Regime dependent modeling and the St. Louis Fed

The STL Fed has made a splash with its new "regime-switching" [pdf] forecasting (H/T commenter eli). Part of the reason is the divergence of one of the dots from the rest of the dots in the FOMC release. Here's Roger Farmer with a critique (who also liked my earlier post/tweet about a falling unemployment equilibrium that is basically the same as his increasing/decreasing states). So here is a diagram of the states the STL Fed categorizes:

Since productivity and the "natural" rate of interest (approximately the STL Fed's r†) aren't necessarily directly observable, one can think of this as setting up a Hidden Markov or Hidden Semi-Markov Model (HSMM) (see Noah Smith here).

I'd like to organize these states in terms of the information equilibrium (IE) framework (in particular, using the DSGE form, see here for an overview). The IE framework is described in my preprint available here (here are some slides that give an introduction as well). What follows is a distillation of results (and a simplified picture of the underlying model). The IE model has two primary states defined by the information transfer index k. If k > 1, then nominal output, price level and interest rates all tend to increase:

If k ~ 1, then you can get slow nominal output growth, low inflation (slower price level growth) and decreasing interest rates:

This organizes (nominal) interest rates into two regimes -- rising (inflation/income effect dominating monetary expansion) and falling (liquidity effect dominating monetary expansion) (graph from link):

This model results in a pretty good description of interest rates over the post-war period (graph from link, see also here):

The two regimes are associated with high inflation and low inflation, respectively (as well as high productivity growth and low productivity growth). In the IE framework, recessions appear on top of these general trends (with worse recessions as you get towards low interest rates). Coordination (agents choosing the same action, like panicking in a stock market crash or laying off employees) can cause output to fall, and there appears to be a connection between these shocks and unemployment spikes. This is a two-state employment equilibrium: rising unemployment (recession/nominal shock) and falling unemployment (graph from link):

Overall, this inverts the direction of the flow of the STL Fed model and we have a picture that looks like this: