The IT interest rate model results in the formula

*log r = a log N – a log M – b*

where

*N*in nominal output (NGDP),*M*is the monetary base minus reserves, and*a*~ 2.8 and*b*~ 11.1 (pictured above). This formula represents a plane in*{log N, log M, log r}*space. If we wrote it in terms of*{x, y, z}*, we'd have*z = a x – a y – b*

And we can see that the data points fall on that plane if we plot it in 3D (

*z*being*log r*, while*x*and*y*are*log N*and*log M*):**Update + 4 hours**

I thought it might be interesting to "de-noise" the interest rate in a manner analogous to Takens' theorem (see my post here). The basic idea is that the plane above is the low-dimensional subspace to which the data should be constrained. This means that deviations normal to that plane can be subtracted as "noise":

The constrained data is blue, the actual data is green. This results in the time series (same color scheme):

The data is typically within 16 basis points (two standard deviations or 95%) of the de-noised data.

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Also, try to avoid the use of dollar signs as they interfere with my setup of mathjax. I left it set up that way because I think this is funny for an economics blog. You can use € or £ instead.