Wednesday, February 10, 2016

One more physics analogy


David Glasner found a back-and-forth between me and a commenter (with the pseudonym "Avon Barksdale" after [a] character on The Wire who [didn't end] up taking an economics class [per Tom below]) on Nick Rowe's blog who expressed the (widely held) view that the only scientific way to proceed in economics is with rigorous microfoundations. "Avon" held physics up as a purported shining example of this approach.

I couldn't let it go: even physics isn't that reductionist. I gave several examples of cases where the microfoundations were actually known, but not used to figure things out: thermodynamics, nuclear physics. Even modern physics is supposedly built on string theory. However physicists do not require every pion scattering amplitude be calculated from QCD. Some people do do so-called lattice calculations. But many resort to the "effective" chiral perturbation theory. In a sense, that was what my thesis was about -- an effective theory that bridges the gap between lattice QCD and chiral perturbation theory. That effective theory even gave up on one of the basic principles of QCD -- confinement. It would be like an economist giving up opportunity cost (a basic principle of the micro theory). But no physicist ever said to me "your model is flawed because it doesn't have true microfoundations". That's because the kind of hard core reductionism that surrounds the microfoundations paradigm doesn't exist in physics -- the most hard core reductionist natural science!

In his post, Glasner repeated something that he had before and -- probably because it was in the context of a bunch of quotes about physics -- I thought of another analogy.

Glasner says:
But the comparative-statics method is premised on the assumption that before and after the parameter change the system is in full equilibrium or at an optimum, and that the equilibrium, if not unique, is at least locally stable and the parameter change is sufficiently small not to displace the system so far that it does not revert back to a new equilibrium close to the original one. So the microeconomic laws invoked by Avon are valid only in the neighborhood of a stable equilibrium, and the macroeconomics that Avon’s New Classical mentors have imposed on the economics profession is a macroeconomics that, by methodological fiat, is operative only in the neighborhood of a locally stable equilibrium.

This hits on a basic principle of physics: any theory radically simplifies near an equilibrium. One way this manifests is through new effective degrees of freedom. I'll take an example from some (I guess not-so) recent news: the Higgs boson. The Higgs mechanism is based on "spontaneous symmetry breaking" where the vacuum state, instead of being zero, has e.g. some positive energy value. What happens is that the universe falls from an unstable equilibrium to a new stable one -- typically illustrated by a potential energy surface shown in this diagram:


The unstable vacuum state of the universe is brown and the stable vacuum state is dark blue (at least one of them). This blue state also "breaks" the rotational symmetry of the diagram (and it falls there "spontaneously"). Additionally, the perturbative theory around the blue vacuum is much simpler -- near the equilibrium it consists of non-interacting massive particles (the degrees of freedom in the upward curved direction) and massless "Goldstone bosons" in the flat circular direction (blue circle). These are new simplifying -- effective -- degrees of freedom. The theory at the brown point is a much more complex interacting theory.

How does this relate to what Glasner says? Well consider a macroeconomic state space with multiple stable equilibria, like this:


Generally, the fundamental theory is complex. However, in the neighborhood of a stable equilibrium (as Glasner says), the theory simplifies with new effective degrees of freedom ... for example: optimizing agents with rational expectations. Glasner's "macrofoundations" of these effective rational agents are analogous to the equilibrium vacuum state of the universe giving us the simplified effective theory.

One way to interpret this is that rational agents are a fiction -- the true microfoundations are the microscopic theory underlying the locations of the equilibria. In the analogy, the true microfoundations would be the Higgs field, not the simplifying Goldstone boson representation in the observed vacuum state. The latter are a simplifying fiction in the neighborhood of the equilibrium.

A second way to interpret this is that it is possible we have an effective theory of rational agents when we are near equilibrium. It is possible we have effective rational agents like in this emergent picture and even an effective intertemporal budget constraint

The first case would be the ultimate paradox for the hard core reductionist view of economics. The rational optimizing agents they think are true microfoundations are just effective degrees of freedom that should be derived from a more complex, more fundamental theory.

