Here is the graph that compares insured unemployment to total unemployment. There is a typical shape of this relationship over business cycles and over time. The unemployment rate has remained elevated as insured unemployment has tested all-time lows, partly due to a contingent of very long term unemployed (with unemployment durations of over 2 years) and partly due to a persistently elevated level of uninsured unemployment among shorter durations. For a while, there was a pretty linear trend of about 0.05% of the unusual long term unemployment declining each month. It seemed like this had possibly leveled out. But, as a close-up view of this graph shows, there was one divergence in July 2014 of about 0.3%, where the expected unemployment rate went down and the reported unemployment rate went up. In the months before and after that, reported unemployment has actually followed very closely with the unemployment we would expect from continued claims. If we add 0.3% to the modeled rate this month, that gives us an expected unemployment rate of 5.3%.
(On each of those graphs, the April insured unemployed level is as reported, and the 5.3% unemployment rate is manually input to show where this relationship would fall for April if unemployment comes in at 5.3%.)
Unemployment at the longer durations has been declining at a healthy pace over the past couple of months. This pairs nicely with the recent decline in continued claims as a strong statement about the breadth of strength in the labor market.
In addition, here is the model of unusual long term unemployment which confirms the trend that has continued in the insured vs. total unemployment relationship. This continues to converge back to historical norms as long term unemployment declines.
Here we can also see the persistent unemployment level at lower durations. Insured unemployment is near all-time lows, but unemployment duration at shorter durations is still elevated enough to inflate the expected long term unemployment levels. The expected level of long term unemployment should be down to 0.5% by now compared to recent recoveries, but it is still at 1%. And, on top of that, there are another 0.6-0.7% of workers at very long durations. It appears that the very long term unemployment has a shorter "half-life" than the persistent short term unemployment. Some of the increased durations in short term unemployment are demographic in nature, so this may bottom out in the 0.7-0.8% range. But, those same demographic trends should pull down employment turnover in general, so that the unemployment rate should still be capable of reaching 4% or less if the recovery is allowed to age.
Just as a clarification, I don't consider a strong labor market to be inflationary. I think a strong labor market tends to coincide with strong real economic growth and this is related to rising real interest rates and rising real wages. These trends tend to make the Fed pro-cyclical, since the neutral rate rises while the Fed's target rate stays in place. It is that lag in Fed rate setting policy that causes strong labor markets to appear to be inflationary. If there is any truth to this conjecture, this is another reason why using target interest rates as the policy tool is not optimal. In any case, I think that falling unemployment and related rising wages (which come from reduced frictions in the labor market, not from some sort of wage inflation) will be interpreted as inflationary, and will cause the Fed to raise the target rate. I don't think the exact target of the Fed Funds rate is that important right now. If the housing market wasn't hobbled, the neutral short term rate would already be well above the current Fed Funds rate. If mortgages don't expand, there won't be any inflation. If they fail to expand, the rate at which short rates top out will be lower. If they do expand, then the peak rates will be higher, both from inflation and from real expansion.