Over at Cosmic Variance, Sean Carroll offers some admittedly uninformed speculation about utility theory and economics, saying
Anyone who actually knows something about economics is welcome to chime in to explain why all this is crazy (very possible), or perfectly well-known to all working economists (more likely), or good stuff that they will steal for their next paper (least likely). The freedom to speculate is what blogs are all about.
I didn’t notice anything crazy but there’s a fair bit that’s well-known. For example, Carroll observes that utility is generally not additive across commodities, and that some goods are likely to be more closely related than others. That’s textbook stuff, covered by the basic concepts of complementarity and substitutability.
This is a more interesting and significant point
But I’d like to argue something a bit different — not simply that people don’t behave rationally, but that “rational” and “irrational” aren’t necessarily useful terms in which to think about behavior. After all, any kind of deterministic* behavior — faced with equivalent circumstances, a certain person will always act the same way — can be modeled as the maximization of some function. But it might not be helpful to think of that function as utility, or as the act of maximizing it as the manifestation of rationality.
I can only agree. Economists and (even more, I think) political scientists in the “rational choice” tradition regularly get themselves tied up in all sorts of knots about this, switching between the trivial notion of maximising a function and substantive claims in which rationality is frequently equated with egoism. Joseph Butler demolished this kind of reasoning nearly 300 years ago, but it keeps on popping up.
* This qualification isn’t necessary, and Carroll notes later on that choices are often stochastic. The resulting probability distributions still maximise an appropriately defined function.
{ 40 comments }
Danny Yee 09.17.07 at 6:52 am
That post is attributed to Sean, not to Cosma…
D’oh! Fixed now, I hope – JQ
Robert 09.17.07 at 8:22 am
There’s no mention of Philip Mirowski. Surely it’s relevant that the structure of utility theory is stolen from nineteenth century physics. Ignoring a transformation needed to make sense of the income constraint, utility is potential energy and income is kinetic energy.
John Quiggin 09.17.07 at 8:31 am
I’ve never looked properly at Mirowski, but there are some obvious problems with this claim. In standard modern presentations, utility is an ordinal concept representing preferences. Even with cardinal utility as in the von Neumann-Morgenstern expected utility model, there’s no zero. It’s hard to see how this can be mapped into energy measures.
That’s not to deny the more general influence of “physics envy” on economists in mid-C20, a compliment that’s now being returned by the econophysics guys.
Hidari 09.17.07 at 9:33 am
For what it’s worth, in the world of psychology, Antonio Damasio, in his work Descarte’s Error has more or less demolished the idea that there is, or ever could be, any such thing as ‘pure’ rationality in human beings (or perhaps in any biological entity).
This link and this one are also relevant.
Ipso facto, if there is no such thing as ‘pure’ rationality there is no such thing as ‘pure’ irrationality, either. This was the basic idea in John McCrone’s book entitled, of course, The Myth of Irrationality.
(I might add that given certain rhetorical tropes in ‘Decent’ discourse, there are political implications of this finding too, IMHO).
alphie 09.17.07 at 9:58 am
Well, the fruitless 43 year search for the Higgs boson sure has taken physics down a peg or two.
Not to mention string theory(hehe).
Economics may only be a “social” science, but I’ve never seen an economist posit a few extra dimensions to make their numbers add up.
Timothy J Scriven 09.17.07 at 11:22 am
“Ipso facto, if there is no such thing as ‘pure’ rationality there is no such thing as ‘pure’ irrationality, either”
Invalid.
John Emerson 09.17.07 at 11:42 am
I thought that it had been established that utility is quantifiable and that the unit of measure is the rat orgasm.
aaron_m 09.17.07 at 12:10 pm
“political scientists in the “rational choice†tradition regularly get themselves tied up in all sorts of knots about this, switching between the trivial notion of maximising a function and substantive claims in which rationality is frequently equated with egoism”
Hun!!!! It seems to me political scientists/theorists tend to use rational choice by appealing to the impacts of self-regarding interests. The rejection of psychological egoism keeps self-regarding and other-regarding interests distinct from each other, and is meant to show that reasoning in terms of rational self-interest is theoretically meaningful.
Are you suggesting something different?
M. Gemmill 09.17.07 at 12:23 pm
The big problem with rational choice in the social sciences is the “preferences” problem, which are generally deduced from the outcome.
Actor A did X because it fit his preferences for Y and Z rational reasons. How do we know what his preferences were? Well, he did X, so it must have been his preferred outcome.
The logical contortions involved in this can be quite amusing.