But in physics, we take the second view -- because physicists aren't that reductionist. A theory that works is the best theory. And that's not necessarily the more fundamental one.

35 comments:

  1. "Possibly the greatest number of physics analogies ever to appear in an econ blog (and a guest appearance from me)."

    It took me a few reads to realize that the "econ blog" you were referring to was Glasner's (right?). But I'd contest that: since it originally appeared on Rowe's blog (in the comments, but whatever), and secondly, YOUR BLOG blows any other "econ blog" away in terms of physics analogies! (Well, it's got to be up there anyway, especially after this post).

    But I see what you mean... physics analogies showing up in the body of a post by a real econ blogger. Yes, I'd be amazed if you weren't right about that!

    (I almost put "real" in quotes there, but that seemed like an insult to David -- not my intention).

    Interesting post here too, BTW.

    ReplyDelete
    Replies
    1. Also, I'm pretty sure it was Stringer Bell who took college classes in "The Wire" while his partner Avon Barksdale served time in prison.

      But I've been known to get it wrong before...

      Delete
    2. You're right -- It's been years since I saw the show.

      Delete
    3. Don't be too sure of the stability of your 'local equilibrium' even if it does exist:

      Keynes message could probably be read as don't put too much faith in the stability of your 'local equilibrium':

      [Ricardian theory], being based on so flimsy a foundation, it is subject to sudden and violent changes. The practice of calmness and immobility, of certainty and security, suddenly breaks down. New fears and hopes will, without warning, take charge of human conduct. The forces of disillusion may suddenly impose a new conventional basis of valuation. All these pretty, polite techniques, made for a well-panelled Board Room and a nicely regulated market, are liable to collapse. At all times the vague panic fears and equally vague and unreasoned hopes are not really lulled, and lie but a little way below the surface (Keynes 1937: 215).

      https://radicalsubjectivist.wordpress.com/2012/09/18/keynesian-uncertainty/

      NK

      Delete
    4. Hello NK,

      I don't assume that an equilibrium exists or is stable.

      I am making the argument that rational agents only exist as effective degrees of freedom near a stable local equilibrium. If the equilibrium doesn't exist then rational agents don't exist ... which is fine by me.

      In general, the information equilibrium picture says that exactly what you quote can happen. It is called non-ideal information transfer and I talk about it more here:

      http://informationtransfereconomics.blogspot.com/2015/03/non-ideal-information-transfer-tail.html

      Delete
  2. "This hits on a basic principle of physics: any theory radically simplifies near an equilibrium."


    Jason,

    Can you add a little more explanation here?


    Henry

    ReplyDelete
    Replies
    1. Any equilibrium is characterized by a local minimum or maximum of some function. Local min or max is a local quadratic, with no linear term (local min or max means derivative is zero), so perturbations around equilibrium are basically isomorphic to harmonic oscillators -- locally.

      One way to visualize it is to know that at a stable equilibrium, your system doesn't move off of it. That's a boundary condition for any theory that is close to it -- for small enough perturbations, nothing happens.

      Delete
    2. So where is the simplification?

      H.

      Delete
    3. Any complex theory is isomorphic to a simple theory near the equilibrium.

      Delete
    4. Are you saying that because the system is at a local min or max that that part of the function which puts the system in this equilibrium is in effect having no effect and all that there is to disturb the system are the terms in the function which appear as small perturbations?

      Delete
    5. "Local min or max is a local quadratic, with no linear term"

      How about y = x^4?

      Delete
    6. Henry,

      It isn't "having no effect" -- it's just approximated by a simpler theory.

      Tom,

      That's zero to o(x^2) so the theory is even simpler locally (equal to a constant, I.e. The equilibrium value).

      Delete
    7. It isn't "having no effect" -- it's just approximated by a simpler theory.

      I haven't chosen my words well.

      H.

      Can we replace the word "theory" with the word "function"? I presume the function describes the surface that you have shown in your second image? At the peaks and valley lows the function's derivative is zero. But there are other terms in the function which only have an impact on the function loco the min or max - these are what you call the small perturbations and what might cause the equilibrium to be lost? And it's these perturbations which constitute the "simpler theory"?

