Dynamic unemployment equilibrium (and sunspots)

I thought I'd add a bit more to a series of posts about defining a "dynamic" equilibrium in unemployment where we don't look at a natural level of unemployment U*, but rather a natural rate of decrease (dU/dt)*. This doesn't necessarily have anything to do with information equilibrium (except to say it looks like the US economy is usually in this particular unemployment equilibrium), but rather a particular parameterization of the data. The first five posts are:

1. Remarkable recovery regularity and other observations This is the first time I noted the regularity in dU/dt.
2. Unemployment equilibrium? Here I minimized an objective function based on entropy to find the best slope (dU/dt)*.
3. Did the ACA decrease unemployment? Here I used the parameterization of the data to motivate an interpretation of the data where the ACA (aka Obamacare) caused unemployment to fall faster than normal.
4. Eurozone unemployment equilibrium Here I showed the parameterization applied to the Eurozone.
5. Defining recessions? Here I used the parameterization to define the center of recessions and note that the definition matches (within about a month) the NBER midpoints. [Also added a bit on predicting recessions and Obamacare as a positive shock to employment on 7 Oct 2016.]

This post just adds a couple of other metrics. I show the deviation between the data and the model in the first graph, as well as how the derivative of the parameterization compares (red) to the derivative of the data (gray) in the second graph -- thereby showing the "recessions" as spikes, with the economy remaining in this "dynamic unemployment equilibrium" most of the time.

The second graph makes me think of sunspots in the solar cycle (and would lend itself to Steve Keen's ideas about nonlinear dynamical systems if only we had longer periods of data and or some kind of microfoundations).

Update 30 December 2016

Here's a post looking at multiple equilibria, and here's another post where I try to use this "model" to do a bit of forecasting.