## Sunday, November 9, 2014

### The information transfer model and the econoblogosphere

Paul Krugman has a post up that criticizes the "neo-Fisherite" view. Oddly I completely agree with his post, yet I wrote a post about agreeing with John Cochrane's post, which Krugman calls the "highest level" of  Keynesian denial. It might be confusing as to exactly where I or the information transfer model (ITM) stands.

I wrote two posts in the past that illustrate a bit of how the ITM fits in with both the history of macroeconomic thought and the debate around the current crisis. Actually, the ITM can help explain the history of macroeconomic thought. At its heart, the ITM says Paul Krugman is always right, but not necessarily for the right reasons. Anyway, this is a post fleshing that statement out with a bit more detail in fun, easy to read listicle format.

First, let me say that the ITM has a critical parameter κ (kappa, basically named after the parameter in this paper by Fielitz and Borchardt), called the information transfer index. In short, it represents the relative size of information chunks received by the supply and transmitted by the demand. Anything you say about the information transfer model has a caveat depending on the value of κ. There are two major κ regimes, and they're not very far apart numerically. When κ ~ 0.5, the ITM reduces to the quantity theory of money (and is similar to the AD/AS model with monetary offset). When κ is larger, getting towards κ ~ 0.8 to 1.0, the quantity theory stops being a good approximation to the ITM and the IS-LM model becomes a better approximation. The details are linked at this post

The thing is that κ can change over time and is different for different countries. That ends up muddling things a bit so I end up agreeing with Scott Sumner, Nick Rowe, Paul Krugman, David Glasner, or John Cochrane on various occasions and disagreeing with them on other occasions.

One additional detail is that the ITM says that κ tends to rise as economies get bigger and can only be reset by changing the definition of money or a monetary policy regime change. Hence you can consider old/advanced economies as generally having larger κ while younger emerging economies have lower κ. This is not always true, but can be a good guide. With that bit of background, on with the listicle!

