"the initial price move ... cannot itself be correct"

Tyler Cowen pointed back to this (on the paradox of no market response) today:

Most generally, it seems the initial price move, in response to the Fed’s choice, cannot itself be correct, but that first price move must itself induce further price movements.

So maybe the initial response of the market is wrong? And then there are price movements toward some other value ... like maybe the information equilibrium value?

I've seen this in interest rates (previous link, and origin of the picture above) and exchange rates (more links at this link).

Hot potatoes and entropy; QE and inflation

Roger Farmer has a picture of QE overlaid with 1-year market inflation expectations (shown above). Something looked very familiar. I also have an issue with his timing ... he says:

From January of 2007, through September of 2008, expected inflation fluctuated between two percent and three and a half percent. When Lehman Brothers declared bankruptcy in September 2008, expected inflation fell by nearly eight hundred basis points in the space of two months and by October of 2008 it reached a low of negative four and half percent. 

Immediately following the Federal Reserve purchase of one point three trillion dollars of new securities, expected inflation went back up into positive territory.

Actually, it appears that the 800 bp drop coincides with the onset of QE. But maybe Roger is referring to the start of the onset of MBS purchases. In any case, this looks a lot like this picture ...

Which shows the simple "hot potato" model linked above (and here) -- the total amount of high powered money (yellow) and the entropy of the distribution (blue). Here are the animations from that link above showing the QE as well ...

If we take the entropy as corresponding to inflation expectations, the QE caused the fall in inflation (interest rates). Base reserves weren't distributed in a maximum entropy distribution (probably a Pareto distribution for banks) and instead were coordinated (concentrated among a few banks). This sudden correlation brought on by QE disappeared over time via random transactions.

Note this is analysis of the non-equilibrium dynamics of market expectations of inflation, not actual inflation which appears to have nothing to do with QE.

Correctly predicting Eurozone lowflation

Paul Krugman mentions Eurozone lowflation today ...

So how’s [the Eurozone] going? Terribly. Despite QE, euro area core inflation is stuck below 1 percent.

Basically, as I predicted back in January [note: this was on 8 Jan 2015, even before Draghi's announcement of additional QE on 22 Jan 2015] of this year.

Here's an updated graph of the information equilibrium model with the new data:

Gambling and information equilibrium

Source: wikimedia commons.

I was asked by a commenter to come up with a good intuitive metaphor for information equilibrium -- something I've been trying to do for awhile now. What popped into my head was a simple dice game. Two six-sided dice are always in information equilibrium with each other as each roll reveals 2.6 bits. The utility maximization approach would require both dice to show the same roll (both roll a 2 or both roll a 4) and matching theory would be something like the numbers on them being close (one rolls a 4 and the other rolls a 3). See e.g. here.

The interesting thing about that metaphor is that the six sided dice don't have to have the same thing on them. One could be a backgammon doubling die or have 6 different colors on it. And that makes sense in economics -- you're not usually exchanging two things that have an exact mapping to each other (e.g. like bacon and money, analogous to colors and numbers on the two dice).

Source: wikimedia commons.

In thinking about that metaphor I realized there is an amazing real world example of an exact conversion of money into information. It's called casino gambling.

You plunk down some money on a number in roulette. The information in a spin of the wheel is log₂ 38 = 5.24 bits. Of course, the payout is based on 36 (neglecting the zero and double zero), so there is some non-ideal information transfer -- a difference of 0.08 bit per spin. So the information in the payout odds is approximately equal to the information revealed by the spin:

I(S) ≈ I(O)

Actually we have I(S) > I(O), but let's assume equality for now. The information equilibrium model then tells us that (in general equilibrium):

S ~ Oᵏ

where k is called the information transfer index. And the the price is

p ~ Oᵏ ⁻ ¹

So what does this mean? Well, we have to resort to empirical evidence to establish our parameters. For one thing, the quantity of payouts (supply) is equal to the quantity of spins (demand). So k = 1. That means the price is a constant:

p ~ O¹ ⁻ ¹ ~ O⁰ ~ constant

The relative odds are the same no matter how much money you put down -- you don't get better or worse odds for playing more than one game. There is no return or growth (actually there is a slow loss due to the non-ideal information transfer). At least in this case.

