I mentioned in the previous post that I would show and updated diagram:
In thinking about this while writing this post, maybe the theoretical price [interest rate] should be fit to the empirical data (as is done here) instead of being fit to an upper bound of the empirical data as is done above [in the post]. This solution would represent the gray "least informative prior" solution running through the data and the blue more accurate expectations would rise above the theoretical curve and the inaccurate expectations would still fall below the theoretical curve. I will update with this version in a follow-up post.
Here is the new graph:
In this presentation, the theoretical model curve (dark gray) follows the peak of the least informative prior (gray histogram). The incorrect expectations (red histogram) match up with negative deviations and the more accurate expectations (blue histogram) match up with the positive deviations.
For completeness, here is the fit to the short term (3-month) interest rate (the graph above falls in the gray box):