I often see Fed officials claiming that the fall in unemployment means that they need to raise interest rates. Sometimes this is based on "Phillips Curve" thinking---the (false) idea that inflation is caused by a booming economy. In fact, the relationship between economic growth and inflation depends on the nature of the shock hitting the economy. A positive supply shock causes growth and lower inflation, while a positive demand shock causes growth and higher inflation. Only in the latter case does growth require the Fed to raise interest rates.
Consider the following AS/AD diagram, right out of EC101:
Between 2007 and 2009, the AD curve shifted to the left. Output and inflation both fell. Since 2009, the SRAS curve has been gradually shifting to the right, as wage growth moderated from its normal 3.5% to about 2%/year. Notice that this sort of growth is not inflationary.
That doesn't mean that the Fed should not raise rates this year, it does have a dual mandate. However it should not pay much attention to the unemployment rate, but rather should focus on variables like NGDP growth and wage growth. Early in the year there was some indication that wage growth was accelerating. But that no longer seems to be the case, and the latest figures show exactly 2.0% hourly wage growth over the past 12 months. That's the same rate as we've been seeing for the past 6 years, and is too low for the Fed to hit its 2% inflation target. There is no justification for raising interest rates when hourly nominal wage growth is below 2.3% on a 12-month basis. None.
Sub-2% price inflation during a period of low unemployment could be justified on "dual mandate" grounds, where the Fed would then run inflation above 2% during high unemployment periods. In fact, the Fed has tended to do the opposite in recent decades, running inflation lower during recessions than booms. And they still have not changed their (interest rate) operating procedures to address this problem. Inflation is very likely to fall during the next recession, just as in the past few recessions. If we go into the next recession with 1.5% inflation, and then it falls further, then the Fed will lose credibility. Fed officials need to think very hard about their long run strategy to hit 2% inflation. Right now I don't see a plan, other than Fed officials crossing their fingers.
Back in 2011 the Swedish Riksbank temporarily ignored its 2% inflation mandate to fight asset bubbles. That tight money policy pushed Sweden into deflation, and they had to reverse course. Today they cut rates again, to minus 0.375%, in an attempt to get inflation back up to target. Nick Rowe has a recent post that explains how "a stitch in time can save nine." If the Fed isn't careful it might end up repeating the mistakes of the Riksbank (and ECB in 2011, and BOJ in 2000 and 2006.)