Here's the model for Swiss interest rates presented both as an upper bound (representing ideal information transfer so that observed interest rates are less than the ideal interest rate r < r*) and as a fit:
Negative interest rates can be seen in the "bound" form as representing un-modeled complex economic interactions as discussed here using an ideal gas as an analogy. In that post, the PV diagram for a gas is observed to be below the "ideal bound" set by the ideal gas law because of molecular forces and condensation from a gas to a liquid.
In the interest rate model, we'd imagine because of e.g. program buying by mutual funds or the costs of holding physical currency information equilibrium would be a bad assumption and since the bound is near zero, negative rates become possible.
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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.
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