There's a lot of discussion about the natural rate of unemployment. Some think we are already close to the natural rate. Others think the labor market is much weaker than the official 6.6% figure would suggest. Evan Soltas has what looks to me like the best analysis of the situation:
The fact that the unemployment rate appears to be a robust predictor of the quit rate both before and after the 2007-2009 recession suggests that the unemployment rate, our imperfect observation of labor-market tightness, is a close proxy for the tightness people think is important when they decide to quit or not to quit.
Evan calls the labor market "tight." I probably wouldn't use that term, but we both agree that 6.6% unemployment is a pretty fair characterization of the actual state of the labor market. The natural rate of unemployment has not changed much in recent decades.
In May 1975 the unemployment rate was 9.0%. And yet strangely enough monetary policy was actually too loose at the time. NGDP grew at a 9.1% rate in the second quarter of 1975, and an astounding 12.1% over the next 4 quarters. The high inflation of the 1970s had nothing to do with supply shocks (RGDP growth was normal) it was simply excessively fast NGDP growth, plain and simple. Easy money.
The Fed should have tried to gradually reduce the NGDP growth rate, over a period over years. Instead the problem got worse after 1975. Indeed even Volcker initially made the problem worse. His sharp swing toward easy money in the run-up to the 1980 election pushed NGDP growth to an annual rate of 19.91% in late 1980 and early 1981. (No, that's not a typo.) Only after Reagan took office did Volcker finally decide to bring inflation down.
The central bank can never really know where the natural rate of unemployment is. If they had a proper monetary policy they would not even pay any attention to unemployment.