Monday, May 23, 2016

Modeling in physics versus modeling in economics

Paul Pfleiderer has some slides on what he called "chameleon models" [pdf] that are in general very good. As always when economists make physics analogies, he makes some mistakes. As I said on Twitter the other day, economists should stick to Newtonian physics when making analogies. There's really nothing in quantum mechanics that is relevant to economics that isn't also present in classical mechanics. When Pfleiderer says "We do observe something about the paths [electrons and photons] take", he should realize that although reality is a lot weirder, a good starting point is that quantum effects result from not knowing which path electrons and photons take.

Aside from that, this pair of slides was interesting (I added the question mark):



Now one pair of statements is a great illustration of the difference between economic (well, finance) methodology and physics methodology for a couple of reasons. It is:
  • Physics: Models do not contradict other things we know about electrons and photons.
  • Economics (finance): Models often contradict things we know about actors 
On one level, this illustrates an issue with economics. On another level, however, physics models often contradict things we know about electrons and photons. An example is right there in Pfleiderer's chart! It shows both a Dirac equation (relativistic, spin-1/2) and a Schrodinger equation (non-relativistic spin-independent). However, physics models will occasionally use the Schrodinger equation to describe electrons, contradicting the fact that we know electrons are spin-1/2 and Einstein was right. The problem is that economic models lack scope conditions that tell us when the contradictions matter. In physics, we can make assumptions about the importance of spin (frequently it is only important in counting degrees of freedom) and relativity (kinetic energy of the electron E << m, velocity v << c the speed of light). This means the theory contradicts what we know, but it also sets scope conditions so that we know the contradictions don't matter.

There's another pair that illustrates a difference on multiple levels:
  • Physics: We don’t observe anything about what “motivates” electrons and photons to make decisions
  • Economics: We observe a lot about decision makers making financial decisions. We can even ask them what they are doing (or at least what they think they are doing)
Well, we don't directly observe the wave function -- it's a mathematical construct that reproduces empirical results. It's not entirely off-base (although it is completely unnecessary) to say that the wave function is what "motivates" electrons to create an interference pattern (there is an interpretation of quantum mechanics where this happens).

However one the major differences is that physicists don't assume e.g. electrons have any properties besides the ones assigned in the model. The electron in quantum field theory (the best we know) is an excitation a spin-1/2 field representation of the Poincare symmetry group with a collection of charges -- a U(1) charge, an SU(2) charge and a SU(3) charge (zero). Full stop. Electrons have zero other properties and anything with those properties is an electron. Economists sometimes call people rational utility maximizers, but are aware that some humans have birthday parties or don't optimize the ultimatum game.

That means any economic theory is always an approximation with some limited scope. The real trouble with chameleon models is that they don't identify their scope -- you take an idealized model with limited scope and say that it has policy implications for the real world (extensive scope).

But I'd like to focus on this statement:
We observe a lot about decision makers making financial decisions. We can even ask them what they are doing (or at least what they think they are doing)
I do like the addition of the parenthetical, but there are two major issues here: post hoc rationalization and complexity. The former just means that asking humans about their decisions isn't always a reliable source of data. We tend to fit events into a story about how and why things work out the way they do. By the way, this is one of my problems with "stories" in economics. This is exactly the kind of thing you don't want to be doing if you're trying to do science because it is exactly one of the ways humans fool themselves [1].

The complexity is more difficult to deal with. We can try to ask why someone does what they do, but we may not know the relevant set of questions. A trader might not have executed a trade because they had an emergency where they had to pick up their child at school (just a potential example) or went drinking the night before and were a little foggy the next day. This gets even more complex when you are dealing with human decision-making in the field. I didn't buy champagne at Store A one day because I can get it cheaper at Store B. But another day, I bought it at Store A because I had a long day at work and didn't want to make two stops on the way home. Did these hypothetical researchers on price elasticity of champagne have the wherewithal to ask about how my work day went? Did I even know that's why I did it? Maybe I thought traffic was bad, but really it was my long day at work that lead to my interpretation that traffic was bad (I had less patience) -- even though traffic was normal. Or maybe traffic is bad, but that was the reason I decided to stay later at work making my day long.

Economists recognize this as omitted variable bias, but really we have two sources of omitted variable bias: the economists and the human subjects. The economists may not think to ask X and the human may not think X is important. And causal loop diagrams can sometimes get pretty complex!

This is why I think we should plead ignorance about why people do things and use random decisions as a start. If random decisions turn out to be a good description, then we know the state space (opportunity set of possible decisions) is more important than the agent state space occupations (agent decisions).

I've talked about this before; it is possible (even likely) that random agents might not work in some (most?) cases. My opinion is that when agent decisions become more important than the state space of available decisions you're really studying psychology, not economics.

...

Footnotes:

[1] Pfleiderer includes the quote from Feynman at the end:
Science is what we have learned about how to keep from fooling ourselves.

4 comments:

  1. Hello,

    A little off topic, but, as a physicist, you may be able to help me.
    These are the comments re 'global warming' that were placed on the Telegraph and Skeptical Science blogs.

