Thursday, August 1, 2013

Econophysics for fun and profit

If you are a physicist planning on revolutionizing economics with your bold new theory, I highly recommend reading Cosma Shalizi's very excellent rant [1] "Why oh why can't we have better econophysics?". For a short version, check out the entry on "scientists" at Noah Smith's Econo-troll bestiary. In [1] Shalizi says:
Let me also complain that there isn't enough physics: the repertoire of ideas taken from physics is very impoverished. Basically, we see random walks, power laws, and spin systems over and over again. These are important ideas, but they're just a small part of theoretical physics! To give an example, Eric Smith and Duncan Foley have a fun paper working through detailed mathematical analogies between the axiomatic versions of utility theory and thermodynamics, leading to a reversible "engine" that runs on credit.
The link is broken and should actually point to this working paper [2] Is utility theory so different from thermodynamics? which has subsequently been published. What follows is kind of an unstructured comment on that paper and borrows liberally from it and other related materials by the authors.

It turns out attempting to find analogies between physics and economics has a long history, including Walras (1909) and Fisher (1926) among others. Eventually, economists got fed up with this. Paul Samuelson has a fit in 1960:
The formal mathematical analogy between classical thermodynamics and mathematical economic systems has now been explored. This does not warrant the commonly met attempt to find more exact analogies of physical magnitudes -- such as entropy or energy -- in the economic realm. Why should there be laws like the first or second laws of thermodynamics holding in the economic realm? Why should ``utility'' be literally identified with entropy, energy, or anything else? Why should a failure to make such a successful identification lead anyone to overlook or deny the mathematical isomorphism that does exist between minimum systems that arise in different disciplines?
Oh snap. Anyway, some of the basic ideas that came out of the thermodynamic analogy seem to be that goods are extensive measures like energy or volume and prices are intensive measures like pressure or temperature. Hey, that's what I found! Prices are like pressure, the quantity supplied is like volume and the quantity demanded is like energy in the information transfer model.

Foley and Smith [2] make a really interesting point about the thermodynamic analogy: economists tend to study what seem to be irreversible processes (people will not make exchanges to undo their utility gains) and physicists tended to study reversible processes (at least when they started coming up with thermodynamic laws). This difference changes the whole approach to problem solving, leaving the fields looking completely different. However, this is the point where I think [2] goes down a rabbit hole the information transfer model avoids. The authors make the mistake that Samuelson derides above: they make a homological association (in order to avoid the word "analogy") of utility with entropy.

The idea of utility maximization is pervasive in economics and inextricably links it with the normative ethical theory with the same concept. "Rational" expectations has economic agents out there maximizing individual utility. Cue Shalizi: "Alas, experimental psychology, and still more experimental economics, amply demonstrate that empirically [the neoclassical framework is] just wrong." If your economic framework has utility maximization as a fundamental theorem in the same way that thermodynamics has a second law, then the framework itself really is just a (likely normative) description of a particular class of states (since utility maximization is not generally true in the real world) and your entire mode of study as a would be econophysicist is to calculate expansions around your theory. This is perverse. It would be like building a particle theory in a quantum field framework, finding the vacuum state and then making up an entirely new theory to study deviations from that vacuum. That is to say the framework should ideally describe the fluctuations around the equilibria. Barring that, the framework should at least allow the kinds of fluctuations you see. If some of your fluctuations are meaningful and actually, whoops, violate fundamental theorems in your framework, then what good are your equilibria? 

My personal feeling is that the normative stuff got economics in trouble in a lot more ways than physicists trying to make analogies with thermodynamics. Homo economicus is an alien. If your models require humans to behave like this in order to be solvable then there is something seriously wrong. (For another interesting take, check out this great article on Nietzsche and Austrian economics -- the successful capitalist as √úbermensch, rather than, as most economics research shows, mostly just lucky or sitting on economic rent. I mean, basic analysis shows that without barriers to entry prices should become the marginal unit cost of production and profit should go to zero, no?)

The information transfer model avoids this morass the same way Shannon made information theory into a field in its own right: not caring about the content of the message. Information content is maximized in a random string! I don't care what the signal being sent from the demand to the supply actually is. This is not to say the information transfer model is right; it's just not normative. For example, diminishing marginal utility sounds pretty dumb if you try and ascribe it to the thermodynamic analogy in the information transfer model (weirdly quoting myself):
Translating [diminishing marginal utility] to the thermodynamic analogy the ridiculousness becomes obvious: it says "when undergoing an isothermal expansion, the pressure an atom is willing to exert falls because of the diminishing marginal utility of extra volume". Diminishing marginal utility for goods is actually a sign choice and is due to choosing demand as the information source rather than destination.
I precede that statement by noting the fact that in the information transfer model, diminishing marginal utility is not even a property of an economic agent (which aren't even defined), but rather an ensemble of economic agents.

I think if you are a physicist with an eye to revolutionize economics, you should keep a few things in mind. Theorems and fundamental laws that always apply don't translate well to the human domain. Be cautious when making normative claims and be aware of normative assumptions that are baked into your model. This is especially dangerous in economics due to its closeness to normative ethics and due to the moral gut feelings humans have about e.g. debt. And be nice: make sure your model reduces to stuff economists already know (for some reason people get angry when you declare their entire grad school education was all for naught).

PS What is it with Smiths and economics? Noah Smith, Eric Smith, Adam Smith. My last name is Smith, too.

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