How bad is unemployment?

So the unemployment rate is 5.5%, which some suggest is the upper limit of the calculations for the natural rate (some estimates suggest between 5.2 and 5.5%). And yes those measures are plagued by logical problems, let alone the empirical problem that the natural rate seems to be tied to the actual rate. At any rate, given the relevance of actual unemployment for the Fed policy it would be nice to know what the actual rate of unemployment means.

It is worth remembering that the rate of unemployment depends on the participation rate that, as can be seen below, has been falling since the late 1990s. The question is how would the unemployment rate look like if the participation rate remained at the same level it reached at the end of the Clinton boom.

This calculation was done before (here and here), and the new graph is below showing that unemployment would be at a much higher rate.

In fact, the rate of unemployment (u*) would be a bit more than double the current rate of unemployment (u) if the participation rate remained at 67% of the labor force. That might explain why real wages have not increased much in this recovery. The recovery is even weaker than it looks.