On taking the people out of economics

I have recently returned from business travel and haven't had much time until now to properly respond to this riposte from Mike at his blog Free Radical and the comments below from myself and Tom Brown. This post originated as a response in the comments at the blog, but has since became so unwieldy that I decided to post it here.

In general, I am am aware that the ideas I am presenting on this blog are outside the mainstream and may well be totally wrong (or worse, trivially obvious) when translated into more traditional economics language. That's why I try to make contact with more traditional economics as much as possible. Some examples: the quantity theory of money, the IS-LM model, some other pieces of Keynes' General Theory, equilibrium in a two-good market, and the behavior of interest rates with monetary policy.

In the following, I cut some quotes from the comments on Mike's post and respond to them below (so please excuse the lack of narrative flow). Most of the points Mike makes are valid criticisms of the theory (or are simply differences of opinion), so I'll mostly focus on answering explicit or implicit questions in the comments and the things that I disagree with.

Mike said: "If [the information transfer model] functional form doesn’t come from the data, I can’t tell where it comes from since, seemingly by his own description, it doesn’t come from some kind of logical analysis of human decision making."

It follows from information theory. The foundational hypothesis is that human decisions are demand information communicated through a channel (monitored by the price mechanism) to the supply. But like information theory, the meaning of the information in the channel is largely irrelevant, only the amount matters. The price moves to bring the information coming from the demand and the information received by the supply into equilibrium under ideal circumstances. Additionally, the total information flowing through a particular market is proportional to the size of that market. In most cases, I assume that the information flowing through a market is equal to the maximum amount of information that can flow through that market. That seems to work remarkably well. Human decisions do appear to have influence -- most of the time reducing the amount of information flowing through a market.

Mike: [questioning whether “dD/dS” is meaningful]

The mathematical object dD/dS is like an exchange rate of demand for supply and is equal (in the model) to the price of that specific good demanded/supplied. It is the infinitesimal change in demand that comes with an infinitesimal change in supply. A really good analogy is that it's a definition of the force due to the invisible hand. Demand must in general be allowed to change with changing supply so any theory of economics that involves supply and demand should state some relationship that includes dD/dS. It may be couched in terms of money -- so that we'd see dS/dm and dD/dm, which come together via (dD/dm) x (dm/dS) = dD/dS.

Mike: "if you have one model with a lot of “shortcuts” built mainly on statistical observations ... "

The information transfer model isn't built on statistical observations. It's built on information theory, and the information theory is consistent with statistical observations. It's more of a standard "posit some axioms and see what results" kind of approach (things are never that simple in practice, but that's kind of what I'm going for). Newton posited some axioms about force and momentum conservation. The predictions from that theory appeared to "explain" statistical observations.

Mike: " ... relationships with no logical justification related to individual decision making ..."

The idea is that humans can't violate information theory regardless of what they decide. Now that idea might not be useful (from looking at the data, it has some success but applicability limited to broad trends), but it can't be wrong -- e.g. humans cannot send more information through a channel than its capacity no matter how hard they try. Information theory represents a boundary of any possible economic theory. Boundaries are only useful if the system pushes up against them, though. Knowing the total available wind power available on Earth for extraction by windmills is a fairly useless number because neither wind power nor human power consumption are anywhere near that limit. Economic systems appear to be operating fairly close to their information processing limits and those limits are independent of the information being processed (e.g. human decisions).

Mike: " ... There is no logical reason why it makes sense for gravity to exist. It just does. It can only be identified through observation."

If you observe the effects of special relativity (a specific symmetry of the universe), then gravity (general relativity) has to exist unless you can produce a good reason it shouldn't exist. I only metion this because it carries over into the discussion here: if you observe long run neutrality of money (an approximate "symmetry" of economics), then functions of the supply and demand functions must obey homogeneity of degree zero -- if D → α D and S → α S, then f(αS,αD)  → α^0 f(S, D) -- which means that the simplest relationship between supply and demand you can write down is (1) dD/dS = c D/S. In the information transfer model, this equation gives you supply and demand curves (alternately holding S and D constant). If this equation (1) isn't true of your micro theory based on human decision-making, then your human theory is going to violate long run neutrality. What is interesting is that the information transfer model gives us long run neutrality as a symmetry without a lot of effort.

Another related point: people frequently say things like such and such result proves Newton was wrong about gravity and Einstein was right. Any theory of gravity must reduce to Newton's theory in some limit because it can't violate some basic mathematics of three dimensional space (and of course, Einstein's theory does). In this same way, any economic theory that at least approximately has long run neutrality must be approximated by the information transfer model -- and that is independent of human decision making. It is possible long run neutrality isn't even approximately true and the reason could well be due to human decision-making (or it could be true because of human-decision making). However, those are empirical points that don't come down to whether or not you think human decision-making is relevant to economics. Either there is an approximate long run neutrality of money or there isn't.

Mike: "For instance inflation runs at 5% forever but people continue to expect it to run at 1%. This is precisely that kind of thing is easy to overlook if you aren’t paying any attention to what makes sense for people to do and that’s what happened with early versions of the Phillips curve and that is why we now have rational expectations."

