## Wednesday, June 24, 2015

### Is information transfer economics hard?

 The basic premise of information transfer economics: if I shake one end of a jump rope tied to a tree in Morse code, the tree feels a force that can be used to reproduce my input signal. If I shake NGDP in Morse code, hours worked should fluctuate in such a way to get that pattern back out. Image from Wikimedia Commons.

I admit I have trouble understanding what others find so difficult about the information transfer framework for economics. For example, Scott Sumner writes:
But he [meaning me] went even further than the other two [Matt Yglesias and Britmouse], creating a revolutionary new type of economics called “Information Transfer Economics.”  Although I’ve tried to understand his model, it’s all way over my head. He knows a lot more math than I do.
I'm pretty sure Sumner was being sarcastic when he called it 'revolutionary'. However, Sumner actually writes down an information equilibrium [1] model on his blog for what he considers to be his own model. In this post we have an hours worked delta (from a "natural rate") related to an NGDP delta (from a future market or central bank target). The key point to understanding the information equilibrium view is to see fluctuations aggregate demand transmitting a signal to hours worked -- i.e. a wiggle in NGDP shows up as a wiggle in H.

$$\frac{NGDP - NGDP^{T}}{H - H^{n}} = \frac{\Delta NGDP}{\Delta H} = \alpha ' \frac{NGDP}{H}$$

This is effectively the information equilibrium model:

$$NGDP \rightarrow H$$

$$\frac{dNGDP}{dH} = \alpha ' \frac{NGDP}{H}$$

with the equation just being what the notation $NGDP \rightarrow H$ is shorthand for. Sumner would assume (in the information transfer framework) that the ratio $NGDP^{T}/H^{n}$ is roughly constant (a good approximation over the short run) and is subsumed into his constant $\alpha$.

There is also his plot of the ratio of hourly nominal wages to NGDP versus the unemployment rate. This appears to be the information transfer model:

$$u: NGDP \rightarrow NHW$$

Of course, the more empirically accurate version (in both cases) is

$$P : NGDP \rightarrow H$$

where P is the price level, which is essentially Okun's law.

What I can only assume are economics students on EJMR appear to get the general concept even when they don't understand everything else:
I could never figure out what he was doing.
He says things like my model is Y~X, where that stands for some large class of (linear?) models. ...
I'd have said log-linear instead of linear (which I'm sure the person meant, but just to make it clear to everyone else), but basically, yes, that's it. I'd write $Y \sim X$ for information equilibrium and $Y \rightarrow X$ for information transfer ... and add a "detector", an abstract "price" $p$ in economics parlance so that $p : Y \rightarrow X$

It's a severe restriction if your initial range of choices includes anything your heart desires, but for the most part lots of models fall into this class. It really is just a bare minimum requirement for how X and Y have to behave if you want to say as the economist "X and Y are related". At a bare minimum -- if you say X and Y are related -- wiggling X has to wiggle Y to some degree. If you sent a Morse code signal by changing X, you should be able to read it at Y.

The biggest difference from mainstream approaches is in the interpretation. In the traditional economic view, permanently increasing the monetary base causes agents to expect higher inflation, so the price level rises. In the information transfer view increasing the monetary base makes higher price level states more likely (most of the time) and agents end up in a state such that we observe higher inflation.

It makes the language a lot more passive. Agents "end up" working more hours or accepting higher prices for bacon. Why do they end up in those situations? That's a really hard problem. A single mother might take on a couple of hours a week more than she wants because she's covering for a colleague that left for a new full time job and thinks her manager would appreciate it. Total hours increase, say, from 20 + 20 = 40 to 22 + 40 = 62. Predicting that extra 2 hours would be a nightmare in terms of an agent based model (a utility calculation based on the single mother's time she wants to spend with her kid, expenses for child care, transportation costs, and how much she thinks her manager would appreciate x extra hours). Information equilibrium just tells us that somehow all those extra hours from monetary or fiscal stimulus (depending on the model) get allocated. The details of the process for each individual agent go into the coefficient $\alpha$ in the equations above.