      Delete
    8. It is a functional of the field, but function is fine.

      Yes. The perturbations are the simpler theory.

      I wouldn't call the equilibrium "lost" -- we are just looking at perturbations around it. When a pendulum is oscillating, the equilibrium isn't "lost"; it's just swinging around it.

      Delete
    9. "The perturbations are the simpler theory."

      Well, isn't there an even simpler theory, without the perturbations?

      I remember a time when the US Navy calculated ephemerides some 50 years in advance using numerical methods. OC, these took all known perturbations into account. But if you wanted to calculate the position of the planets 5000 years in the past, you were better off just using Kepler's laws and ignoring perturbations. Your errors were on the order of one degree, but so what? When economists appeal to equilibrium, for the most part aren't they ignoring perturbations? That is, all shocks are exogenous? As Nick Rowe so often says, we start at equilibrium and then suddenly something happens.

      And how simple are perturbations? Again with reference to the solar system, wasn't it shown in the 1990s that known perturbations are enough to make the solar system unstable on the order of hundreds of thousands of years?

      And as far as economies go, don't both modern depressions and ancient jubilees suggest that economies that run on debt are unstable on the order of a human lifetime? (Not that debtless stability is a blessing.)

      Delete
  3. "What happens is that the universe falls from an unstable equilibrium to a new stable one -- typically illustrated by a potential energy surface shown in this diagram:"


    Jason,

    This suggests the universe exists within a system - that it is part of a system. How can that be? Isn't the universe the "system" by definition?


    Henry

    ReplyDelete
    Replies
    1. The universe has a vacuum expectation value for the Higgs field. It could have had other values for the Higgs field -- including zero (as it would have been early on). The fact that there are many possible values (and thus many possible universes) does not contradict the idea that there is one "universe" we observe.

      Delete
  4. Jason, it's cool that a physics story made the lead on Google News today. I checked CNN, it's there too. (Not Fox though... not even in their science section!... actually not MSNBC or ABC either)

    I so hope the moderators slip a question about gravity waves into the next debate! Lol.

    ReplyDelete
  5. In case you didn't see it on twitter, Glasner did an update incorporating pretty much the entirety of your post here.

    ReplyDelete
  6. I am Responding to an IdiotFebruary 19, 2016 at 9:47 AM

    This blog consists of two morons talking to each other (Jason Smith and Tom Brown) and occasionally posting nonsense on other, more capable people's blogs (like Steve's). I cannot urge you two nitwits enough to just quit -- you're embarrassingly uninformed and ill-equipped.

    ReplyDelete
    Replies
    1. Lol!... No, I don't think that's Noah Jason. I've seen someone with that handle comment at Noahpinion though. I started to reply to him there... But i didn't get much past my introductory salutation...

      "I am Responding to an Idiot, er... well that's all really."

      I guess he took it personally. That was more than a week ago though.

      Delete
    2. ...and BTW, AFAIK, you didn't come up. It was just me responding to what I recall being a generally obnoxious comment. See, for example, exhibit A above.

      Delete
  7. I know that I am a bit late to this party, but I just saw this discussion over on Uneasy Money.

    I am a (former) physicist, so I was quite amused by these discussions. In fact Avon Barksdale is even wronger than you are getting at. In physics, both historically and as a matter of principle, one always starts with the macro theory and proceeds to the micro. Macro tests micro, not the other way around.

    For example: The modern science essentially started with Newton's Law of Gravitation explaining the motions of the planets. Planets are pretty macro after all. What goes into that? Well, for one thing you need a rigid body approximation - the planets don't collapse to points under their own weight.

    The composition of matter wasn't understood for more than two centuries after, but one of the things that had to be explained was the existence of rigid bodies. That is brought about by quantum mechanics and the antisymmetry of fermion wave functions, ensuring that atomic orbitals take up space and can't sit on top of each other.

    Had a proposed theory of the structure of matter failed to explain rigid bodies, it would not have been the rigid body approximation that would be invalidated, rather the proposed micro theory.

