Friday, August 1, 2014

Zen kōan inflation targeting

Tyler Cowen suggests the rather silly "target 4% to achieve 2% inflation" monetary policy for the ECB. I'm not sure if he actually meant it as a joke or not, but it certainly illustrates the utter ridiculousness of model-independent expectations that aren't the constrained "rational expectations" typically used in economic models.

Rational expectations are perfectly fine: you have an underlying model and the economic agents expect e.g. the level of inflation predicted by the model. In some sense, rational expectations make the economic agents superfluous. If the agents are just going to parrot back the expected values of model random variables, why not just say they aren't there. A better word for "rational" expectations would be model-dependent expectations, which I contrast with model-independent (MI) expectations above. These MI expectations are those typically invoked by e.g. Scott Sumner and Nick Rowe.

Cowen suggests that the ECB could target 2x% in order to achieve x% inflation relying on MI expectations. With MI expectations however, if the ECB doesn't keep this a secret, the agents will learn 2x really means x, and then the 4% inflation target will really be a 1% inflation target since 4% means the ECB is aiming for 2% so will only achieve 1%. Okay, then.

But here's where it really gets silly. If you see the ECB's current 2% target as not credible, then aiming for 4% and resulting in 2% manufactures a credible 2% inflation target out of an incredible one by renaming "two" as "four". Incredible!

Another solution, proposed by Scott Sumner, is that the ECB doesn't actually want 2% inflation, even though it says it does, but rather the ECB communicates its inflation targets by talking about unemployment and competitiveness. Yes, the official inflation target is 2%, but that is irrelevant: the actual inflation target is 1% because that is what makes the PIIGS competitive.


Yes, that was Occam's razor.

Sure, countries seem to be able to achieve their inflation targets most of the time (in fact, the quantity theory of money works for a lot of cases), but now we have a series of countries that seem to be undershooting them a bit: Japan, US, EU, Canada ... etc. Maybe there is a maximum achievable inflation rate i* for an economy? For countries with inflation targets below this maximum, inflation targeting works: the central bank says 2%, it gets 2%. For countries with inflation targets above this level, all you get is the maximum i*.

The information transfer model produces this result. At every point on the price level surface (see e.g. here, or at the top right of this blog if you're not viewing it on a mobile device), there is a maximum gradient (inflation rate). This is the inflation limit at that point. During the 1960s in the US, this maximum inflation rate was 10% or more.

EU i* is predicted to be low by this model (almost zero) -- below their target of 2%. For the US, i* is just below 2%.

Where does this maximum come from? Money has two purposes: it is the medium of exchange, allowing transactions to occur and it is the unit of account, Fisher's measuring stick. In the information transfer model, money allows people to exchange information and measure the units of the information. As you increase the amount of money, the relative impact of these different capacities changes. You can imagine the unit of account as a box that gets smaller as more money is added to the system, while the medium of exchange is the number of boxes. The height of that stack is proportional to the price level. And it looks something like this:

Japan is on the right side of this diagram, while, say, China in on the left. The maximum inflation rate i* is the slope, higher on the left and lower on the right.

This is Cowen's "most economical model".


  1. Jason: "These MI expectations are those typically invoked by e.g. Scott Sumner and Nick Rowe." ??

    1. Hi Nick, I was referring to e.g. this post of yours

      where the same expectations argument works for driving on the right side, daylight savings time and monetary policy ... and for each one, it doesn't matter what the "concrete steppes" are (i.e. it is model independent, even operating across domains).

      In general the belief that a central bank can achieve any inflation target it sets its (collective) mind to is "model independent" in this sense. You can take this and turn it into rational expectations by building a model in which it is possible. However if the general principle is considered more important than its instantiation, it is "model independent".

      "MI" expectations also would refer to Paul Krugman's "promise to be irresponsible".

      Sumner's step 2 in this post is model independent:

      I discuss that post in more detail here
      but the key point is that Sumner doesn't tell us how far the price of gold plunges when the discovery is announced (the plunge is a model independent result).

