David Sloan Wilson's latest piece at Evonomics brings up a good frame for my trilogy on production possibilities from this past week:
- Production possibilities and the slope of the supply curve
- Production possibilities and Brownian motion
- Fitness, trade-offs and macrofoundations
The argument I make at the end of  connects to this post about effective degrees of freedom near equilibria : that rational agents are an effective theory for small perturbations around a macroeconomic equilibrium. I realize that Milton Friedman's The Methodology of Positive Economics [pdf for 1966 version, here for 1953 version] is an attempt to say that rational agents are an effective theory:
The abstract methodological issues we have been discussing have a direct bearing on the perennial criticism of "orthodox" economic theory as "unrealistic" as well as on the attempts that have been made to reformulate theory to meet this charge. Economics is a "dismal" science because it assumes man to be selfish and money-grubbing, "a lightning calculator of pleasures and pains, who oscillates like a homogeneous globule of desire of happiness under the impulse of stimuli that shift him about the area, but leave him intact" ...
It is frequently convenient to present such a hypothesis by stating that the phenomena it is desired to predict behave in the world of observation as if they occurred in a hypothetical and highly simplified world containing only the forces that the hypothesis asserts to be important.
Emphasis in the original. The humans function as if they were rational agents is analogous to saying the theory of quarks and gluons acts as if it was a theory of color-neutral bosons called pions.
There are two problems with this. The first is the "asserts" in the last quoted sentence. You need some empirical fact from which to draw your effective theory. These empirical facts can lead to limits (Newtonian gravity is a limit of general relativity for slow speeds and low field strengths) or symmetries (the approximate chiral symmetry of QCD leads to the pion description). For example in economics, I've taken the limit of low inflation to show that the AD-AS model has an effective description using the IS-LM model and taken an approximate long run neutrality as a symmetry principle to motivate information equilibrium.
The second problem is that there are always boundaries on your effective theory (defined by a scale), and the effective degrees of freedom represent perturbations from some equilibrium. The pion description of QCD is effective between roughly the masses of quarks (m ~ a few MeV) and the QCD scale (chiral condensate or RG scale Λ ~ hundreds of MeV). So you have energies E where m << E << Λ. For E ~ GeV, you need to resort to QCD. For E much less than m, you can really just use quantum mechanics.
In  above, I argue that rational agents are an effective description only near a macroeconomic equilibrium. The limit in the information equilibrium description would be e.g. I(AD) ~ I(AS) -- i.e. approximate information equilibrium between aggregate demand aggregate supply. Therefore rational agents would only really apply outside of recessions.
Sloan summarizes Friedman's analogies (n.b. these is in the 1953 version, not the 1966 version Sloan links to, which confused me at first):
Yet, [Friedman] claims that they are still predictive of human economic behavior by way of three analogies. First, trees distribute their leaves as if they are maximizing their exposure to sunlight, yet no one pretends that they are performing optimization equations. Likewise, an expert pool player acts as if he is performing complex calculations when making his shots, when in fact his behavior has been molded by countless hours of play. Finally, a firm acts as if it is maximizing its profits, when in fact its continuing survival is the result of a selection process in which the non-optimizing firms were eliminated.
Sloan further says these are evolutionary arguments [f1]:
The first is an example of genetic evolution, the second is an example of individual learning, and the third is an example of cultural evolution. In all cases, a process of selection results in entities that behave adaptively, as if they are solving complex optimization equations, when mechanistically they are doing nothing of the sort. ...
So far, Friedman is standing on firm evolutionary ground with his “as if” argument [that agents are maximizing]. Evolutionists frequently reason about the properties of species “as if” they are maximizing their fitness, without worrying about the proximate mechanisms.
In a sense, maximizing fitness is an effective (an as if) theory of evolution. One way to achieve it (as I talk about in ) is to recognize that the maximizing state of that tree is actually just more likely than a non-maximizing state assuming there are a lot of traits that go into the exposure to sunlight (leaf size, shape, branching ratios, height, thickness of trunk and branches, etc ... ).
Sloan then provides some caveats via Gould [f2] and Lewontin; in particular the "as if" effective theory is only valid if you correctly identify the trait as the result of selection and identify the selection pressures. I don't agree with the latter piece (selection pressures aren't always necessary per  unless it is something e.g. controlled by a single gene), but the former is essentially the statement that the "as if" effective theory of maximized fitness is only valid in the neighborhood of an equilibrium (e.g. the sandy brown coloring of desert creatures). And that equilibrium requires "macrofoundations"  -- i.e. a stable ecosystem (the desert has been a desert for awhile).
From this discussion we can conclude that assuming maximizing rational agents in economics during a recession is like assuming maximized fitness for species subject to climate change. If the changes (or recessions) are small, you might be able to assume maximization, but in general this is not a valid assumption.
We can construct a list of requirements for simple effective ("as if") descriptions in complex systems:
- Macro-scale (i.e. system) equilibrium
- Empirical facts on which to base your effective degrees of freedom
- Scope conditions defining the neighborhood of validity for those effective degrees of freedom
Additionally, maximum entropy gives us some simplifications in cases where the number of dimensions is large.
Since I used [n] to indicate the blog post references above, the footnotes have the form [fn].
[f1] A minor quibble at this point: I don't think Friedman is actually talking about how trees or billiard players achieved their maximizing state, so he is not making an evolutionary argument. He is talking about describing a maximizing state in terms of detailed rules and calculations required to determine the maximizing state versus just saying it is a maximizing state. The billiard players behave as if they are doing complex physics calculations, and you can describe that effectively with either the physics calculations or assuming maximization -- even though neither is actually happening. Trees behave as if they are doing a complex optimization, and you can describe that effectively with a complex optimization or assuming maximization -- even though neither are happening. Sloan's interpretation is that you can describe these states either as maximization or as the result of an evolutionary process -- even though only the latter is happening. But Sloan's interpretation is useful for my purposes here, hence I put this in a footnote.
[f2] Here's Paul Krugman mentions Gould in the course of this article.