Monday, March 9, 2015

Undershooting inflation

Scott Sumner has a post up today that references a prediction market's estimate of inflation over the next five years (from a NYT article by Justin Wolfers). The prediction market is telling us the Fed will undershoot its inflation target. I commented on Sumner's post, but here is the information transfer model's prediction of the same thing. The latest update for the prediction itself is here. I generated 1000 random paths (using both a Gaussian and empirically derived probability distribution [1] for the errors), and integrated them over the next 5 years to produce a 5-year inflation prediction [2].

Here are the first 200 of those 1000 random paths:

And here is the resulting prediction using roughly the same graph as the NYT article (which I adjusted using Sumner's PCE inflation correction of -0.35% [3]):

Here it is with higher resolution for the IT model prediction:


[1] The empirical distribution didn't come up with a very different result, so I am only showing the normal distribution results.

[2] Note that the 5-year prediction is right in the sweet spot of the IT model's capability.

[3] The prediction market used CPI inflation, so I adjusted the distribution to show PCE inflation by fitting an empirical distribution to the CPI prediction market data and shifting that distribution by 0.35%, per Scott Sumner's adjustment in his post linked at the top of this post.


  1. Jason, you may want to respond to the econjobrumor post that questions you regarding the issue of P:demand->supply - that information does not necessarily flow from demand to supply. Or to think of one myself, possibility that one learns information not just from market (price) but from other non-price/non-market sources. It is certainly possible to know every information in a hypothetical theoretical world without price being determined - like in a Walrasian auction.

    1. Thanks for the heads up. I responded on the econojobrumor post.

      One thing I forgot to mention there is that the direction of flow doesn't matter in equilibrium: A = B and B = A have not meaningful difference.

      I wrote a bunch more on the direction of information flow here:

      ... and I admit it might be something that I am wrong about. But it isn't critical except in non-ideal (non-equilibrium) case.

    2. One thing I did want to add; when you say:

      "one learns information not just from market (price) but from other non-price/non-market sources"

      I think this makes very clear the distinction I am making. The demand represents a massive multi-dimensional probability distribution. The information entropy of that distribution is huge. There is no way to represent that information entropy in a price (a single-dimensional probability distribution).

      The number of bits required to specify a roll of 10 dice is much larger than the number required to specify the roll of a single die.

      That's why I move the price from being a "receiver" or "transmitter" of information on the end of a communication channel (how it is seen in economics) to being simply a detector of information flow through the channel.

      Also note that information on this blog is being used in the information theory sense, not the colloquial sense. The kind of processor in an iPhone is a piece of "colloquial information" about an iPhone. However the information I am talking about here is the information entropy in the probability distribution of iPhones.

      The kind of processor only makes a difference in the sense that it is a characteristic of an iPhone. If all iPhones have the same processor, then the information in the distribution of processors is the same as the information in the distribution of iPhones. If there were two different processors, that would potentially impact the result as one processor would have one distribution (among regular users) and the other would have a different distribution (i.e. among power users).


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