There are even some partial equilibrium results. For example, in order for the quantity of spins demanded to stay the same given an increase in the number of payouts per spin, the price (the exchange rate for spins to payouts) would have to fall. Basically, the casino would have to provide worse relative odds (lower price) in order to keep the same number spins with an increased number of payouts.

Imagine if the casino was offering two payouts for every spin at the old 36:1 odds? There's no way you'd have the same number of spins. But if the odds offered fell to 18:1, you'd get the same number of spins as before (two 18:1 payouts are equal to one 36:1 payout). Note that the relative odds of the spin (38:1) and the payout odds (18:1) are now 2:1 (the price p is now 1/2).

These are the basics of the information equilibrium model. The model lets you have some freedom in choosing k to fit the empirical data so you can end up with slightly more complicated relationships that the simple linear relationship at the roulette table.

But where the model really makes a difference is when we look at a huge number of roulette tables and a huge number of spins. That's because even if the odds are 38:1, you only win 1 out of every 38 times. You don't win every 38th time. The actual path of any particular player is going to show random fluctuations in total winnings. That is to say the relationships above hold on average with a large number of spins.

No specific player is required to exactly win 1/38th of the time and some may actually go broke even with 38:1 odds [1]. And some might get rich. There may be a person that exactly breaks even over time, but there doesn't have to be. There is no specific representative agent. The representative agent that breaks even is emergent.

These relationships also hold regardless of whether some players have "a system", or even if they don't know how to play the game. They hold for robots, Vulcans, babies, pirates and whatever other trochees are out there.

Basically, the information equilibrium picture is agnostic about the details of what actually happens. It cares about information content.

Footnotes:

[1] The fact that people have a finite supply of money means that people will tend to go broke and be unable to play, lowering the overall relative payout -- a factor that would contribute to non-ideal information transfer. Actually, everyone will eventually go broke in this example given a finite supply of money.

Will they?

Source: wikimedia commons.

Will the Fed raise rates or keep them where they are (actually keep a 0.25% ceiling)?

Who knows? Tim Duy seems knowledgeable. But in our universe we put these things to a vote by a couple dozen people so the result should essentially be dominated by noise ... because nobody knows what they are doing. It's all randomness.

All I can tell you is that if rates rise, the monetary base will fall. And pretty much nothing else. The stock market might fall. But then the market might take a rate rise as confidence in the future and go up. Who knows? The markets have no idea what they are doing either.

It's all dither. We're grappling around an abstract space following entropy gradients. Excuse me, I should say it's all tâtonnement. It's a serious thing and we should use serious technical jargon.

Misunderstanding inflation in the WSJ

Mark Thoma links us to this at the WSJ:

If consumers believe that inflation will remain high, they tend to save and not buy goods and services, thus tempering demand in the economy.

What?

The cause of inflation (at least in mainstream economics) is that consumers want too many currently produced goods and services because they don't want to hold as much cash (e.g. because its value is decreasing because of loose money).

The behavior described in the WSJ is a potential mechanism to bring inflation down (i.e. a drop in AD)!

See also Nick Rowe on why economists think inflation could be bad (emphasis on the could):

Economists would instead talk about shoeleather costs, menu costs, relative price distortions, difficulties of indexing taxes, confused accountants, etc.

In the ITM, if you have high inflation, you're in luck: the quantity theory of money is a good approximation, monetary policy is effective and you can use it to control inflation!

Physics!

There were a couple of posts in my feed recently that make some references to physics, and as the econoblogosphere's resident Phd physicist (Noah Smith was an undergrad major, so were John Cochrane and Paul Romer ... sort of) I thought I'd weigh in.

