Monday, March 16, 2015

Predicting unpredictability

Paul Krugman, an economist who actually does understand special relativity [pdf], points us to an old post by David Levine:
I feel a little like a physicist at the cocktail party being assured that everything is relative. That isn't what the theory of relativity says: it says that velocity is relative. Acceleration is most definitely not. So were you to come forward with the puzzling discovery that acceleration is not relative...
I don't quite get why economists think the experience of physicists is more relatable than e.g. their own. Let me think of a way to make my point to the readers of Huffington Post using an example they'd be more familiar with ... how about ... a physicist.

Anyway, the principle of relativity is actually a more general principle that the laws of physics are unchanged if observed in reference frames that have a relative velocity to one another. So strike one.

I also think Levine is using the English phrase "X is relative" in the philosophical sense of e.g. moral relativism. X is wrong (or big or small, etc) only relative to something else; there is not some absolute scale by which to measure X. Special relativity actually says the exact opposite: all velocities can be compared with the speed of light and are less than or equal to it. Velocity isn't relative, it is absolute -- compared with the speed of light. So there's strike two.

Brad Delong points out the flaw that accelerated frames are incorporated in general relativity. That would be strike three.

However, let me take a somewhat more charitable view of Levine's statement in order to get at something deeper. He is using it as an analogy for rational expectations -- and instead someone is coming forward and saying that the inability to predict financial crises disproves the EMH. Levine is saying unpredictability is actually a prediction of the theory.

Rational expectations and the EMH aren't being used as intellectual constructs to arrive at the truth here. They are being deployed in a manner similar to creationist "intelligent design". In that case, complicated systems are put forward for which there is no theory as to how they evolved as proof that evolution isn't real. A flagellum is so complicated [1], there is no way it could have evolved!

One's personal failure of imagination is never evidence for or against any theory.

The fact that mainstream economics can't predict financial crises isn't evidence for the EMH. We don't know the fundamental theory of economics yet. Maybe you can predict financial crises. We don't know.

In quantum mechanics, outcomes of measurements are random. That observation is not the evidence for quantum mechanics. The evidence for quantum mechanics are the precise predictions for things that are not random ... and that success is the reason we accept the randomness in quantum mechanics.


[1] This example is particularly funny because there is a pretty convincing evolutionary pathway for a flagellum.


  1. if you are going to be so uncharitable to should be just as uncharitable to Krugman. It was Krugman's failure of imagination that saw the financial crisis and subsequent recession as evidence against RE and EMH. All of this useless posturing since 2009 is his fault for that truly childish article "How Did Economists Get it So Wrong".

    if you are reacting so poorly to Levine's informal treatment of Physics I think you actually understand perfectly well his point: non-experts stepping in and trying to use vocabulary they don't understand. Even worse is when Krugman writes articles deliberately allowing a misinterpretation of the word "efficient" in the EMH.

    Congratulations to Brad Delong for once again tearing down evidence in a manner that proves the argument of the author...

    1. Hi LAL,

      The main point I was trying to make was that the EMH doesn't "predict" unpredictability (hence the title). The EMH is better cast as the EMA: the Efficient Markets Assumption and assuming the EMH is assuming unpredictability.

      As an aside, the use of the word "information" defining what is meant by efficient is problematic. A one-dimensional variable cannot contain the information required to represent multi-dimensional states of the world [1]. There will always be information loss even in weak form efficiency if prices are receiving the information from the world.

      [1] Fractal representations can take a 1D space and make it behave more like 2D, but I don't think anyone has seriously put forward the idea that prices encode information fractally.

    2. fair enough on the EMH being better as an assumption...but as far as prices as fractals go, a friend of mine once showed me this paper...

    3. Thanks for the link; interesting.

      The kind of encoding I was thinking of is a bit different -- where you could read a single price change and it would tell you two or more pieces of information (like the demand shift and the supply shift). Essentially solving the identification problem, for example.

      Or another way, like Godel numbering, each price number encodes some state of the world.

    4. I guess in that sense the fractal hypothesis makes the problem worse as now it is taking a path that reflects the trading strategies on top of the states of the worlds...


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