info: Hi econ! I'm working on a new economic theory -- can I get some input?
econ: Why are physicists always drawn to economics? You probably just want to show off how good you are at math again. I'll bite. What's your theory, info?
info: Actually, the math is really simple. Simpler than a DSGE model, anyway. It's based on information theory, and ...
econ: Information theory? Economists already use information in their theories. There's a whole field of information economics ... it's even got its own Wikipedia page.
info: That's not exactly the same thing. The content of a piece of information matters in information economics, right?
econ: I don't follow. How does a piece of information differ from its content? Information is its content.
info: There is a difference between saying you have a 10 GB flash drive and saying you have a 10 GB image file of a kitten, right? The first is only a quantity of information and the second is a specific instance of that quantity of information.
econ: I see. But I still don't see how that makes your information theory so different from information in ... oh, let's say game theory.
info: That's a good place to see the difference! In a game with perfect information, like chess, the locations of the pieces matter ...
econ: Of course the locations matter. It wouldn't be chess if they didn't.
info: Well, in the information theory I'm talking about, they don't. Actually, it's more like they might matter, but we don't really care. Anyway ... the information in the chess board can be encoded in a number less than 13^64 (six possible pieces of each color, plus no piece, in 64 squares) that would take about 237 bits of storage. That even includes impossible positions, such as a rook on every square.
econ: How could the impossible positions even matter?
info: That's a good question, but the only reason we know that some positions are impossible is that we know the microfoundations of chess -- the rules of the game. We don't really know the microfoundations of macroeconomics, yet.
econ: So you're not making any assumptions about the microfoundations of chess, you're just looking at it as 237 bits going back and forth between players?
info: Exactly! That's information equilibrium. The information received is the information sent. That's a great analogy ... I'll have to remember that one.
econ: You're welcome.
info: There's also something detecting those 237 bits going back and forth ...
econ: The win-loss ratio?
info: You're good! It would be the win-loss ratio of one of the players, though. We'd probably want to take a logarithm, too.
info: If two players are basically equal, or basically making random moves, you'd expect a win-loss ratio of about 50%. If it changes, one player is probably better than the other.
econ: But what does the 237 bits have to do with this?
info: Well, we'll need to consider if the chess board gets bigger or smaller for economic growth. And if there is a shade obstructing half the view of the board, only 118 bits are getting through. You'd expect a good player's win-loss ratio to fall under those conditions.
econ: What is that supposed to be, a recession?
info: I am not completely sure at this point. I'm still working on the theory.
econ: I'm just looking for the connection to economics.
info: Ok, ok. You can make the analogy of one player winning more than usual as a positive shift in the demand curve, raising the win-loss ratio. That's the price. It could also be a negative shift in the supply curve.
econ: We economists usually say the curves shift right or left, or up or down ... if we even use supply and demand curves at all outside of undergraduate economics 101.
info: So you'd probably not be impressed that information equilibrium leads to supply and demand curves?
econ: Not really.
info: Or the IS-LM model?
econ: Your ad hoc theory lets you come up with ad hoc models? Pass.
info: I've made some predictions of the future path of inflation.
econ: Economics isn't really about predictions. We're more like doctors than The Weather Channel. When something goes wrong with the economy, we tell you how to fix it.
info: Well, the theory allows you see the different effects of fiscal and monetary policy ...
econ: Well that's interesting. And relevant! Let's hear it.
info: Remember the 237 bits in the chess game? Well let's say NGDP is an encoding of a given economic scenario -- a chess board position --- with dollars being something like bits.
info: Now lets posit that NGDP is in information equilibrium with another number encoding the same economic scenario. Let's use the money supply.
econ: Which money supply?
info: It doesn't really matter right now.
econ: I assure you, it does matter.
info: We'll figure that out empirically later. Just hear me out for now.
econ: All right.
info: And the price that is detecting the information moving around, keeping both numbers in equilibrium like the win-loss ratio, is the price level.
econ: PCE or CPI? Core or headline?
info: [Sigh] ...
info: They're barely different from each other!
econ: Isn't there a joke about a physicist and a spherical chicken?
info: Anyway, when you put these pieces together you ...
econ: ... get the quantity theory of money. Yes, yes. But that's like a hundred years old and has pretty much been discredited by empirical evidence ... unless you add inflation expectations terms, I guess.
info: But it's not exactly the quantity theory of money. That's just the high inflation limit. As the economy grows, inflation tends to fall and that eventually leads to something that looks like a liquidity trap.
info: The reason seems to be that as an economy grows, a typical dollar is more likely to be used in a transaction in a low-growth market.
econ: But why is that?
info: Of all the possible economies you can have with an given NGDP, most have a bunch of low growth markets and a few high growth markets ... and that ratio gets bigger as the economy gets bigger.
econ: You still haven't explained why.
info: If you don't make any assumptions about how the economy works, that is just the most likely configuration. There are more ways an economy with a given NGDP can have a bunch of low growth markets than a bunch of high growth markets. It's like there are more ways you can send out a given amount of energy with a bunch of low energy photons than with a few high energy photons. It's a maximum entropy argument. Information entropy. There is an entropic force preventing high inflation that gets stronger with the size of the economy.
