April showers brought more hours. Hours of work, that is, as Friday morning’s employment report showed that employers added 211,000 jobs in April, as the unemployment rate ticked down to 4.4 percent, its lowest level since May 2007.Other measures of labor market slack also showed notable gains. The underemployment rate, at 8.6 percent, is about at the level I consider to be consistent with full employment. Long-term unemployment – which was very highly elevated throughout earlier years of this recovery – is back down to about 1 percent of the labor force; that’s the lowest since May 2008 and almost back to its pre-recessionary low point. The number of involuntary part-timers – the group that, along with the unemployed, drives the underemployment rate – is down almost 4 million from its peak (it was 9.2 million in September 2010 and was 5.3 million in April). So, we’re at full employment, right? By which I mean that highly desired state wherein the number of jobs matches up very tightly to the number of job seekers. If so, that would be an important advance along many dimensions: Full employment is the exception to the rule in recent decades. From the late 1940s to the late 1970s, we were at full employment 70 percent of the time. Since then, we’ve been there less than 30 percent of the time.So if we’re there, that’s long-awaited good news for workers, because tight labor markets deliver more of the bargaining power they lack in weaker labor markets. It’s no coincidence that the period when we were least likely to be at full employment corresponds to the period of real wage stagnation and rising inequality.It matters a lot for the Federal Reserve, because if we’re at full employment, then they must watch out for building wage pressures bleeding into price pressures. Which brings me to my punchline: For all the indicators that we’re at full employment, there’s a very important one that leaves me at least somewhat skeptical, and that is wait for it inflation! The main way economists decide we’re at full employment is by observing the correlation between inflation and unemployment. Here’s the alleged sequencing: First, the tight labor market leads to faster wage growth. That squeezes employers’ profit margins and thus leads them to pass as much of those increased labor costs forward to consumers, lifting inflation. Okay, but look at the figure below, which includes Friday morning’s results. Unemployment has indeed fallen to levels consistent with the Federal Reserve’s version of full employment, and wage growth has accelerated a bit. It was around 2 percent; it’s now about 2.5 percent. But inflation – I’m using the PCE core measure here, one favored by the Fed – hasn’t picked up much at all and remains below the Fed’s target rate of 2 percent, where it has been for years now. Now, if you’ve gone shopping for groceries or filled your tank recently, you’ve probably noticed higher prices than a few months ago. But the inflation line in the above figure leaves out food and energy prices, because they’re set in global markets and thus don’t really inform the labor market story. The next figure shows the yearly growth in the overall price index along with a bunch of measures of inflation. They’re drifting up, for sure. But not very quickly, suggesting either we’re not really at full employment yet or at least some of the links in that chain I talked about above are broken. Here’s what I think is going on, though I’ll have more to say about this Monday. (I hope the anticipation doesn’t ruin your weekend!) Inflation expectations are extremely “well-anchored,” meaning people expect the Fed to keep inflation around their 2 percent target, and that expectation becomes self-reinforcing. The tight labor market is delivering some wage growth but not all that much. As the yellow line in the first figure shows, wage acceleration doesn’t look so threatening. Even at low unemployment, in the non-unionized U.S. workforce, worker bargaining power is still constrained.Though it has come down off its recent peak, the dollar remains pretty strong in international markets, and this lowers inflation (by making imports cheaper). Most importantly, I suspect, wage growth isn’t bleeding into price growth, at least not very much.Why not? I’ll get into that next week, but my point today is that while I happily welcome and celebrate the much tightened job market, it’s hard to make a compelling case that we’re at full employment with inflation, while accelerating a touch, still largely puttering along.