Expectations
I personally think the way expectations are used in macroeconomics make the field unscientific. They appear to be important in microeconomics (and game theory) -- and I have no particular problem with the way they are used there. However, mainstream macroeconomics does not appear to have any kind of constraints on what form expectations take, and hence allow anything to happen in a model. This reaches an almost absurd level with e.g. Nick Rowe's insistence that if a central bank is credible with its NGDP (or inflation) target, the economy will reach that NGDP (or inflation) target ... without the central bank actually having to do anything (besides 'be credible'). I've encountered many other theories and papers in my short few years of studying economics that effectively assume the conclusion through expectations. One economist called these chameleon models (although the author does not specifically call out expectations as the source ... however the questionable assumptions in economic models are typically about expectations or human behavior).
That aside, in the information transfer model, 'expectations' as such take the specific form of probability distributions over market variables (they parameterize our ignorance of the future). Since these distributions always differ from the actual probability distributions (we do not have perfect foresight), they represent information loss and hence a drag on economic growth (relative to perfect foresight). Additionally, prices are not only lower than they would be if we knew the actual probability distribution of market variables, but frequently lower than if we parameterized our ignorance as maximal (which is what the information transfer model does).
The monetary base
The monetary base is directly related to short term interest rates in the ITM. However, only the currency component of the monetary base (I've called it M0 as they have in the UK in the past) has any impact on inflation and then only when κ is closer to 0.5. Monetary base reserves have little to do with inflation ... except in the sense that movements in reserves can sometimes cause movements in the currency base.
Liquidity trap
The ITM model has a lot of similarities with the liquidity trap when κ ~ 1.0 -- I've called it the "information trap". Monetary policy does not have strong impact -- neither raising nor lowering interest rates, nor expanding nor contracting the currency base. The "information trap" differs from the modern liquidity trap in that it doesn't have to happen at the zero lower bound (ZLB) ... it is more like Hawtrey's credit deadlock or Keynes original liquidity trap that didn't have to happen at the ZLB.
The ITM is, in a sense, identical to Paul Krugman's mental model (or what seems to be his mental model) if you replace "normal times" with κ ~ 0.5 and "liquidity trap" with κ ~ 1.0.
The Phillips curve
This sounds reasonable, but doesn't appear to have a strong signal in the data using the ITM. The two variables (inflation and unemployment) have a complicated relationship and the ITM doesn't describe the fluctuations leading to unemployment -- unemployment seems to be the result of, for lack of a better set of words, irrational panic that could only be modeled by modeling human behavior.
(New) Keynesianism
Essentially, the ITM is well-approximated by the ISLM model when κ ~ 1.0, but not when κ ~ 0.5. So the ITM is sometimes Keynesian inasmuch as the ISLM model is Keynesian. New Keynesianism is based on the expectations-augmented Phillips curve. Given what I've said about expectations and the Phillips curve above, you can guess that the ITM probably doesn't agree with new Keynesian methodology. This isn't to say the models are wrong or won't outperform the ITM against data -- just that methodologically they represent completely different viewpoints.
Also, since in the US κ has been close to 1.0 both today and during the 1920s-30s, the ITM basically says Keynesianism has been the right theory at those times ... as Paul Krugman says, our world today (and Japan in the 90s) represents the return of depression economics.
(Market) Monetarism
If you take out the expectations piece (the "market" in market monetarism) ... and instead of M2 or MB use M0 ... and give a specific form for the velocity of money, the ITM basically agrees with monetarism ... when κ ~ 0.5. That is to say that Milton Friedman was (almost) right about the US during the 1960s and 70s (but wrong about Japan and the Great Depression). Scott Sumner and Nick Rowe are also right about the 1970s. Additionally, κ < 1.0 for Canada, Australia, China, Russia and Sweden (currently), so monetarism gets those right. However monetarists frequently try to appeal to data from these countries to prove their point about the US, Japan or the EU; in the ITM this is comparing apples and oranges.
Neo-Fisherite model
The only two things that the ITM has in common with this idea/model is that lower interest rates run you into low inflation faster than higher interest rates, and, if κ gets too large, the dependence of the price level on M0 (currency base) becomes an inverse relationship ... i.e. deflationary monetary expansion (as evidenced by Japan). This latter mechanism will lead to even lower interest rates over time.
However! An economy with a constant rate of inflation and a constant interest rate is impossible (unless RGDP grows at an increasingly exponential rate), and the mechanism has nothing to do with expectations, but rather is closely related to the liquidity trap. This makes it different from the typical neo-Fisherite view.
Fiscal policy
Debt-financed fiscal policy always boosts NGDP as it represents an independent process from economic growth. It also raises interest rates (aka 'crowding out'). However, when κ ~ 0.5, if the central bank is targeting inflation or NGDP, fiscal policy will fail to produce inflation (or NGDP) due to monetary offset (q.v. Scott Sumner). When κ ~ 1.0, then there is no monetary offset and the impact on interest rates is minimal. Again this view almost perfectly matches up with Paul Krugman's views, except that "liquidity trap conditions" mean κ ~ 1.0.
(My personal politics on this issue say that even if e.g. unemployment insurance negatively impacted NGDP, we should still do it because we are human beings not heartless automatons optimizing economic variables.)
Coordination failures
David Glasner and Nick Rowe have several posts that present the idea that coordination failures are the cause of recessions (Nick Rowe tends to put the onus on monetary policy, while David Glasner does not). The ITM motivates the idea that coordination causes the recession in the first place (i.e. people en masse becoming pessimistic about the economy) and that the economy does not naturally re-coordinate (create the 'inverse coordination' of the original pessimism) in order to undo that loss in NGDP. That re-coordination would require resources (e.g. debt financed fiscal policy) comparable to the original NGDP loss ... basically the idea that government spending should approximately equal the output gap per Keynesian analysis.
Other ideas?

...