In that sense, information transfer economics is much easier than traditional economics. It also becomes a much more empirical framework. If I say M1 is the source of all fluctuations in NGDP, then we should have an information equilibrium relationship (for some $k$):

$$\frac{dNGDP}{dM1} = k \; \frac{NGDP}{M1}$$

If this isn't true empirically, then there is something missing in your model.

Footnotes:

[1] I try to say information transfer model for the general case and where we allow non-ideal information transfer -- $I(D) \geq I(S)$ -- and information equilibrium model for cases where information transfer is ideal -- $I(D) = I(S)$.

1. Hi, Jason. Were you at Los Alamos, or just vacationing in NM? I used to live in northern NM.

Sorry to bother you, but I am trying to get my head around this. When you say

dNGDP/dH=α′(NGDP/H)

I naturally think

δNGDP/δH = α′

So, OC, a log linear model makes sense.

But then I think, Huh?

But the equation holds in equilibrium, right? Since the information transfer is from NGDP to H, α′ is a maximum. A certain relative change in NGDP results in at most a certain relative change in H.

If that is right, then at this point I have a couple of unrelated questions in my mind. First, my impression of marginalism, which may be quite incorrect, is that it is about absolute differences, not relative differences. IOW, the economics student really is thinking about linear models, not log linear models. Perhaps that is one reason for resistance among economists to the information transfer approach.

The second question has to do with what Sumner is doing. He is vague in the post you referred to. Maybe his model fits an information transfer equilibrium, maybe not. In equilibrium a recession in the present, a relative drop in hours worked, could be caused by a relative drop in future NGDP -- but wait! Wouldn't that be a relative increase in future NGDP, as people spend the money they have accumulated in the present? Anyway, there is no obvious equilibrating mechanism, which is perhaps one reason why Sumner wants to have a futures market for NGDP.

One more thing, ΔM/M is reminiscent of Bernoulli's moral value of money, but he was talking about its value to an individual, not to the economy as a whole.

1. Hi Bill,

I'm not sure what you mean by saying α′ is a maximum -- the prime notation there doesn't mean derivative. It is just a constant and the prime just distinguishes it from the constant α in Sumner's post.

Actually in that post:

$$\alpha ' \frac{NGDP}{H} \equiv \alpha$$

Where the second α without the prime is Sumner's α. I actually have more to say about Sumner's theory here:

http://informationtransfereconomics.blogspot.com/2015/01/is-this-market-monetarist-model.html

I'd never heard of Bernoulli's moral value of money -- I will check that out. Sounds interesting.

2. Thanks, Jason. :)

I figured that α′ was a maximum because information transfer is maximal at equilibrium, right?

I will check out your post on Sumner's theory. One problem may be that in the post linked to earlier he is talking about recessions, and the correlation holds up during recessions.

I read about Bernoulli's moral value of money years ago in a small book by Lancelot Hogben. As I recall, Bernoulli used it for the St. Petersburg paradox. The moral value of ΔM, how much you risk or spend, is relative to M, how much you have. I don't know why Bernoulli chose that ratio. Perhaps it had to do with the probability of losing one's stake in iterated wagers, a problem that he may have been the first to solve.

2. Another question.

Assuming a transfer of information from the future to the present in financial markets, do the increasing profits of the middlemen represent a loss of information?

Thanks. :)

1. I don't know if you'd seen this post where you can interpret the ITM in terms of transferring information about the future to the present:

http://informationtransfereconomics.blogspot.com/2014/12/how-money-transfers-information-from.html

However, I don't know if I can answer that question at present ... I will think about it.

2. Thanks again, Jason. :)

Is the transfer of information from the future to the present related to the increase of entropy over time in a closed system? Secular stagnation = the heat death of the economy? ;)

3. That would be one way to look at it -- I came up with an economic temperature that goes as 1/log M:

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

3. I still think it would help if you published, then you wouldn't have to explain everything every 10th post, and we would not have to dig through 100s of posts to figure out what you are talking about ;)

1. Yes, Jason, I would be quite happy for you to refer me to where you have already dealt with my questions, instead of explaining things once again. :)

2. Ah, but blogging is fun! You get to make sarcastic comments and refer to an entire field as a bunch of idiots.

[Joking]

Bill -- I don't mind explaining things again because it helps me understand things better.