Thursday, May 22, 2014

Limits of the information transfer model

No, this isn't about limitations of the information transfer model. I discussed some of those here. I'm talking about two limiting cases. 

One limit is the high inflation limit; according to this calculation, high inflation means that κ ≈ 1/2 and the information transfer model reduces to the quantity theory of money.

A second limit is the large Monetary Base (currency component) limit. In this calculation, I show that for some value of MB > MB0, we have ∂P/∂MB ≈ 0. This result means changes in the monetary base don't affect the price level P and hence don't strongly affect NGDP. Therefore, in terms of the price level NGDP can be considered approximately constant (aggregate demand is a constant information source) with respect to central bank operations, the IS-LM model is valid for the effects of interest rates and the information transfer model reduces to (Hick's description of) Keynesian economics.

Thus the two big theories of the last century in economics are specific limits of the information transfer model.

Now if I could just attract the attention of the economics Nobel committee ... or really any economist at all.


  1. Jason, it's truly bizarre how unappreciated MB/NGDP is.

    The currency component caveat above is important. Would it be worthwhile breaking down the currency components into imputed NGDP activity? $20 bills could be more closely linked to NGDP, while $100s may simply head abroad ($100 bills that are actually used should create an ecosystem for smaller denomination change requirements.) If 99% of US currency expansion is $100 bills (that go abroad, say), the information transmission mechanism could be different than simple dilution. The data exists.

    Also, Weimar could be a great exploration for one side of your limits. I understand that the MB data exists, but I for one have had trouble tracking down the proper numbers.

  2. The thing is that if we look at the "exchange rate" of MB for say MZM or M2, it is about constant ... but the data is super noisy. It would be empirically difficult to extract an effect of the distribution of currency denominations -- although in theory that could matter. My intuition is that all of the bills are all approximately "small" compared to the economy ... in calculus terms they are all infinitesimal dm's.

  3. Could be. I've wondered whether currency formation timing could shed some light on causality -- (currency - price push) or (currency - price pull). (Assuming they print denominations to respond to bank demand, that is. Maybe they don't.)

    Constant? Yes, but. MZM money (the flip liability side of mostly bank created debt assets) used to have a very close, almost policy-like relationship to bank reserves until 1997. Then, policy changed, imputed bank leverage exploded, and imploded in 2008.

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    2. Interesting graph ...

      Actually MZM works fairly well for interest rates on its own ...

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  4. What would you say to the theory that when a CB carries out things like QE the increase in the MB is just a side-effect of the policy and not the primary aim?. QE swaps assets for new base money. The new base money just sits idly in bank reserves. But if the things being bought are risky assets that have a positive interest rate then bidding the prices of these assets up and reducing their interest rates will have a positive effect on NGDP independent of the (unnecessary) MB increase ?

    1. It is difficult to tease out the "causality" ... does the central bank set interest rates and let base money adjust? Or does the central bank determine the level of base money/reserves?

      For example, I look at the interest rate setting version based on a post by Nick Rowe:

      ... so maybe the base jump is a side effect.

      Regarding the second part of the question, I think that was part of the idea behind the Fed's purchases of mortgage backed securities -- the Fed bought up a lot of the toxic waste and was just holding it until the crisis calmed down -- that would definitely ameliorate falling AD (aka NGDP). But I am not an expert on such things and you'd probably need a more detailed model than the one I'm using here.

  5. Jason, O/T: I'm getting behind on my reading on your site!... but I happened upon the following video the other day (I usually listen to something like this to put me to sleep at night)... and I wondered if you have an opinion on it. The "conspiracy" in the title makes it sound like a tin foil hat thing, but he puts that to rest at the start... that was just to get people's attention I guess. I wonder what your opinion is if you have one:

    1. I've seen that video -- actually, I think I watched it right around the time I started this blog. It is a nice re-framing of some of the weirdness of quantum mechanics in terms of information theory. I didn't look into it in too closely, though ... "interpretations" of QM have a problem with occasionally predicting things that don't actually happen.


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