econ: That doesn't explain anything. You need to tell a story ... how do the incentives change for firms to raise their prices less when the economy is bigger?
info: You want me to tell you the Calvo fairy gets tired over time? Or can't get around to all of the firms as fast as it used to when the economy was smaller?
econ: At least that's a start.
info: That would be like adding a Goldilocks force to an atomic model that makes the atom move to where the density is not too high or not too low in order to explain diffusion. It's not only unnecessary ... it's actually wrong. Like Calvo pricing. Firms change their prices all the time. Menu costs are trivial.
econ: The Calvo fairy is just an example of a micoeconomic model assumption to get effects that are observed in empirical macro data into the model.
info: Then why don't you put your models up against empirical data?
econ: The data rejects too many good models!
econ: That's a bit of a joke. But there are lots of successful real-world tests of economic models. Auctions use economic theories to produce better outcomes. Did you hear about that prediction of how many people would ride a new BART line in San Francisco?
info: I have. In fact, I believe it used a random utility model that says the utility someone derives from making a choice has a deterministic component plus a random component.
econ: That's the one.
info: How is the random component different from what I am talking about? In a random utility model, people will not always make the best chess move they can think of that we can sometimes predict, but will also make random chess moves that we can't predict.
econ: It's still based on individuals making choices -- we just allow that there is a component we can't observe.
info: In that case the number of choices and the distribution those unobserved choices are drawn from -- the information theory -- become your only macroscopic constraints. Your deterministic piece is like the cell phone metadata and the random piece is like the content of a text message. That is exactly what information theory was designed for!
econ: Macroscopic constraints?
info: Sorry -- physics jargon. Empirically observed values of aggregate data. Like NGDP.
econ: I'm still not convinced. And it seems like you've come up with a quantity theory of money that can have a liquidity trap. This won't go well. I'll show you why. Let me call up a couple of friends. [dialing ... ] Hello? Hey, Paul, Scott, listen to this.
Paul: What's up?
Scott: Go ahead.
econ: You probably had no idea you'd be on the same telecon today. Anyway, so my friend info here has this new economic theory that's basically the quantity theory of money with a liquidity trap. Thoughts? You first, Paul.
Paul: Mainstream macroeconomics already has pretty good models of the liquidity trap. And the IS-LM model is a simple way to try and explain it without going all intertemporal. We don't really need new models unless they tell us something new.
econ: What's your take Scott?
Scott: A liquidity trap is a result of incompetent monetary policy -- if the theory really is a quantity theory in the spirit of Friedman, then why can't the central bank just create expectations of inflation or NGDP growth? A quantity theory liquidity trap is a bit of an oxymoron. Just create expectations of a permanent increase the quantity of base money!
econ: Ok, thanks, guys!
Paul: No problem.
Scott: Talk to you later.
econ: See, info?
info: You're right. I have my work cut out for me. The people who would like the liquidity trap in my model think their models are working just fine, and the people who would like a quantity theory don't believe in a structural liquidity trap.
econ: In economics, it's really hard to tell who is right because the data is uninformative. We mostly try to come up with a set of assumptions we like the most and see what we can derive from that.
info: Isn't there a joke about an economist assuming a can opener? Wait ... did you say "like the most"?!?
econ: Yes. And we as a profession really like the assumption that at the root of all economics is a complex ocean of human decisions and expectations. What the representative agent thinks determines the course of the economy.
info: Isn't there a contradiction between the complexity of human decisions and a story with a representative agent?
info: That doesn't sound very scientific. And the statement that macro data is uninformative is dependent of the assumed complexity of your models. If you think the models have a lot of dimensions, like millions of agents or an infinite number of expected paths of NGDP consistent with current conditions, then the data is uninformative. If you think RGDP is an exponential curve with a constant slope on a log chart, then the macro data is completely informative!
econ: But of course the macroeconomy is complicated! People are complicated and the economy is made of people!
info: An oxygen molecule is a really complicated diatomic system of electrons and quarks confined in baryons held together by meson fields, but an ideal gas is really simple. All the details of quantum mechanics, Yang-Mills theories with mass gaps and SU(3)xSU(2)xU(1) symmetry come down to a single number.
econ: But the economy's really complex!
info: It's about 260 J/kg K ...
econ: I said complex!
info: I guess I'll just keep writing on my blog ...
econ: Good luck with your theory! Remember, think: "complex"!
info: More like intractable.
econ: What was that?
Some of the dialog is based on actual questions from, quotes by or blog posts by Noah Smith, Chris House, Robert Lucas, Scott "Scott" Sumner, Paul "Paul" Krugman, Karthik Athreya, Nick Rowe, Simon Wren-Lewis and Robin Hanson. But many are my own lowly attempts at snark and humor.
An alternate title was "A dialogue concerning two high-GRE disciplines", but I thought that was a bit much.