Wednesday, October 14, 2015

Gary Becker's emergent rational agents

The second graph is my maximum entropy version of the Diamond-Dybvig model, but NR and B correspond to p' and p in Figure 2 from Gary Becker's paper below.
David Glasner identified the argument I was making here (and in the links here) as one made by Gary Becker in 1962; here's the comment from David:
Jason, Thanks for the link and your follow up post as well. Your argument reminds of the paper "Irrational Behavior and Economic Theory" published in JPE in 1962 and reprinted in Becker's The Economic Approach to Human Behavior in which he showed that budget constraints were sufficient to imply negatively sloped demand curves and other standard microeconomic results. He credited Alchian's 1950 paper in JPE "Uncertainty, Evolution, and Economic Theory" for anticipating his argument. As I recall, Israel Kirzner wrote a comment published by JPE criticizing Becker for not sticking with utility maximization. It might help you to use Becker’s argument as a way of improving your communication with economists who, if they are like me, have trouble comprehending arguments that aren't made in the language we're accustomed to speaking. One other point to consider is that in an intertemporal context with incomplete markets there is no such thing as a true budget constraint because the prices in the budget constraint are largely expected prices not actual prices, so if prices turn out to differ from those that were expected, budget constraints may be violated (households or firms go bankrupt).
Regarding the language, I completely agree that is an issue. Regarding the intertemporal budget constraint, a post is forthcoming (though it basically involves combining these three posts [1], [2], [3]).

Speaking of language, language was the reason it took me a little while to parse Becker's version of the argument (I have a hard enough time parsing even physics papers [pdf] from the 1960s), but it is pretty much identical to ones I've been making. There are three key differences as I mentioned in a reply to David on his blog and thought I would expand here.

1) [I give] an argument that if the number of different goods [or intertemporal periods] d being optimized (the number of axes) is large, there is no need to restrict to the budget constraint (as ‘maximization’ happens automatically as d → ∞)

As Becker writes:
If opportunities were initially restricted to the budget line AB in Figure 2 [reprinted above], the average consumption of many households would be close to p, the midpoint of AB, with different households uniformly distributed around p.
And later:
Inefficient impulsive households might assign equal probabilities to all points in the opportunity set, not just to those on the boundary. The average consumption of a large number of these households would almost certainly be at the set's center of gravity, with households uniformly distributed around this point. ... For example, point c in Figure 2 [reprinted above] would be the center of OAB and c', to the left and above c, would be the center of OCD.
The existence of a large number of goods (or intertemporal periods) d leads to the average being near p without restricting to the line AB. As d → ∞, we have c  → p because most of the points in a high dimensional volume are near the surface, not the interior.

2) [I present] an interpretation of the equilibrium in terms of entropy

When Becker says uniformly distributed (and equal probabilities) in the quotes above, he is making a maximum entropy (least informative prior distribution) argument. Therefore, information equilibrium relationships will apply.

3) [There is] the possibility of falling away from the ‘maximum’.

A simple random walk around the simplex leads to cases where occasionally the budget constraint isn't saturated as illustrated (for a single period and d >> 1 goods markets) at this link.

Overall, Becker's paper is a pretty cool common point of reference.



I would like to emphasize that while Becker refers to agent actions as irrational (in the title) or "Inefficient" or "impulsive", I take the view that those actions may just be more complex than we can model efficiently ... for example, so complex as to appear random from an outside viewer.

Update, the second:

This Socratic dialog could be seen as Gary Becker arguing with Kirzner ...


  1. O/T, Jason, do you generally agree or disagree with this statement:

    "The Laws Underlying The Physics of Everyday Life Are Completely Understood"

    1. Unfortunately, I have to equivocate on this. Given initial conditions, I'd say yes -- the scale of interactions in human experience are less than the grand unification scale. But unfortunately there is a lot covered by those initial conditions including why the universe isn't empty or hasn't collapsed (non-zero but small cosmological constant) or just photons (baryogenesis).

      If pressed, I'd say no and cite the latter reasons.

    2. Thanks Jason! Yes, I'd say I was interested in the "given the initial conditions" case. Those conditions certainly have a huge affect on our everyday lives, but the universe as it existed "initially" is something we don't experience in every day life.

    3. Ah, but we experience the solution with those initial conditions as the boundary conditions. The existence of protons and neutrons is basically unexplained by physics ... so every time you look at a physical object in your daily life, that is something that is unexplained.

    4. Good point. I knew my response was lacking after I hit "Publish." ;^)

      Here's what I'm really after: I'm willing to accept protons and neutrons as unexplained givens. What I'm concerned with is explaining an everyday phenomena. I don't want to be surprised by the existence of new fundamental forces and particles operating under everyday conditions (energy levels, etc). Do I have anything to be worried about?

    5. High Tc superconductivity -- how it works is still unknown.

    6. Thanks Jason! Do you think the explanation for high Tc superconductivity (should we find it) will involve a new fundamental force or particle? If you were in charge of a project to explain it, where would you allocate resources? How many more examples are there like Tc superconductivity?

    7. It might involve a new quasi-particle (like a polaron or phonon), but not a new fundamental one. If in charge of such a research program, I'd devote computing resources. My intuition is that the specifics of the lattice build a structure that either channels or creates a resonance/correlation for phonons (like a set of shock absorbers) -- lowering the effective temperature in certain directions by isolating thermal vibrations allowing cooper pairs to form.

      I can't think of any other examples off the top of my head ... but I'm sure they exist ...

    8. Thanks again Jason,... it's funny, I was just about to email the author of that claim (in my original post) with your high Tc superconductivity example, when I went back to his post and found that he'd already addressed that. Lol. I'm glad I took a second look!

      This is a good example of a non-expert (me) doing something short of getting my PhD in physics to attempt to discern "the truth." As you pointed out once, that can be a tricky business.

      I very much appreciate your responses. To my non-expert ears, it sounds like this statement by you above "but not a new fundamental one" coincides with the author's point, that the eventual explanation for unexplained "everyday" phenomena like high Tc superconcuctivey will "fit comfortably within the framework of known fundamental physics." Do you agree? Elsewhere I've seen him explain (to laymen) how we can know this.

      Sorry to drag this O/T out so long. I probably should have just given you the link to the post in question and and asked your thoughts. Again, I really appreciate you taking the time to humor me here.


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