Yes, I completely agree that observing the Phillips curve and using the regularity as a basis for a theory is not always good methodology (it can be an interesting thing to try, but then your theory becomes vulnerable to whatever unknown effects you aren't modeling, not even restricted to changes in human behavior). However in the information transfer model, we start with ideas that must be true regardless of what human behavior is. Information transmitted through the price mechanism cannot be less than the information received at the other end, for example. If information in equals information out (the assumption in the information transfer model), you can say more -- especially about changes in the information on one side of the transaction vs the other. This approach doesn't have to result in anything useful (in physics, the information approach results in a rather simplified view of the expansion of the universe that doesn't say much more than "the universe can be expanding"); it is a happy accident if it does (in physics, the approach can be used to derive the ideal gas law). In economics, it seems to have some useful results.

Mike: "I’m not exactly sure what you mean by “analog.” Maybe a single molecule can’t “evaporate” but there is still something happening on the molecular level regarding the behavior of molecules relative to each other or something like that which you wouldn’t notice if you had no concept of a molecule to work with."

Entropic forces do not exist (have no analog) at the micro level (they are weakly emergent per Tom Brown's comment).  At the molecular level there is nothing happening that isn't captured at the macro level by the boiling point and heat of vaporization for a general fluid. Most of the laws of thermodynamics were worked out (correctly!) before anyone knew of the existence of atoms. Atomic theory allows you to predict the numbers (boiling points, heat of vaporization). In this sense, microeconomics and human behavior should allow you to e.g. predict the coefficients in the information transfer model and the deviations from it.

Mike: "I can’t remember who ([Tom Brown] or Jason) said it or where and I think I already said this once before but demand does exist at the individual level."

It was me. I was saying demand curves for single markets don't exist at the individual level, at least not in any way that could be captured mathematically. Nor does "aggregate demand". I'm not challenging the idea that an individual person will want to purchase something they want, though. They just won't necessarily have a smooth curve vs price that is independent of other goods. In a sense, a statement of demand for an individual is something like this:

I'd buy an android tablet if one is available soon between 100 and 200 dollars, or an iPad if the price drops to 350 dollars**. Maybe my wife will buy me an iPad for my birthday, so I'll stop shopping around when my birthday gets closer. I don't need more than one tablet, so regardless of price, I won't buy more than one.

This is just one piece of the information that is being transferred to the tablet supply when this person buys a Nexus tablet on sale for 200 dollars the next day. It strongly depends on more than a single good (iPad, Nexus tablet), has a non-linear dependence on price (constant between 100 and 200, but also totally different for an iPad), the preferences of other economic agents (his wife), and time (the birthday). If you aggregate every such desire in the information transfer model, you get something like a demand curve (the total quantity demanded vs price) even though most individuals will buy only one tablet (this is not critical and doesn't apply to all goods, but is at least one way demand curves don't really exist for individuals). The reason you can aggregate these desires in the information transfer model is because you really don't care about the content of the desire -- you just know it exists.

This is my opinion, but I'd say any micro theory that purports to model the content of that indented block of text above is, in a word, hubristic. (Maybe the ITM is just a different kind of hubris.) It's even more difficult than it seems because humans exhibit many cognitive behaviors that would render that block of text totally irrelevant. The preference may change in an Apple store (framing effects) or may not even represent an accurate description of the preference at the time (affective forecasting and rationalization). And even if you were successful, the details of the human model can't have any impact at the macro level if macro can be reduced to a small set of variables like the price level, NGDP, monetary base, etc (an kN dimensional space of N heterogeneous agents with k attributes cannot be collapsed into an M-dimensional space of M macro variables with M << kN unless human behavior doesn't matter except as small collection of parameter values). If macro is tractable as a finite dimensional model, then individual behavior can't matter as anything more than a coefficient.

Mike: "The only way to be able to predict [changes in economic relationships] is to try to identify that structure which is based on human decision making."

This may be more of a yin-yang or figure-ground thing. I'd say the only way to know how to incorporate human decision-making in economics is to first understand what is independent of human decision-making (or another way: what is true regardless of human decision-making). Maybe that isn't the best approach, but I'm giving it a try.

...

Tom Brown did a great job giving an accurate account from a different perspective of what I've been saying; if you don't want to take my word for it, Tom's account is great. Therefore I have only a couple of things to say about his comments (and an answer to a question):

Tom: "“If [microfoundations survive aggregation to into a macroeconomic model as anything other than a coefficient], the resulting model is likely intractable.” ... I take the idea to be one of his hypotheses, not necessarily a statement of absolute fact."

I'd liken it more to intuition (based on my experience with complex systems), but I guess statements of intuition are essentially hypotheses. And actually, I was quoting something I said that a commenter had an issue with.

Tom: "I wonder if Jason would describe his theory as looking at macro as a weakly emergent phenomena, rather than a strongly emergent one?"

Yes, weakly emergent is a good description. It should be possible to compute the macro theory from the micro theory, but the behavior of the macro theory doesn't necessarily follow directly from the micro theory.

** I don't write dollar signs because they mess up the LaTeX stuff on the blog via mathjax.