    Or to use another example: thermodynamics was a well-validated theory - one that was used to design steam engines for example - for long before the atomic theory of matter was accepted and statistical mechanics gave "micro-founded" meanings to the macroscopic variables such as "pressure" and "temperature". And, as in the above case, it's the macro theory that is the test of the micro theory, not the other way around.

    Philosophically, this is because the world we actually observe is that of the macro variables, not the variables of the micro theory we're using to explain things.

    The analogy to economics is direct. When an economist draws a supply curve with a "price" on one axis, that is not a variable with micro meaning. We have individual transactions each with something being sold, and the price on the axis is a function of the aggregate of transactions. The micro models Avon Barksdale is referring to are just guesses as to the "physical laws" (i.e. the motivations) obeyed by those entering into the transactions. Nothing about these motivations is itself an observable quantity; only the behavior of the transactions can be measured. (And to top it off, the "laws" are obviously egregious simplifications that no one would mistake for a real explanation of the behavior of an actual human being.)

    If those making the claim that IS-LM should be rejected because it is not microfounded could actually prove some sort of "no-go" theorem, showing that it was not possible with *any* micro model to derive IS-LM, that would be interesting. In the absence of that, the observed truth of IS-LM can be used to rule out particular micro models, but that's pretty much the end of the story.

    ReplyDelete
    Replies
    1. Thanks for the addition.

      I like the idea of a "no-go" theorem.

      Regarding your supply curve picture, that's kind of the idea behind this blog -- the basic theory is in my paper (linked on the sidebar and in the blog subtitle), but I put together some animations at this link:

      http://informationtransfereconomics.blogspot.com/2015/03/supply-and-demand-as-entropy.html

      (I should have probably said "entropic forces" in the title.)

      Delete
  8. This is Avon Barksdale. Just saw this. Jason, you purposely misrepresented what I wrote. I did not talk about microfoundations of a model, I talked about the foundations of the theory. It's not effective field theory that's at issue here. It's the foundational stuff like Lorentz invariance, conservation of energy and charge, etc, not the inner works of any particular model. Think spin-statistics not chiral perturbation theory. That's the foundational stuff that the macro revolution got right and it's what Levine is getting at.

    ReplyDelete
    Replies
    1. Hi Avon,

      I am not sure I understand the distinction you are making between "microfoundations of a model" and "foundations of a theory". To me, those phrases have identical meanings except the former explicitly refers to a scale. I do not think you are accepting Glasner's "macrofoundations" of micro, so the "foundations" would essentially have to be microfoundations.

      What is the economic equivalent of Lorentz invariance or the spin-statistics theorem (the latter being a consequence of the former)? [Actually everything you note is either a symmetry principle or a consequence of a symmetry principle, and symmetry principles are deeply connected to the construction of effective field theories.]

      I've personally considered "homogeneity of degree zero" as it is referred to in econ (in physics, we'd call it a conformal symmetry) to be an example -- scaling the nominal values of everything yields the "same" economy. But I know of no similarly widely accepted principle in mainstream economics.

      Delete
    2. Jason,

      I don't trust economics that doesn't start from two fundamental laws:

      1) People are self-interested and they organize their lives around that self-interest.

      2) People are good at making choices that reflect their self-interest.

      Keynesian economics does not reflect these basic laws. There are no “people” in a Keynesian set up in which I can see how people are making choices. Compare Keynesian explanations about what happens with shocks to a person's income with that of the permanent income hypothesis. The “effective theory” that is the permanent income hypothesis posits that people have utility for consumption and that they are trying to maximize a lifetime discounted utility for consumption flow. A simple effective theory posits a quadratic utility function with a mean reverting income, a random walk in consumption and a discounted utility for consumption flow over an infinite number of time periods. People can borrow but with no Ponzi schemes allowed. Now in this effective theory we see that people smooth consumption and in particular that consumption and borrowing both follow a random walk, but as cointegrated time series. Now, that's top notch econ. The model is recursive and forward looking. It gives falsifiable predictions; it is based on the two fundamental laws above. You can make these models more complicated and realistic – you can extend the effective theory, but always under the restriction of the two above laws. The people in the model must extremize something connected to their self-interest over an anticipated future. If anything like the permanent income hypothesis holds, it tells us that one off shocks to income gets saved, and that higher level consumption paths only occur with a permanent shock to income. Keynesian economics can make no such statements. The permanent income hypothesis is a macro model with micro foundations – that is how the terminology is used in economics. This is the beginning of the macro revolution.