      However, even I use MI expectations -- for example, I believe that trend interest rates can be calculated from NGDP and the monetary base but deviations from that trend are caused by market expectations (that I don't have a model for -- hence they are model independent):

      PS I think your phrase "people of the concrete steppes" is brilliant.

  2. Take the "which side of the road do we drive on?" example. This is a model with 2 equilibria. There are two rational (model-consistent) expectations.

    1. There are also two adaptive expectations equilibria. Any model is going to map from the space {L, R} to R or L, so any expectations argument is consistent with every model ... and therefore model independent.

      Ok, an expectations argument that maps to R is going to eliminate the class of models that can't map to R, but there are still an infinity of models that map to R. It still doesn't depend on any specific model.

      An expectations argument that says the central bank can achieve any inflation rate eliminates a broad class of models where the economy cannot achieve any inflation rate (e.g. the information transfer model), but is still consistent with a large number of models where any inflation rate is possible. Therefore the idea that a central bank can achieve any inflation rate is still largely model independent.

  3. Jason I especially like the final illustration above with the yellow boxes, and your explanation. It gives me a visual for what you mean when you make your usual statement about UoA vs MoE.

    1. Re: that final plot of stacked boxes: would it be fair to say that as we go from left to right that the total amount of information exchanged in the economy continues to go up, but at a smaller and smaller rate, while the information content per unit of money exchanged goes down?

      It's almost like you're stacking blocks of jello... the more you stack, the higher you go, but also the average height of each jello block decreases (due to weight of those above them). That doesn't exactly describe your diagram (since all the jello blocks have the same height in any one column).

      Also, I was trying out an analogy to explain your 90% 10% dichotomy that you expressed over at pragcap to commenter pliu412. I used an analogy that may not be very apt, but I'll run it buy you: I said perhaps all the human decisions are like waves on the ocean: They each contribute to the mean sea level at some geographic point, but mostly the magnitude and direction of travel of each of the waves isn't so important, just the amount of water from each contribution. Occasionally though they line up to create a "rogue wave" the crest and trough of which vary significantly from the mean sea level (at that one point). [now I know the %ages are way off here but] I said, suppose that 90% of the time the mean sea level is a good approximation, and the particulars of human decisions (individual wave intensity and direction of travel) don't matter much, but sometimes they do line up (10% of the time) and create a substantial deviation from the mean.

      I don't think that really captures your point about humans reacting, for example, to a mass panic, because the rogue wave doesn't really have any positive feedback mechanism like a mass panic presumably does.... but perhaps it does capture a bit of the reason why only occasionally human behavior appears to cause a significant effect.

      Perhaps to improve the analogy we could speak of forest fires. Mostly there are a lot of small fires going on at any one time, all of which contribute to the total pollution level, but no one fire contributes that much, and it's more a function of the time of year. However, occasionally, the fires start to grow out of control, merge into one another, jump containment lines, stretch to the breaking point fire fighting resources, create their own wind and drying heat... etc, and we get a general conflagration which takes pollution beyond a seasonal explanation. The image of a fire making it's own wind and drying heat seems an appropriate analogy to a panic or a boom somehow.

    2. That graphic comes from an animation I've been trying to put together ... I just posted a piece of it:

      The rogue wave analogy is pretty good, but you are correct that human behavior can become coordinated by the news or market indicators (DOW, S&P500). I think it is possible that human feedback turns the occasional random 2-sigma event into a 4-sigma event (relative to the original distribution).

  4. If you go over to check pliu412's comment, you might be amused (horrified?) at my attempt to tie something he said to your recent (month or two ago) post on partition functions. I was too lazy to restart my screwed up browser after starting my reply, so I bravely continued typing in a fact free manner... even going so far a field as trying to remember how Planck came up with the idea of quantized energy... Lol. I seriously just did that from memory of a youtube video on the subject I watched this year... you will probably get a laugh out of it if nothing else. This did inspire me to actually take a stab at understanding your partition function post (and I got a little farther this time I suppose), *after* I made my lengthy uninformed reply to pliu412 of course (I was in maximum "modern Jackass" mode). Oh well... I'm sure pliu412 will either run screaming or ask you directly next time. That'll learn him!!


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