1. As a researcher in psychiatry and neuroscience, and amateur student of economics, I find your model fascinating, and have a hunch that you are onto something very important. However, I am a bit confused about your all-important constant of kappa. It seems that you define it several different ways in differnent contexts (either that or I am not following your math). Could you explain again in more or less layman's terms what you mean by kappa?

1. Hi Todd. Thanks, and thanks for reading!

There are a couple of interpretations I've found.

The original definition κ = (log σr)/(log σt) is the ratio of the information in a single character of the alphabet used by the receiver (alphabet size = σr) to the information of a single character in the alphabet used by the transmitter (alphabet size = σt). It comes from the original paper by Fielitz and Borchardt I link to in the sidebar (and the post above). That's a bit abstract, but it really means in economics terms the amount of information revealed by identifying which dollar of the aggregate supply (receiver) matches up to which dollars of the aggregate demand (transmitter). The second "dollars" is plural on purpose since NGDP is larger than the currency base, so each dollar of currency base is used for multiple dollars of NGDP, so that generally κ < 1.

That still is a bit abstract, but you could think of it as the information revealed (transferred) when a dollar is spent on something that contributes to aggregate demand.

Even that is still a bit abstract ... and κ(NGDP, M0) is an approximation anyway ... however, in this post:

http://informationtransfereconomics.blogspot.com/2014/06/the-macroeconomic-partition-function.html

... I found a more exact representation, and in that representation 1/κ is proportional to the average growth rate of all the individual markets that make up the economy.

That means that for a country with κ ~ 0.5 the average growth rate of the typical market in that country's economy is higher than for κ ~ 1.0. At even larger values of κ, the average market is shrinking.

Another important thing to note is that I'm sloppy and tend to refer to any information transfer index in any market as κ. However the only market where κ appears to change is the money market ... in the other markets κ is just a constant with the meaning given at the top of this comment: the amount of information revealed by a transaction in that market.

I hope that helps a bit. I think I will do a post on κ to clarify what I mean since I admit I've been a little less clear than I would have liked.

2. Thanks for your response. It does help (a little). I will review your post listed above and think a little bit more and see if it makes more sense. More questions to come.

3. OK another question if you are still watching this thread- obviously the "size" of the NGDP (M0?) is a very important parameter for the complexity of an economy, thus influencing the "information transfer efficiency?", thus you can predict growth rates, inflation, etc along with knowledge of the kappa. All well and good, but it seems to me you are measuring NGDP not in an entropic/information/complexity sense, but rather as a number of arbitrary units, be they U.S. dollars, Polynesian conch shells, or Weimar Republic deutschmarks. How is it that this arbitrary unit of currency becomes such a good proxy for the complexity of an economy? Also, given that M0 is the GDP/monetary parameter that seems to be most important for growth and inflation, does your model imply that countries should more actively manage M0 to target a certain growth, inflation, or unemployment rate?

4. Hi Todd,

I still watch all of the threads (it's a small blog) so if you have questions about any of the posts, I can respond there, too.

Treating NGDP as arbitrary symbols is the essence of treating it in terms of information/entropy. Information theory is effectively the math of arbitrary symbols.

The actual measure of entropy is ~ log (NGDP/c)! ... That's a factorial, not shouting :), and it turns out that is basically the same functional form of the Boltzmann entropy for a system with NGDP/c states.

So the complexity of the economy is partially given by NGDP -- it is proportional to the number of states in the economy (a more complex economy has more states). However the constant c seems to parameterize the relative complexity of two economies with the same NGDP measured in their individual currencies. I have more about this at a link I will try to find when I'm not using my phone to respond.

Regarding M0 management, that does seem to be a potential option. However, another thing I've discovered is that the path of NGDP vs M0 seems to be fixed for many economies. That's another link I will find. I don't really know all the answers about this, hence the blog a a living, working paper.

5. OK slowly starting to come to some understanding. Thank you for the clarification. I finally had a chance to read the original information transfer theory paper you reference and I have to say it was one of the more amazing scientific papers I have ever read. The fact that so many physical processes can be derived from information transfer relationships mostly irrespective of the actual physics involved is mind-blowing!