      If you are serious about understanding, read Ljungqvist and Sargent, Recursive Macroeconomic Theory. Whatever its faults, it's much closer to reality than Keynes.

      Delete
    3. But again 1) & 2) are empirically false. People behave as social animals, exhibiting altruism and punishing those that don't adhere to norms. Additionally, many experiments/surveys show that most people do not make good choices (see e.g. here).

      It is possible that you can start with an incorrect theory and end up with something that works pretty well (an Einstein solid comes to mind as an example), but I don't understand why anyone would say:

      "I don't trust economics that doesn't start from two laws declared fundamental by fiat that are empirically false"

      I'd prefer to start from something that is actually fundamental (information theory) and doesn't make assumptions about something that isn't well understood (human behavior).

      Delete
  9. Jason,

    Read more. After I switched out of theoretical physics, I did not assume that I knew more than everyone else. There are lots of very, very smart people who have developed modern economics. It is based, in part, on the the rationality assumptions that I listed. Those assumptions are not empirically false at all. There are so many successes of this framework that they are just too numerous to count. (If you've done any quant work – why is it again that all discounted assets are martingales under the risk neutral measure...?)

    If you seriously want to see how information flow gets incorporated in investment decision making, I suggest Investment Under Uncertainty, by Dixit and Pindyck. Also try Asset Pricing by Cochrane. Both Dixit and Cochrane know a thing or two about quantum field theory as well. In fact, Dixit and Pindyck make the connection to investment under uncertainty and the path integral formulation of quantum field theory, and Cochrane emphasizes Hilbert space technology with the Riesz representation theorem throughout. These people are not stupid.

    Start from the beginning, start with Arrow-Debreu and continue through to modern macro. It's a bold statement to say that you have it figured out and the world is 180 degrees wrong. Maybe you're the new Issac Newton of economics. But Newton completely understood everything that went before him. Learn how the whole thing works before you judge an entire field. Just like heterodox physics is quickly dismissed by professional physicists, so is heterodox economics. It takes a considerable amount of knowledge to realize the extent of your own ignorance.

    ReplyDelete
    Replies
    1. You assume I haven't done these things.

      I started getting into quantitative finance in the 1990s (monte carlo methods), and before I decided to take my current route I was considering jobs on Wall Street in the mid-2000s and studied up on stochastic calculus and path integral methods. This book was my reference.

      I have actually derived Cochrane's asset pricing equation from the information theory approach and looked extensively at Arrow-Debreu (here, here, here, and here).

      You seem to be under the impression that if only I had seen this stuff, I'd realize what a fool I've been. But I have seen this stuff! Assuming someone with a "heterodox view" hasn't done his or her homework is probably a good heuristic to separate the wheat from the chaff, but sticking to it regardless of evidence to the contrary is epistemic closure. Just because I have different views from you is not evidence that I am wrong.

      I don't think I'm smarter than anyone else, and I have no doubt these are smart people. However assumptions about the way the world works can be a heck of a drug. To paraphrase, I saw the best minds of the previous generation destroyed by ideology. Just read Cochrane's blog! If he writes about something remotely political, it's total garbage. The technical topics are generally sensible. To show balance, Corey Robin is a brilliant thinker on the left, but makes absolutely no sense when it comes to Bernie Sanders.

      The thing is if you assume information equilibrium at all times there is really no difference between the information transfer approach and a lot of traditional economics. The key place to look is Gary Becker's 1962 paper -- you can get a lot of neoclassical economics without assuming rational agents. I just take this in a bit more formal direction based on information theory (some slides are here). Like a good physicist, I created a new model that reduces to the old model under certain conditions.

