Following this post on the information transfer plucking model for the interest rate, I wanted to try to show the interest rate in the context of this information transfer plucking model for RGDP and inflation. Note that the interest rate and inflation rate "interact" through the Fisher equation (I say interact because I'm a physicist and the Fisher equation reminds me of a minimal coupling in QED). Eventually, I hope to be able to describe the price level and the interest rate as a particular path defined by the nominal gross domestic product (NGDP) and the monetary base (MB) across a manifold. Here is a picture of the model interest rate (black, acting as a bound as it does here) and the empirical interest rate (blue) in (logarithmic) NGDP-MB space:
Lines of constant interest rate (gray) are shown as well. Note this maximum path is the exact same empirical path shown in this post. Note that this empirical path appears to approximate an upper bound for e.g. RGDP on its own. It is possible this path through NGDP-MB space represents an upper bound from which RGDP (hence the inflation rate) and interest rate are deviations coupled by the Fisher equation. If I use the blue empirical interest rate path above with the original fit to the price level you can see it doesn't deviate too strongly from the empirical price level (green):
PS The videos are still coming. I just haven't finished narrating them.