6. I thought it was pretty cool, too. It's good to remember there's no "free lunch" though -- the model can address a bunch of different processes (essentially by equating information entropy aka macro ignorance of the micro state), but has limited dynamics. You can go a lot farther with statistical mechanics.

But yes, it's pretty cool and leads to supply and demand too:

http://informationtransfereconomics.blogspot.com/2013/04/supply-and-demand-from-information.html

2. Jason: "This reaches an almost absurd level with e.g. Nick Rowe's insistence that if a central bank is credible with its NGDP (or inflation) target, the economy will reach that NGDP (or inflation) target ... without the central bank actually having to do anything (besides 'be credible')."

Then think about a cop car parked next to the speed limit sign. Is it what the cop car actually does, that causes people to slow down? Or is it expectations about what the cop car would do if they did not slow down, that causes people to slow down? Can we have an equilibrium in which parking a cop car causes people to slow down, and the cop car does not actually need to do anything? Yes.

1. It may be BS in the sense that it is wrong, but I don't think it's an unfair characterization of your view.

Regarding the cop model: that could be a good model when the individual has a speedometer and a gas pedal, but we do not have NGDP or inflation pedals/meters ... And the central bank does not monitor individual behavior.

I see you have a new post. Ok, read it.

Again, the model seems fine if we all had NGDP pedals and inflation meters.

CPI has hedonic and quality adjustments ... How does a car company increase prices by 3% and have customers enjoy the cars 1% more to target 2% inflation ... Many of these factors are outside individual control.

Also, imagine a world where speed is undefined for individuals. Only collectively do we have speed (inflation). In that case the model makes no sense. That's the gist of the information transfer model.

3. Nick, To be fair you've suggested things along the lines of that paraphrasing, or at least I've gained that impression reading your blog. Which btw is my fave econ blog by a country mile.

Jason, it's all well and good to derive a model form based on some information theory, but I don't quite get how some parts of the model fall out of that. Like the use of m0 for instance - was that just a result of an empirically better fit?

Plus this mysterious kappa, which allows your model to be all things to all people somehow, encompassing both the QTM and ISLM, certainly appealing, but it sounds like you merely fit kappa to the data, and you have it change over time. Doesn't this extra degree of freedom let you match whatever you need to as the case suits it?

1. Ben -- thanks for the defense. And yes, the choice of M0 is purely empirical. However it works really well across several countries so that is some evidence it is not completely off base. I tried several measures (most that are available) and M0 works best. It's also the least ambiguous measure ... E.g. Why include checking accounts but not other things that work as money (M1 vs M2)?

I mention above in the reply to Todd the theoretical motivation for kappa. The kappa model actually trades one constant parameter (the original constant kappa) for a different constant (c). It results in an improved fit, so by the AIC the varying kappa model represents an unambiguous improvement, not overfitting.

I actually derive the functional behavior of kappa in two ways (via information theory, and via considering a large collection of random markets) so it isn't that mysterious ... And while it does allow the QTM and ISLM to be correct, they can't be correct simultaneously and you can't change from one to the other at will. This allows the model to be falsifiable and I'm keeping tabs on the data to see if it continues to work. Kappa was essentially fixed for the entire post-war period by about the 1980s (data from 1960 to 1980 fixes kappa ... Or really c). If the U.S. suddenly starts behaving like a QTM I can't change kappa to fit the data (and if that happens, the model is likely wrong).

There is one caveat on that last statement. If the definition of money changes significantly (going off the gold standard, pegging US currency to another country's currency) then many of the model parameters change. Even the functional form might change to a hyperinflation solution. There aren't a lot of these "monetary phase transitions" in the data that I've explored ... WWII/Breton Woods (US, UK), the introduction of the Fed (1914) and one instance where Switzerland drastically changed monetary policy in the 1990s. It's something I'd like to understand more.

