Thursday, April 25, 2013

The philosophical motivations

I have been following these discussions of "DSGE models", microfoundations and the Lucas Critique. My own take is: how could microfoundations possibly survive aggregation into a macroeconomic model as anything other than a coefficient? If they do, the resulting model is likely intractable!

Does this look intractable? Does it even look like more than two numbers (slope and intercept) survive to the macroeconomic scale?

Snark aside, I'm motivated by the many cases in nature where the details of the microtheory end up as single numbers in the macrotheory: thermodynamics, quantum chromodynamics (there was a great letter published in a 1960s era Scientific American where there was a mysterious factor of three difference from the expected cross section), Galilieo's law, etc. Thermodynamics is an especially appropriate model as Boltzmann didn't know about atoms or how they worked (and in thermodynamics, it doesn't really matter), he just needed to know there were a lot (~ 10^23). Nature has a way of inventing new degrees of freedom (quarks give way to hadrons at low energy) or destroying the details (why Hydrogen forms a diatomic gas at STP based on its orbital structure and electrons being spin 1/2 simply becomes a heat capacity at constant volume of 5/2 vs 3/2 for e.g. Helium to good approximation). I imagine the details of why and how humans  decide what to spend their money on pretty much get subsumed into the slope and intercept above. However! This doesn't mean the details are unimportant -- many (most?) policy ideas in macroeconomics try to cross the boundary from micro to macro (tax incentives, health care economics) where economists try to figure out how changes to the microtheory affect the macrotheory. No one really knows how to do this very well -- in nature, the applicability of the degrees of freedom in the macrotheory usually breaks down before the applicability of the degrees of freedom in the microtheory really kick in. You go from hadrons to a mess and only then to quarks as you zoom in. In String Theory this is actually explicit -- with T-duality the physics at scale R is the same as the physics at scale α/R and neither can be small (in perturbation theory) at the same time.

Second, and on a more personal level (and speaking of string theory), from the outside, the whole DSGE model discussion reminds me of how String Theory is seen in physics: awesome models, awesome mathematics, little connection to experiment, pretty much intractable except with various simplifying assumptions, and kind of a big deal for a limited reason (DSGE has microfoundations and can look like an economy, string theory has something that looks like what we think quantum gravity should look like). I would hope that maybe this blog-paper could come along like Verlinde's paper on entropic gravity and say: maybe we don't need the details of the string theory to derive gravity ... maybe quantum gravity doesn't really even exist at a fundamental level because it is an entropic force much like diffusion that goes away when you look at a single molecule. We just need to know there are a lot of degrees of freedom and some basic concepts from the string theory microfoundations (emergent dimensions,  AdS/CFT correspondence). It seems something like inflation would go away  at a small enough scale ... but I don't want to prejudge anything and I as yet have no idea how inflation fits in the information transfer framework.

It is in that sense that I am going to try and describe the "emergent" theory of macroeconomics rather than build up a model from the ground up ... or another way: what would we say about macroeconomics if we didn't know about the existence of people in the same way Boltzmann didn't know about the existence of atoms? Imagine we are aliens measuring fluctuations in CO2 production from a distant observatory. There would be a story of various natural factors but a piece would be missing. It would grow exponentially (as Earth industrialized) and changes would happen (the "Great Recession" has reduced CO2 production by a significant amount, the "technology shock" of changing from coal to natural gas in the US has also reduced emissions). An alien comes along and proposes the idea of a "civilization" on that planet that does something faster than organisms generally grow through network effects so that maybe the individual components of this civilization interact and exchange information. The CO2 measurement would be a proxy for the information exchange -- and is essentially the price level in the economy in our model.

3 comments:

  1. Not to say that Boltzmann wasn't with the atomists at the time -- he certainly believed they existed! It's just that he didn't know about atoms' experimental reality. Depending on the strictness of your positivism, that experimental reality came either just after Boltzmann's death with Einstein's theory of Brownian motion or in the 1980s with the first pictures of atoms from STMs.

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  2. "how could microfoundations possibly survive aggregation into a macroeconomic model as anything other than a coefficient? If they do, the resulting model is likely intractable!"

    Not quite intractable, but certainly difficult to use. Models that explicitly contains lots of different agents each of which is "micro-founded" do exist. But while easy to describe and write down they are almost impossible to manage analytically (without assuming that all the agents are pareto-distributed, or something similar). This leaves computing the models, which can be and is done, but it still comparatively a young area and has the main problem that to deal with the heterogeneity you have to throw out a lot of other details of the economy you might otherwise be interested in or else the computation simply takes way to long.

    (Classic papers here would be Aiyagari (1994) and Krussell & Smith (1997))

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    Replies
    1. Thank you for the references! By "likely intractable" I didn't mean to presume human ingenuity couldn't come up with a solution :)

      My main point was that if there are N (say, m-parameter) agents, then a macrostate solution that depends on the details of the microstates would reside in an m*N-dimensional space ... for the US economy that is over 150 million dimensions for the labor market alone (the size of the civilian labor force).

      The usual dimensional reduction is to a "representative agent". The Aiyagari and the Krussell and Smith papers also perform some dimensional reduction (the latter seems to say the final macrostates depend on the ensemble average over the heterogeneous agents ... integrating over the N dimensions leaving the m-parameters above, so that the final space is "only" m-dimensional).

      This large space is similar to the linear programming problem Shalizi discusses here:

      http://crookedtimber.org/2012/05/30/in-soviet-union-optimization-problem-solves-you/

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