The government reported today that the unemployment rate has fallen to 4.4%. To give you an idea of how low that is, consider that since 1971 the only period of lower unemployment was the tech boom of the late 1990s:
That's right, the current unemployment rate is well below the lowest rate of the 1980s boom, and equal to the lowest rate achieved during the 2007 housing boom.
The Fed aims for an unemployment rate that is roughly equal to the natural rate of unemployment. The problem with this policy is that the Fed doesn't have any way to precisely determine the natural rate.
A few years ago, the Fed estimated the natural rate of unemployment to be over 5%. Since that time, the actual rate has fallen to 4.4%. You might assume that the Fed would respond to that by tightening monetary policy with the intention of raising the unemployment rate back up over 5%. In fact, the Fed has not adopted that sort of unemployment target; instead, they've steadily reduced their estimate of the natural rate of unemployment, as the actual rate has fallen below their previous estimates.
The Fed's response to the unexpectedly sharp fall in unemployment is not quite as capricious as it might seem. They've looked at other data, and concluded that either they were wrong in the past, or that the natural rate may have fallen in recent years (or both). For instance, inflation, inflation forecasts (TIPS spreads), NGDP growth and nominal wage growth all seem quite subdued, consistent with an economy that is not overheating. (BTW, I prefer NGDP growth and wage growth over inflation, as an indicator of the condition of the economy.)
But if the Fed looked at these other indicators and concluded (correctly in my view) that they had overestimated the natural rate in the recent past, then that suggests those other variables may be better indicators of macroeconomic stability than unemployment itself. Instead of targeting unemployment (or the output gap) and then ignoring what it tells you when the NGDP growth rate conflicts with it, why not just target NGDP growth?
Note that this does not require abandoning the "dual mandate". The Fed might reasonably conclude that the best way to achieve stable prices and high employment is via NGDP targeting. That's certainly my view, and it's what I'd tell them if Congress asked me how their dual mandate could be most effectively achieved.
PS. Last year, commentators pointed to the elevated level of U-6 unemployment, which includes discouraged workers and part-timers that prefer full time work. Since then, however, the U-6 rate has fallen sharply, from 9.7% last September to 8.6% this April. So even the U-6 unemployment rate is now pretty close to normal.
PPS. I predict that RGDP growth, NGDP growth, and payroll employment growth will all slow sharply in 2018. A few years from now, the 2% RGDP growth achieved under President Obama will be seen as unusually high. (Actually, 1.9998%) That's because even that mediocre growth rate occurred during a period when the unemployment rate was falling sharply, a process that will likely end within a year.