First is this one ('You're Not Irrational, You're Just Quantum Probabilistic') linked to by Mark Thoma (and brought up by Tom Brown in comments). I might be missing something, but it seems that the "quantum" is unnecessary. They're really just using properties of non-orthogonal state vectors and non-commuting operators -- that is, the basic mathematics of vector spaces. The Hilbert space of quantum mechanics (and its non-commuting operators of position and momentum) is an example of such a model, but it's not the only one. Therefore using that specific model is probably not entirely accurate. It's like saying your model is a Ferrari, when what you're actually presenting is a model of car. Sure, "X is like a Ferrari" is a better headline than "X is like a car". That makes me think that the only reason they use the word quantum is because it's cool. You're Not Irrational, Your Brain Just Uses Noncommuting Operators isn't as exciting of a title. Nor is What Is the General Linear Space Model of Cognition, and How Is It Applied to Psychology? That, or the authors don't really understand what it is they've come up with.

The second one -- which is far more nit-picking on my part in what is a great post -- is this quote from Robert Waldmann:

Physicists are quite sure general relativity is not the truth (because it is inconsistent with quantum mechanics and therefore a lot of data).

I'm not sure "truth" is a useful concept here. Physicists don't think of general relativity as a thing that is true or false in a way that you could choose "false". They think of it as an effective theory: a theory that captures the phenomenology (describes the empirical data) and a theory that you could derive from whatever the "truth" is. String theory may be the "truth" -- and you can derive general relativity from it. Entropic gravity based on states on a horizon may be the truth (i.e. gravity isn't 'real', it's just thermodynamics) -- and you can derive general relativity from it. So general relativity is as much "truth" as the theories that contain it. As a mathematical consequence of truth, it must be truth, too.

General relativity is not empirically inconsistent with quantum mechanics (you can't use canonical quantization on it without the time dimension disappearing, but that is a theoretical consideration, not empirical). The two theories have non-overlapping regions where they have been empirically tested. All empirical tests of quantum mechanics are at short distances and all tests of general relativity are at long distances. You actually can't test them at the same time because the effects of general relativity beyond Newtonian gravity on the quantum scale are basically zero.

Actually, we could say quantum mechanics is inconsistent with general relativity -- it predicts a value of the cosmological constant that is off by 100+ orders of magnitude!

PS

I am under the impression that there is as big of a schism between undergraduate vs graduate economics as there is in undergraduate vs graduate physics. It's not that anything taught is wrong (or wrong-headed), it's just that it seems there are different ways of going about things -- so different that in other pursuits, they might even be considered different fields.

When someone makes the claim of being an undergraduate physics major, they're usually well versed in Newtonian mechanics, Lagrangian/Hamiltonian approaches, thermodynamics and quantum physics (and some other stuff like math). Unfortunately, this tends to leave out two major organizing principles and one major perspective shift:

Physics is the study of symmetry. You learn energy and momentum conservation as an undergraduate. As a graduate, you learn time and space translation invariance (symmetry). Newton's laws are basically a consequence of Poincare symmetry at speeds less than the speed of light.

All theories are effective theories. This is referenced in my discussion of Waldmann's post above. Physicists don't think general relativity is "wrong" because it isn't quantum. General relativity is an effective field theory of physics at large length scales. Actually, general relativity is the effective field theory of physics at large length scales. Whatever the fundamental theory of everything is, it must reduce to general relativity in the proper limit. So whatever the fundamental theory of everything is, it contains general relativity. That's why people like string theory: it contains general relativity. Entropic gravity also contains general relativity. All empirically valid theories are viewed sort of like Taylor expansions, analytic continuations or ensemble averages of a more fundamental theory. Newton's laws are derivable from quantum mechanics and you can show < F > = m < a >. It's quite fun to look at the Earth-Moon gravitational system as an extremely high energy level of the Hydrogen atom solution to the Schrodinger equation with a different coupling constant.

Mathematical objects have physical reality. There are some objects called D-branes and NS-branes in string theory. Those names come from Dirichlet (function value) and Neumann (function derivative value) boundary conditions from your undergraduate differential equations class (they determine how you treat the ends of strings). The assumptions and theoretical constructs you make (or derive) in your theory have a physical reality. That's why Dirac proposed the positron (a consequence of making the Schrodinger equation relativistic for spin 1/2 particles). That's why physicists were convinced the Higgs existed and why people are out there looking for supersymmetric particles.