2. I'm still not sure why you assert, as you do, that physical currency has an 'impact on inflation'. This suggests that issuing currency somehow causes people to spend more, whereas creating other forms of money, such as central bank deposits or commercial bank deposits, doesn't. I can see why higher spending and inflation would be correlated with more currency in circulation, but I don't see why currency would actually cause inflation. After all, if you have more currency than you want you can simply deposit it at your bank, in turn they can deposit it at the central bank... so if central bank deposits (reserves) don't 'impact inflation', why would currency 'impact inflation'?

3. Hi Phillipe,

When you deposit unwanted cash at the bank, it either stays as physical currency or is destroyed and turned into central bank reserves (or destroyed/repo'd). I could be wrong about that, though. It largely doesn't matter as long as the physical currency exists and can re-enter the economy.

One interesting exception seems to be 500 € notes, which behave more like central bank reserves than currency -- they seem to be almost entirely used on the black market.

There's a link I'll add about that when I get to a real computer (on travel right now).

Causality is interesting in this model --- the "force" creating inflation is an entropic force. If you put salt on one side of a semi-permeable membrane, water will flow from the other side to the salty side until the salinity is the same. The water isn't "attracted" by the salt. What happens is that the state with equal salinity on both sides becomes more likely (higher entropy) and thus the new equilibrium and osmosis happens.

With money, it seems to work the same way (at least in this model). When additional currency is printed, the economic state with the higher price level is more likely. It can also work the other way as you identify: higher spending and inflation can lead to a state with more printed currency. However while NGDP and price increases can spontaneously occur (stores change their prices, people invent things), the central bank controls the amount of currency in circulation. Thus that seems to be the "causal" factor, but it's really just the economy randomly finding a state with higher price level (and NGDP) when new currency gets printed.

Since it's a random process, the immediate effect could be a rise or fall in the price level. But in the long run, you'd expect a higher one if there is more currency, but not monetary base reserves (unless a bank requests some of its reserves in currency).

If we could all keep reserves and request cash from them, the story would likely be different.

4. If a commercial bank has $100 in unwanted cash, it can take it to the central bank and swap it for a$100 reserve deposit at the central bank.

If a commercial bank has a $100 reserve deposit at the central bank, it can swap it for$100 cash (i.e. withdraw cash from the central bank).

In that sense there is no difference between cash reserves and reserves held on deposit at the central bank.

If the Fed literally printed a masive amount of cash and swapped it for all of those excess bank reserves it currently has on deposit, what difference would that make? The cash would just sit in vaults either at the central bank, or in commercial bank vaults, until people wanted to withdraw it.

5. "It largely doesn't matter as long as the physical currency exists and can re-enter the economy"

It doesn't matter if the cash is destroyed by the central bank when banks swap the cash for deposits at the central bank. The CB can just print more cash if banks later want to swap their deposits for reserves.

"If we could all keep reserves and request cash from them, the story would likely be different"

We do 'keep reserves and request cash from them'. You can withdraw the full amount of your bank deposit in cash at almost any time you want.

6. Phillipe-- A bank doesn't just deposit or withdraw 100 dollars from their reserve account at the Fed. Cash that re-enters the commercial banking system goes through an approval process where, if approved, the Fed sends the request to Treasury for printing. It then is released with a repurchase agreement.

Your argument proves too much: it says M0, MB, and M1 are the same. And I as an individual do not have an account at the Fed that I can get converted into cash at will.

But as I said, the underlying mechanism for the green pieces of paper doesn't matter. What matters is that they've been printed and can get into the economy -- at least in the ITM. In that model, the cash moves around the economy randomly. But only cash can do that. Central bank reserves stay at their banks ... And our checking accounts are money created in response to aggregate demand via fractional reserve banking. Neither reserves nor checking accounts define money; that's only done by the green pieces of paper.

The benefit of using M0 as the explanatory variable for inflation is that it gives an incredibly accurate model. If you have done better model that uses M1 or MB that explains the price level, I'm interested in hearing about it! But if you're just making hand waving arguments without any empirical evidence, that seems like a step backwards from the ITM.