    "AlecM  • 
    “The author of SkepticalScience admits he was taught incorrect radiative physics so much of his analysis is simply wrong. However, it uses the false Consensus argument to claim Authority.
    Here is the incorrect Physics as taught to MIT students today:
    http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node134.html

    The claim that the S-B equation predicts Energy radiated/unit area is simply wrong. It predicts Radiant Exitance, the Potential radiant energy flux from the emitter in a vacuum to a radiation sink at absolute zero
    Standard Physics predicts net unidirectional radiant flux from the vector sum of Irradiances at a plane. this satisfied Maxwell's Equations AND Conservation of Energy.
    The Climate Alchemists from 1989 have imagined a spurious bidirectional photon diffusion argument for which there has never been experimental proof..
    Also, the next MIT module transposes Emittance, an old term for Exitance, for Emissivity, which is the ratio of real Exitance of a radiant emitter to that of an hypothetical black body emitter.
    Hence Climate Alchemy is a pseudoscience with its practitioners unable to communicate properly with real science. This has led to the 40% imaginary energy in the climate models, a Perpetual Motion Machine of the 2nd Kind, the biggest Science Failure in history, our version of lysenkoism.

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    Replies
    1. This and the comment below seem to be gibberish. It is true the Stefan-Boltzmann law is in terms of power, not energy. But I wouldn't in any way call that MIT website authoritative (and is easily fixed by adding the phrase "in one second", which makes me think it's a typo).

      I am uncertain as to which side of the climate "debate" you've taken, so I have no idea if this will anger or delight you. However the basics can be understood in terms of an entropy argument. The Earth converts a few high energy photons into many low energy ones (entropy production). Due to that conversion, the existence of CO2 absorption in the infrared, and the random emission direction of the absorbed photon (quantum mechanics), the final result is a higher temperature on Earth with CO2 than without. Without any CO2, the Earth would be about 40 K colder (the temperature of the Earth without atmosphere). Obviously changing CO2 levels by upwards of 20% should -- assuming the coefficient is natural -- produce approximately 20% of this warming effect. That would be about 8 K -- or at least it's equivalent in thermal power divvied up among the water and land, which is the the more uncertain bit. Even a silly allocation where 75% of the power goes into the water and doesn't raise its temperature at all leaves you with 2K. Both the 8K and the 2K are perfectly in line with the range of climate forecasts.

      Any of the arguments against global warming have to claim an unnatural coefficient for the impact of CO2 (i.e. a 20% change in CO2 leads to x << 20% of temperature change), which is why they'd tend to be dismissed out of hand -- at least by physicists. It's just not consistent with what we know about CO2. And if they claim an unnatural coefficient for CO2, then they have to explain why the Earth is 300K and not 250K.

      Funny enough, my father worked for the oil industry, so I thought I'd seen every possible argument that global warming is wrong, a hoax, etc. But an argument based on a typo at an MIT physics website is a new one!

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    2. Thanks.

      I am 'with this'!

      “Today, the most comprehensive analysis of peer-reviewed climate research to date was published in the journal Environmental Research Letters. Our analysis found that among papers expressing a position on human-caused global warming, over 97% endorsed the consensus position that humans are causing global warming. Overwhelming agreement among scientists had already formed in the early 1990s. And the consensus is getting stronger.”
      https://theconversation.com/its-true-97-of-research-papers-say-climate-change-is-happening-14051

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  2. Prove any of the above incorrect, and you're a better man than me Gunga Din!”
    AlecM  • 
    Do you now understand from where I am coming? I have measured radiative heat transfer in process plant, made optical pyrometers, done the theory ad nauseum in the days when we used slide rules and Carslaw and Jaeger.
    What we have now is a grotesque parody of science based on the 1989 mistake by Goody and Yung where they arbitrarily assumed Schwarzschild's 'two-stream approximation' could translate to bidirectional photon diffusion, forgetting Schwarzschild knew he was dealing with Irradiances.
    Houghton, taught standard physics, knew this as well and in Fig 2.5 of 1977 'Physics of Atmospheres' showed why there can be no Enhanced GHE. When he co-founded the IPCC he supported he EGHE.
    We now have climate models based on 40% more SW thermalisation than reality, the only way the Hansen group could get the numbers to add up in the incorrect physics. The other part of the scam, to use ~double real low level cloud optical depth as a hind-casting parameters to get the right 'positive feedback' was discovered in 2010 by G L Stephens. He hasn't been able to publish this.
    AlecM  Postkey • 
    I see your plan: SS' author was taught incorrect physics so he is simply reiterating it: http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node134.html
    The S-B equation does not predict energy radiated/unit area. It predicts Radiant Exitance, Potential energy flux in a vacuum to a sink at absolute zero.
    Professional scientists use the vector sum of Irradiances at a plane to deduce real net unidirectional IR flux. This satisfies Maxwell's Equations and Conservation of Energy.
    The next MIT module transposes Emittance, another term for Exitance (the SI Unit) for Emissivity, the ratio of real Exitance to that of an ideal black body.
    Because the climate alchemists use a spurious bidirectional photon diffusion argument which has never been proved experimentally, they end up claiming 40% more energy input to the models than reality, 94.5 W/m^2 mean value.
    88.8 goes to the oceans 5.7 to the atmosphere; neither is real. This is why the models have failed: bad physics. SS' author is a propagandist not a scientist otherwise he would have picked up on this fundamental breach of the Principle of Conservation of Energy.

    http://www.telegraph.co.uk/finance/economics/11633745/Fossil-industry-faces-a-perfect-political-and-technological-storm.html#comment-2052298630

    Unfortunately the Telegraph are not accepting comments and past comments have been removed.

    P;ease feel free to ignore the above if you think it is nonsense.

    ReplyDelete