and job growth accelerating in 2014. But the point of raising interest rates shouldn’t, of course, be simply to sabotage the labor market anytime it starts generating lots of jobs and reducing unemployment. The point of rate hikes in the face of economic strength is supposed to be preventing incipient inflationary pressures. But there’s an important link in the chain between falling unemployment and accelerating inflation: wages have to start accelerating. Importantly, they need to start accelerating faster than the sum of the Fed’s inflation target plus productivity growth.

What’s the logic of this wage target? For one, note that nominal (i.e., not inflation-adjusted) wage growth that simply equals productivity growth puts no upward pressure on prices at all. Say that wages rise by 2 percent but productivity rises by 2 percent too. What has happened to the cost per unit of output? Nothing. Hourly wages are up 2 percent, but the amount produced in each hour of work has risen by 2 percent as well, so costs per unit of output haven’t budged. Assume trend productivity growth of around 1.5-2 percent, and this means that only nominal wage growth over 1.5-2 percent puts any upward pressure on prices at all.

And the Fed isn’t committed to zero upward pressure on prices—they say they’re comfortable with 2 percent inflation (I’d argue they should be comfortable with inflation well above that, up to 5 percent, but we’ll take their target as given for now). That means nominal wage growth can be 2 percent higher than trend productivity growth before wages are threatening to put any upward pressure on prices above the Fed’s inflation target—wage growth of 3.5 to 4 percent, nearly double what it has been since the recovery began. Out handy nominal wage tracker covers a lot of this ground and provides the numbers.

So, the economic rationale for a rate increase that comes sooner rather than later just isn’t there. What would be the downside of such a premature rate increase? A continuation of the near stagnation in inflation-adjusted wage growth for the vast majority of American workers, and a missed chance to let the economy actually self-correct against some of the rise in income inequality that has characterized the past generation, by generating low rates of unemployment. Simply put, low- and moderate- wage workers need low rates of unemployment to give them the bargaining power they need to see serious real wage growth. It’s no coincidence that the only episode of across-the-board real wage growth for American workers in the past generation was the very tight labor markets of the late 1990s—when unemployment actually averaged 4.1 percent for two full years. And given that so many other policy levers that have provided some bargaining power in the past have been kicked away (usually through intentional policy decisions), these workers need low unemployment rates more than ever.

So, a rate increase that came sooner rather than later and short-circuited a recovery before serious wage growth began would be a bad thing. But do yesterday’s events really make it more likely? Here’s where I think there’s been excess focus on (im)patience in the Fed’s statement.

It’s true that the Fed dropped the word “patience,” giving up some rhetorical ground to those who’d like to see these rate increases happen sooner. But the sweep of Chair Yellen’s remarks yesterday signaled to me pretty clearly that she doesn’t think economic conditions merit an increase any sooner today than they did in the last couple of Fed meetings. She pointed to the economy currently undershooting the 2 percent inflation target, said that FOMC participants thought that overall economic slack may have increased in recent months, and noted pointedly “just because we removed the word ‘patient’ doesn’t mean we’re going to be impatient.” And she did all of this without even dwelling on recent strength in the U.S. dollar, which will drag on growth and push down inflation.

Finally, and most importantly, in the economic projections released with yesterday’s statement, the Fed lowered their estimate of the natural rate of unemployment—the lowest rate consistent with stable inflation – from roughly 5.4 to 5.1. This was an evidence-based acknowledgement of reality (though it likely doesn’t go far enough). We’re currently awfully close to 5.4 percent unemployment, yet wage increases that might push up inflation are nowhere in sight. So, it makes sense to think “hmm, maybe the natural rate really isn’t 5.4 percent.”

Will the Fed eventually succumb to pressure to raise rates prematurely? Maybe. And it would be a mistake. But luckily, simply dropping the word “patient” from the monetary policy statement is not a guarantee that it will happen.