Noah Smith starts his post on physics envy with:
I hear all the time that economists have "physics envy". This doesn't seem even remotely true. I'm not sure whether "physics envy" means that economists envy physicists, or that economists want to make physics-style theories, or that economists wish their theories worked as well as those of physicists. But none of these are true.
I don't think this captures what people mean by "physics envy" as applied to economists. The second one comes close, but the real charge that is being made is that macroeconomic theories are way too abstract and complicated given both the available data and how well the theories work at empirically describing the data.
The context of "physics envy" is evident in Noah's charge that macro data is uninformative. Yes, the macro data is uninformative ... if your theory is really complicated (as I've talked about before). You don't need graduate level mathematics (like the fixed point theorems used in proving the existence of Arrow-Debreu equilibria) when you can't really describe NGDP. Physics envy is one way to put it ... polishing a turd is another.
I think this post from Duncan Black aka Atrios nails it (Black has a PhD in economics himself). There is quite literally no reason for an economist to refer to the real numbers as ℝ or even refer to real numbers at all. To say x ϵ ℝ+ is pretentiousness compared to x > 0. That is physics envy. Orwell comes to mind  as well. In physics, there are reasons to refer to the set of real numbers ... the one loop correction to the anomalous electron magnetic dipole moment is ~ α/π. There is π, a transcendental number, right there in the formula. If an economist came out with an interest rate being ~ 1/π I would be suspicious.
That is what I think is meant by the phrase physics envy.
To be fair -- Noah himself doesn't appear to exhibit physics envy. He has two papers on his CV that are devoid of unnecessary mathematical abstraction for what they are attempting to describe. See here [pdf] (with some lovely long descriptive variable names) and here [pdf]. Maybe that is why he doesn't recognize it.
PS. There were two great developments in the history of mathematics: algebra and calculus. Algebra comes from commerce (the math of money and transactions happening in an abstract space of numbers, brought to Europe, especially Italy, via the Arabs -- hence the name from al jabr) and calculus comes from agriculture (the areas of land, the motion of the sun and planets). So I'm not sure this from XKCD that Noah links really gets these right. There should be two pyramids with physics and economics at the top of each and mathematics in the intersection. Money and physical reality are the two major drivers of mathematics and the mathematics that is actually developed tends to be constrained by this.
 I am thinking of Politics and the English Language: "Bad writers, and especially scientific, political and sociological writers, are nearly always haunted by the notion that Latin or Greek words are grander than Saxon ones ...". x > 0 in the example is the simpler way to say exactly the same thing. Of course am guilty of a lot of things Orwell was fighting against; I have a bad habit of too many e.g.'s, i.e.'s and q.v.'s.
Why do they need real numbers anyway? Everything is discrete in economics. I guess they wouldn't have existence/uniqueness of equilibria in a discrete setting.ReplyDelete
The above picture seems to reflect "math envy" more than "physics envy", but perhaps these are one and the same. It really looks like something out of a math book (although a mathematician would almost always write R in a blackboard bold style when referring to the real numbers).
My interpretation of the "physics envy" charge is that one is saying economists apply abstract mathematics, mathematical language and complex computations to reality just like physicists, but it's unwarranted in the economics case because of the lack of useful results.Delete
It's like economists see physicists using supercomputers to solve QCD and getting the proton-neutron mass difference out of it and say "me too!" -- putting a DGSE model on a supercomputer and getting something that's way off.
I think another way to put it is that "physics envy" is similar to labeling economics a "cargo cult" ... going through all the mathematical motions, but not ending up with much.
Now I'm not making this charge so much myself (I do think the macro models are too complex to be supported by the data) ... it's just my interpretation.
The proposition "there's no reason for a economist to refer to real numbers" is false within microeconomics, which is the content of that snippet. But I'll assume that you mean it in the context of a general theoretical position e.g. one that does away with utility, in which case it still wouldn't be right, but now it isn't even wrong. That's just your opinion, man.ReplyDelete
Overall, you've made an accurate portrait of "physics envy", but from the perspective of a physicist. I don't know if anyone outside of economics cares enough to know what "physics envy" is, and I've mostly seen economists using that expression, in order to attack other economists and economic schools. There had once groups entirely hostile to the use of mathematics in economics, like the German Historical School, and whose practitioners would have fault with any mathematical statement at all (not just a reference to the set of Reals). But such groups died out as they made increasingly larger concessions to the orthodox school and/or got absorbed by other disciplines. I currently don't know of any heterodox economist who is against the use of mathematics in economics today, but they still aren't excited about it. Point is that "physics envy" is largely dependent on what one thinks is the "appropriate" level of mathematics in economics, and once
even a simple integral was too much. Information Theory certainly would have been too much.
Also, references to Orwell are unnecessary, and somewhat dubious. Orwell complained about unnecessary, uninformative jargon, specially when used in order to couch the delivery of propaganda. Microeconomics is over-informative, and esoteric enough that it would never properly function as propaganda except on other economists (I refuse to pass judgement of the necessity of microeconomics, however).
By "no reason to refer to the real numbers" I meant both notationally ("as R") and as opposed to just calling them numbers like most people do. Economists definitely use real numbers (even transcendental ones like e), but there is no reason to make the distinction from rational or complex numbers or worry about Dedekind cuts, every sequence having a limit point or a Lebesgue measure.
[That is unless the gauge theory of utility turns out to be right!]
To be clear -- I am not making the accusation myself. I love math. We should use more of it. I'm just saying I understand the accusation and that sometimes the mathematical rigor in an economics paper is a bit over the top. And in macro specifically the rigor and complexity of the models seem to be well beyond what could be supported or rejected given the limited available data.
Otherwise your comments are well-taken. Cheers.
Another way: you can use calculus without knowing how it works -- Newton and Leibnitz came up with it before the real numbers were well defined (by Dedekind in the 1900s) and it's used by millions of people who haven't taken a real analysis course!Delete
Thanks for replying, I'm a regular reader and very much interested in your blog. Now I understand what you actually meant and I agree, economists sometimes do go overboard with formalism. This isn't the same problem as the one of macro, which is over-fitting their data. But perhaps they go hand to hand?
Thanks, and I agree that the over-formalizing and the over-fitting aren't the same thing. It does seem that they are related, though.Delete