PPS

This last bit is why I tend to look at utility, expectation operators (those E's) and even equilibrium conditions in DSGE models as posing a lot of questions. If your model has these things, they must represent an economic reality. An equilibrium condition must be measurable economic construct that has dynamics just like a Dirichlet boundary condition is a D-brane with an energy density flying through an 11-dimensional universe. A good example (in my head) is that your Taylor rule in your New-Keynesian DSGE model has a physical reality as the central bank. The Taylor rule is the central bank. At least, in that specific model.

The rest of that NGDP growth vs base growth graph

Scott Sumner shows a graph of year over year NGDP growth alongside a graph of the year over year growth of the monetary base. Here's the rest of that graph:

You can see the change from an approximate 1:1 correspondence to at best a 10:1 correspondence.

This doesn't go through a big change in relative impact 2008:

Of course, this is a good model, as opposed to this. Maybe the Fed should target the number of jobs ...

Maximum entropy better than game theory

From NPR's Planet Money.

Richard Thaler has an article up where he discusses the Keynesian beauty contest. He does the test that he did with the Financial Times in 1997 again in 2015. That test is as follows: You win if you correctly guess 2/3 of the average of all entrants' choice of a number between 0 and 100.

• The Nash equilibrium of this game is zero (essentially an infinite regress of guessing and second-guessing 33, 22, 15, ...).
• The maximum entropy (information equilibrium) solution is 2/3*(50) = 33 (all states are equally likely, therefore 2/3 of the ensemble average of 50 is 33).

The final results of the contest were 18.9 (in 1997 with 1382 contestants) and 17.3 (in 2015 with 583 contestants) which means the error is:

• 19 (17 in 2015) for Nash equilibrium
• 14 (16 in 2015) for maximum entropy

So the two models are about the same.

However! This also illustrates the negative impact of expectations via non-ideal information transfer as the "price" (i.e. guess) in this case "should" be 33 -- the average guess should be 50 if we weren't second guessing each other and driving the price to zero.

The information transfer model in its full generality would say x ≤ 33 if you don't know that the market is ideal. An ideal market would have x = 33.

Since the information transfer framework understands its own limitations, it is a better model than the game theory result of x = 0. Basically x ≤ 33 beats x = 0 as an answer.

This also explains the the Keynesian idea that Paul Krugman put on his blog today:

Economies sometimes produce much less than they could, and employ many fewer workers than they should, because there just isn’t enough spending. Such episodes can happen for a variety of reasons; the question is how to respond.

Sometimes markets aren't ideal and you have non-ideal information transfer. That results in lower prices and less output (measured in money).

...

Update:

I am thinking about how MaxEnt would be applied to the cutest animal contest in the picture at the top (a picture I also reference here). My best guess is 1) something like the Monty Hall problem leads us to 2/3 = 67% and 1/6 = 16% for the other two or 2) that the logic that 1/3 will choose a given animal and 2/3 of those people will choose a different animal, leading to an approximate floor of 1/9 = 11% for the low performers (and a ceiling of 7/9 = 78% for the best).

Thought experiments in alternate universes

Alternate universes ... [reference]

A couple of days ago, I did an update to this post on Dani Rodrik's new book and his view that various economic models are actually just experiments on systems that are theoretically isolated via assumptions -- a view that I think is actually pretty silly.

I realized that there's a better analogy for what Rodrik is trying to say.

In a sense, Rodrik is saying economic models are thought experiments in alternate universes. Those alternate universes are created from the different economic assumptions. The picture above has a collection of universes with positive, negative and zero cosmological constant; however, the assumptions in economic models of perfect competition or satiation of preferences (or transitive preferences themselves) create e.g. different Arrow-Debreu universes with different properties.

What it comes down to is that if you want to use your alternate universe model to address policy in our universe, you're going to have to:

a) Have fundamental theory that tells you when the assumptions are valid
b) Empirically determine the assumptions are valid
c) Prove that your model is independent of your assumptions
d) Some combination of the above three