I saw this tweet today, and it just kind of frustrated me as a researcher. Why do we need yet another measure of unemployment? These measures all capture exactly the same information.
I mentioned this before, however I thought I'd be much more thorough this time. I used the dynamic equilibrium model on the U3 (i.e. "headline"), U4, U5, and U6 unemployment rates and looked a the parameters.
Here are the model fits along with an indicator of where the different centers of the shocks appear as well as a set of lines showing the different dynamic equilibrium slopes (which are -0.085/y, -0.084/y, -0.082/y, and -0.078/y, respectively):
Within the error of estimating these parameters, they are all the same. How about shock magnitudes? Again, within the error of estimating the shock magnitude parameters, they are all the same:
Basically, you need one model of one rate plus 3 scale factors to describe the data. There appears to be no additional information in the U4, U5, or U6 rates. Actually in information theory this is explicit. Let's call the U3 rate random variable U3 (and likewise for the others). Now U6 = f(U3), therefore:
H(U6) ≤ H(U3)
Update 13 October 2017
The St. Louis Fed just put out a tweet that contains another alternative unemployment measure. It also does not contain any additional information: