Monday, October 19, 2015

Utility maximization and crystal spheres




Atrios gave Justin Wolfers one of his world's worst humans 'awards' for his rather stunning lack of reflection. My co-worker and I happend to discuss Kuhn the other day and it is particularly relevant here. I'll just quote from this summary instead of Kuhn directly because it's shorter:
The theory-dependence of observation, by rejecting the role of observation as a theory-neutral arbiter among theories, provides another source of incommensurability. Methodological incommensurability ... denies that there are universal methods for making inferences from the data. The theory-dependence of observation means that even if there were agreed methods of inference and interpretation, incommensurability could still arise since scientists might disagree on the nature of the observational data themselves.
In a sense, there is disagreement between humanities and social science/economics over what constitutes fact. And that's because you need theory in order to make sense of facts. There is no such thing as theory-neutral facts.

For example, a sociologist or historian might consider an economic system in terms of institutions. In that case the existence of institutions (law, marriage and family, religion, media, ...) counts as an important fact in moving towards understanding the system. And in fact, there are institutions!

Now contrast this with an economist considering an economic system in terms of utility maximization with (possibly bounded) rationality. We don't really know if this is true -- many experiments and 'stylized facts' seem to show we're not terribly rational as humans: money illusion, endowment effect, hyperbolic discounting, etc [1]. Therefore the construct you are attempting to understand the system with may not actually exist.

As an analogy, Wolfers was potentially saying: if other people made more convincing arguments -- prizing crystal spheres over rhetoric -- maybe we'd listen to you about astronomy.

We don't know if utility maximizing agents exist (much like how Aristotle didn't know if crystal spheres existed), but we do know institutions exist.

Now it is entirely possible (even likely) institutions are not the best way to understand economics. But I think it is more likely utility maximizing agents (even including perturbations around rationality) are the crystal spheres of economics -- and that utility maximization represents an unscientific approach to economics.

Like crystal spheres, utility maximizing agents have not been observed.

Even experiments in economics (that won a Nobel prize) don't really observe utility maximizing agents. They observe that given well-ordered preferences (i.e. defined by real numbers), agents maximize utility. But that's a bit like saying given utility and told to maximize agents maximize utility. The best predictive result in economics that Noah Smith is fond of pointing out used a random utility model (that isn't terribly different in structure to the partition function approach on this blog). Some of the most robust findings in economics are deviations from utility maximizing agents (money illusion, hyperbolic discounting, endowment effect). Utility maximizing agents do not seem to have been observed -- if you can think of any experiments that observe them, let me know in comments!

Ok, what about atoms and statistical mechanics?

Yes, atoms were not observed when they were postulated. However, when atoms were postulated, they were considered too small to be observed. Crystal spheres are actually more scientific than utility maximizing agents because crystal spheres were thought too far away to be observed. Utility maximizing agents are a model of human beings -- they are readily observable.

Like crystal spheres, utility maximizing agents are motivated by a specific philosophy.

Utility maximizing agents are motivated both by utilitarianism (Bentham, Mill) and how self-interest can self-regulate (Adam Smith). The crystal spheres are motivated by the idea that circles are perfect and that the universe itself must be perfect.

Like crystal spheres, utility maximizing agents make calculations tractable given mathematical tools at the time.

Sure, many epicycles and deferents were added to the crystal sphere model to make it more accurate -- regressions hadn't been invented, but would have greatly simplified the process. in the end, it's just geometry and Anaximander was a contemporary of Thales. Utility maximizing agents solve Lagrange multiplier problems invented in the 1700s (Lagrange was a contemporary of Adam Smith).

I just thought that last one was interesting. Most mathematical solutions to problems use mathematics available at the time. An exception is string theory which is not really tractable except in maybe the most symmetric of cases.

Utility maximizing agents: not observed (when they should be) and motivated by a specific philosophy (only) equals unscientific (in my view) [2].

But then, it is the standard approach in economics, so I will dutifully express information equilibrium results in terms of epicycles, I mean, utility maximizing agents and perturbations from rationality.

...

Footnotes:

[1] Note that these things exist as stylized facts because of the utility maximizing framework. They might not be deviations in the 'correct' economic theory. It's like having a frame where all swans are black and saying: except that white one ... and that white one ... and that white one.

[2] You might ask: how does the information equilibrium approach fare under these criticisms? Well, information has been observed (it runs communication theory) and it's not motivated by a specific philosophy. There are general philosophical motivations (more for the methodological approach -- Kuhn's differing weights of simplicity, scope, accuracy, fruitfulness and consistency) but it doesn't really depend on a particular world-view. Unless you count nihilism -- I am motivated by a nihilistic approach to economics, that macroeconomic aggregates are as meaningless as the universe. We largely can't know the future and in the cases where we can, we can't change it.

14 comments:

  1. I'm going to have to read this one a few more times. Ha!

    One mostly O/T comment though on this:

    "...if you can think of any experiments that observe them, let me know in comments!"

    I don't have an example for you. However, this reminded me of a professor I had in college who taught numerical methods in linear algebra. Alan Laub is his name. He told the class that he'd never seen a reason to compute the inverse of a matrix... that it's always the product of the inverse with something else that's important in his experience, and that if we ever found what we thought was a legitimate reason to calculate the inverse itself, to please contact him, because he'd love to find a good example. I imagined his former students running across what they thought were candidates in their careers, sending him a note about it, and being shot down every time. I've often thought about this, and certainly sometimes it's just easier to calculate the inverse (say in writing a Matlab script), but in my limited experience it's true that I could always find a way to avoid calculating an inverse if I thought about it. When doing so I imagined I was making a more numerically stable or efficient calculation in some sense (probably of tiny significance in most cases). Well, I figure if somebody has an example for him, you probably do. Ha!

    Also, (back on topic... sort of), one of the 1st econ blogs I ever looked at was that of Steve Keen. He's a harsh critic of mainstream economics (especially what he calls "neo-Classical" economics). That's where I first encountered the SMD theorem, AD, AS, DSGE models, representative agents and utility functions, or a layman's explanation of them anyway. Once in a great while I'll see him comment over at Nick Rowe's blog (usually when Rowe is writing a post trying to figure out what in the heck Steve is trying to do). He and Rowe get on OK actually. Mostly what I see is criticism of him though, and he likewise is not shy about administering healthy doses of criticism to others. Sadowski & Sumner are two that have laid into him, but so have "neo-Classicals," MMT folks, Cullen Roche and post-Keynesian types (e.g. Ramanan), who you might think would be more favorably inclined towards him. I bring him up only because I see you criticize some of the same things he does in economics, but in a different way. I often wonder what Steve would make of your blog.

    BTW, this man ("Matheus") from the Field's Institute co-wrote a paper with Keen apparently, and was apparently subjected to some criticism of it by some of the post-Keynesians (he calls them "accounting police"). Considering the dry subject matter, I thought this was a pretty hilarious blog post on account of a couple of sentences he adds here and there (you can hear his frustration at the critics - who start in on him again straightaway in the comments below! ... one of them has commented on your blog actually):
    http://fieldsfinance.blogspot.ca/2012/10/of-course-its-model-duh-final-post-on.html

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    1. Yes, matrix inversion is very inefficient... Probably the most inefficient algorithm I ever encounter besides linear programming.

      My guess would be STAP (space time adaptive processing), but I think you can get around the matrix inversion with a sparse solver.

      Regarding Keen, one issue is that he seems to think he predicted the financial crisis (maybe he did). One thing I don't think really applies are his nonlinear differential equations ... Maybe if you build circuits you could get something like he proposes, but it's hard to imagine in a real economy.

      Nonlinear terms in stochastic systems tend to average into a kind of background because you can never know the initial conditions well enough to follow the path of the model to any degree of certainty.

      But I haven't followed it too closely, so I may be way off base.

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    2. Yes, Keen does think he predicted that. Along with Peter Schiff (who lets his doom and gloom prediction ride ... pretty much constantly).

      My thought was regarding your "trying to shout through soundproof glass" comment the other day... it *might* be the case that you'd have a better chance being well received by Keen... however, that may not buy you much given Keen's standing in the world of econ! I don't know.

      Keen also famously lost a bet about Australian house prices: Steve was convinced their was a bubble and it would pop... when it didn't in the allotted time period, he went ahead and followed through with the terms of the bet, and took a long trek across a part of Australia on foot wearing a T-shirt stating "I was wrong about X... ask me why!"... he tried to turn that to his advantage by putting some extra info on the shirt. I have to hand it to him though: he did follow through with it! I think Robert Murphy also lost a bet about hyperinflation... if I recall correctly it was a more conventional monetary bet. He too didn't welsh (I think).

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    3. BTW, Nick Rowe was horrified that my first exposure to all those concepts I list above was through Keen's criticism of them. He implored people like me to crack open an undergrad text on the subject... Lol... I still haven't really done that. Here and there on particular topics, but not a complete course. On my to-do list! I'm sure it's a good idea.

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  2. The twitter bit made more sense the 2nd time through.

    What's the illustration? Crystal spheres? They don't look very crystalline.

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    1. The spheres are supposedly made of aether in later versions. But originally they were condensed air or crystallized air. Celestial is the right term, but I say crystal from watching too much James Burke.

      The picture is the offset sphere containing Venus and its boundaries.

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  3. Since you bring up the question of institutions and economics, I have been wondering about the effect of institutions for the information transfer approach. It seems to me that institutions make for non-random behavior and therefore may constrain information transfer.

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    1. I kind of imagine institutions establishing which information equilibrium relationships are used for policy.

      But I do think some institutions -- the media and centralized exchanges, for example -- exacerbate economic crises.

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    2. Not to mention the institution of class. The effects of class on the macroeconomics of the recovery (or not!) from the recent financial crisis are fairly clear. But they are ignored by the assumption of representative agents, for example.

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  4. Mr. Smith, please leave these subjects to other bloggers, and post more about your model. Criticisms about rational agents are tiresome: they are nearly old as rational choice models themselves, and by now even the proponents of said models are more than aware of their purported "lack of realism" (e. g. see Friedman's "as if", as in "agents behave 'as if' they were rational"). Many (mostly heterodox economists) seem have made their entire careers out of making such criticism. That in which you differ from them is that you bring something new.

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    1. You're welcome to skip these posts -- but I think you may have missed the point of this one. A lack of realism is not the problem with utility maximizing agents (UMAs). The Einstein model of a solid is unrealistic, but not in the way UMAs are unrealistic. In fact, I am struggling to come up with an analogy in science that is unrealistic in exactly the same way -- and it's not for a lack of unrealistic models.

      The best I can do is the emission theory of vision -- that light comes out of your eyes that makes you see. This is not just unrealistic, but easily measurable at the human scale. The difference between this and UMAs is that the learned people who believed the emission theory lived at a time before the idea of experiments.

      A Friedman would have been saying something about people knowing the emission theory isn't real, but "vision behaves 'as if' there were lights coming out of people's eyes". This does not make any sense as a defense.

      Physicists never said anything remotely like: we know the theory of the aether is incorrect and unrealistic, but we will continue to proceed 'as if' there is aether.

      Part of the reason I post things like this is to show not only that there are some big incorrect assumptions at the heart of the way economics is approached, but these assumptions are incorrect in a way that is very different from the way scientific paradigms are incorrect.

      So it's still kind of shocking.

      And I will continue to post about the model ...

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  5. Jason: “I will dutifully express information equilibrium results in terms of epicycles, I mean, utility maximizing agents and perturbations from rationality”

    I agree very strongly with almost everything in this post. However, I disagree equally strongly with your conclusion. It seems to me that you are trying to do two incompatible things with your blog. First, you are trying to develop information transfer economics. Second, you are trying to present information transfer economics in a way that appeals to mainstream economists.

    In amongst the detritus of the various schools of thought in economics, I think that there are two fundamentally different basic outlooks. I call these outlooks the atomists and the interactionists.

    Atomist economists start with a basic unit of thought (UOT) of a single agent or even a single decision by a single agent e.g. why did Jason buy a bicycle and was it a rational decision?

    Interactionist economists start with a basic UOT of a single exchange e.g. Jason bought a bicycle from Jamie for €20.

    Right from this extremely simple starting point, these outlooks are fundamentally different. The interactionist UOT is observable. The atomist UOT is not. The interactionist UOT supports the concept of conservation under change. The atomist UOT does not. The interactionist UOT allows structures to develop in the same way that physical atomic sub-structures interact to create atoms, and atoms interact to create molecules. The atomist UOT does not. The interactionist structures form networks. Once you have the concept of a network, information (and money and materials) can travel though the network. The atomist UOT allows for no such concept.

    When you talk about the physical micro world, you are an interactionist. You talk about a world with structure. You don’t just present an atom. You talk about how atomic sub-structures interact to create atoms. You could also talk about how atoms interact to create atomic super-structures i.e. molecules. It seems to me that it is the structures which allow for emergent properties.

    However, when you talk about the economic micro world, you are an atomist. There seem to be no sub-structures, no super-structures, and, vitally, no network though which information can travel. That doesn’t make sense to me. It feels like you have adopted an atomist analogy because that will appeal to atomist economists. However, an interactionist analogy would be more like the physical world AND would also provide more support for the concepts of information transfer.

    The problem you face with your dual objective is that only an atomist approach will appeal to mainstream economists. This post tells me that you are uncomfortable with the ‘rather stunning lack of reflection’ of the atomist world view. Crystal spheres are not mandatory.

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    1. Hi Jamie,

      I was being a bit tongue-in-cheek with that line at the end.

      But you also say:

      "There seem[s] to be ... no network though which information can travel."

      There is no (obvious) network through which information can travel in an ideal gas from volume to internal energy. However, the particles traveling at different velocities (kinetic energy) bounce off the walls of their container (volume) imparting a pressure. Information flows from energy to volume, and that flow is detected by pressure. p V ~ U. Information is flowing from the distribution of particle velocities to the distribution of volume elements containing particles.

      In an economic system it's simpler: people buy (demand) supplied goods (supply) imparting a market price. p S ~ D. Information is flowing from the distribution of demands to the distribution of supply.

      If there wasn't any information flowing between supply and demand, then the distributions of supply and demand would be totally different from each other -- they wouldn't have any reason to be the same. You'd go to the store and they wouldn't have any bread or the entire supply of bread would be in Canada.

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  6. Well according to Maslow, agents would want to maximize their self-utilization, I guess there will be times when this coincides with utility maximization.

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