      The key difference is that the information transfer view sees that equilibrium as fragile and the crux of that fragility is human behavior. When we behave in ways that correlate our actions (that move away from maximum entropy distributions), traditional economics fails. Most economists seem to think that even under conditions of failure, some economic theory still applies. The information transfer view says that traditional economic theory becomes just a bound; that output and prices will only at best be the rational agent solution.

      Delete
  10. Jason,

    If you read this stuff, you didn't understand it. Do you understand how the Arrow-Debreu equilibrium has no spot markets? Do you understand its relationship to the Radner equilibrium?

    I am familiar with the book you mentioned and I use Quasi-Monte Carlo in my own work. As soon as you see a quant book that says “for physicists” it means that it's a mile wide an an inch deep and its trying to take shortcuts. In my experience, physicists usually don't have a strong background in measure theory and so these books try to delay introducing it or give it only a cursory treatment. But there is no way around it – if you really want to understand quantitative finance, you need to get a handle on measure theory in stochastic processes and measure theoretic probability. Read Shreve, Oksendal, Shreve and Karatzas, Duffie, Musiela and Rutkowski, Cont and Tankov, Applebaum, Brigo and Mercurio, Wystup, Carr, etc.

    I saw your “derivation” of the basic Euler equation in Cochrane's book. First, this is not Cochrane's equation – its been in the literature forever. Cochrane writes the solution to the simple two period model, but the result holds more generally. I encourage you to read Ljungqvist and Sargent to gain a better understanding of the dynamic programming involved. I'm glad to hear that you think Cochrane's technical work is “generally sensible”. If you carefully look at the Euler equation for payoffs, you will see that it's a measure change that is going on. Normalized to unit expectation (the expectation of the stochastic discount rate is the inverse of the gross risk-free rate), the object is the Radon-Nikodym derivative.

    I've seen your position before – “Look I'm a physicist, I have it all figured out! You people are all ideological fools. If you'd only pay attention to me!” Those people don't last long in my kind of work. But this is the same nonsense I used to see as a physicist with the unsolicited emails telling me how Einstein was wrong or how they have a new interpretation of quantum mechanics. They used to say I would see the brilliance of their work if only I wasn't so blinded by ideology. When the world refuses to see your genius because of “ideology”, it's time to look in the mirror and ask, “What have I missed?” But oh well, we've all gotta have a hobby, don't we?

    OK, my crackpot quota is filled for a lifetime. Good luck.

    ReplyDelete
    Replies
    1. I think the only way I can make sense of what you have said is if you assign zero weight to empirical data.

      Arrow-Debreu is a pure theoretical result based on a fixed point theorem on a compact set being mapped to itself. Think about that for a bit in light of the real world and empirical data.

      Ljungqvist and Sargent contains no comparison to empirical data and in fact says so in the front matter. This would only be useful if zero weight is given to empirical data.

      Your characterization of me declaring to "have it all figured out" only makes sense if I was putting forward pure theory. I am not; I actually compare things to data. (Additionally, I am not calling all economists ideological fools -- just those that insist on rational expectations/microfoundations that are empirically false. And even then, I think the whole optimzation approach is an effective theory near an equilibrium.)

      Those people who say "Einstein was wrong" or have a "new interpretation of quantum mechanics", regardless of the questionable merits, are addressing purely theoretical issues. Both theories are empirically successful -- you can't be more empirically successful. Drawing that analogy implies zero weight to the fact that economic theory is not empirically successful.

      It is especially funny to compare economic theory to general relativity or quantum mechanics. Only someone who puts zero weight on empirical data would think that is an appropriate comparison.

      The definition of crackpot is at its root an empirical question. Is what a person says consistent with the state of the world? Or do they hold on to ideas regardless of what the data say?

      My personal view is that someone who ignores empirical data and establishes empirically false principles by fiat (as you do above with your #1 and #2) is more likely the real crackpot here.

      Delete

Comments are welcome. Please see the Moderation and comment policy.

Also, try to avoid the use of dollar signs as they interfere with my setup of mathjax. I left it set up that way because I think this is funny for an economics blog. You can use € or £ instead.