Sunday, May 4, 2014

The effect of expectations in economics (addendum)

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):


5 comments:

  1. Jason, the part I don't understand is how you determine the black line (corresponding to the maximally ignorant case, right?).

    ReplyDelete
    Replies
    1. Whoops, didn't reply on your comment -- see below.

      Delete
  2. Tom -- The dark line is the information transfer model fit to the empirical data. It's given by the function log r = c log NGDP/MB - k. The coefficients appear in a graph here.

    See here
    http://informationtransfereconomics.blogspot.com/2013/08/the-interest-rate-in-information.html

    Since the information transfer model assumes the least informative prior, the model result will be the peak of the gray distribution. This is akin to the thermodynamic limit where e.g. the pressure becomes just P instead of some average < P > with fluctuations.

    Another way, since the dark line is the model calculation in the limit n >> 1 (large number of economic agents), fluctuations around that limit are small.

    Yet another way, the dark gray line is the expected value of the gray distribution, which is the information transfer model result.

    ReplyDelete
    Replies
    1. Thanks Jason. I'm sure I'll have more questions at some point, but that gives me something to ponder.

      Delete
  3. I believe this interpretation could constitute a derivation of the plucking model.

    http://economistsview.typepad.com/economistsview/2006/01/new_support_for.html

    ReplyDelete

Comments are welcome. Please see the Moderation and comment policy.

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.