The other thing that I find disappointing about economics as a predictor of human behavior is that it often assumes that people are walking cost-benefit analyzers. That turns out to be grossly false–the vast majority of human decisions are made on impulse and emotion. And these decisions on impulse and emotion often have little to do with utility, as people will pick options that *sound* better (save 30 out of 100 is better than letting 60 die).
abb1 09.17.07 at 1:16 pm
He’s going too far. In many cases people do act rationally to maximize their utility – for example when they’re buying a car or TV set or vacuum cleaner. Some decisions are made mostly on impulse and emotion, others are based mostly on research and logic. Certainly everything can’t explain by this utility theory, but it can probably explain some things.
C S 09.17.07 at 6:27 pm
“Joseph Butler demolished this kind of reasoning” – This isn’t so clear. See Elliott Sober’s paper “Hedonism and Butler’s Stone” in Ethics 103: 97-103 (1992) for what is wrong with Butler’s argument.
(Also see chapter 9 of Sober’s book with David Sloan Wilson, _Unto Others: the evolution and psychology of unselfish behavior.)
notsneaky 09.17.07 at 7:57 pm
I like David Colander’s call to just replace “rational” with “purposeful” in order to avoid all this unnecessary hoopla and move on leaving pretty much everything intact.
hidari 09.17.07 at 8:41 pm
‘In many cases people do act rationally to maximize their utility – for example when they’re buying a car or TV set or vacuum cleaner.’
Speak for yourself. I choose my car based solely on the colour. It’s a well known fact that white ones go faster.
Robert 09.17.07 at 8:43 pm
No, John. The borrowing from pre-thermodynamics physics was a lot more direct than suggested by some vague “physics envy”. (Mirowski also discusses other physics and economics interactions.) If one has a serious interest in path dependence in consumption and how utility theory resembles the physics of a field, one should have an interest in Mirowski’s More Heat Than Light and the later critical literature.
And of course he discusses the relationship between utility and preferences. (If I recall correctly, one does not assume a non-arbitrary zero to potential energy in typical applications of Newtonian mechanics, anyways.)
Tracy W 09.18.07 at 11:03 am
Tyler Cowan has an interesting article about how economists use “rationality”, at http://www.gmu.edu/jbc/Tyler/rationality.pdf.
Well it’s really about how different economists use different concepts of rationality.
M Gemmill – in my Econ 301 Microeconomics, the lecturer proved, on us his class, a number of the violations of irrationality you referred to. Coming from an engineering background it impressed me, I was used to everything that wasn’t mathematically proven being tested in a lab that same week, doing the testing while presenting the material struck me as very impressive. Though I hardly blame my engineering lecturers, they were doing the best they could. And certainly the macroeconomics lecturers were complete failures at lab work.
Economists are definitely away of anchoring problems and the Allais Paradox and a lot of other violations of rationality. How much of this should be taught in Econ 101 is a far more difficult question (because it means deciding what else should be sacrificed to make the space, eg should we cut out environmental economics, economic growth, recessions, monetary policy, etc?)
This is gradually I think showing up in policy advice as people realise that the way in which material is presented affects what decisions people can make – eg the Sunstein and Thaler paper on “Libertarian Paternalism” argues for making joining a pension fund the default choice.
However, I think it is definitely possible to exaggerate people’s irrationality. People do respond to prices, people are good at figuring out loopholes in tax rules, etc.
Tracy W 09.18.07 at 11:14 am
Comment 2 – Robert. I’m lost. How is utility potential energy and income kinetic energy? The formula for kinetic energy I know is E = 1/2*m*v^2, where m = mass and v = velocity (which is squared). What relationship does this have to income? I can think of a number of formulas for income, eg I = H*W (income equals hours worked times hourly wage) or I = f(education, experience, hours worked, investments, interest rate). None of them look like the formula for kinetic energy. I presume you could write one that does, but that hardly seems enough to connect the two.
And how is utility potential energy? There are a lot of ways of calculating potential energy, eg gravitational potential energy = mass*standard gravity* height. Or elastic potential energy = lamba*x^2/(2*l) where l = the natural length of the spring, x = its extension, and lamba the spring’s modulus of elasticity.
Meanwhile, I don’t know of any standard form for utility functions. Economists tend to avoid actually defining them, beyond saying they are convex, while gravitational potential energy is of course linear in all its variables, while elastic potential energy is linear with respect to lamba, concave with respect to x and inversely proportional to l.
Of course, in a practical sense, potential energy is energy that is potentially available to do work, and kinetic energy is the energy an object possesses from being in motion. How can utility be made to do work? What do you think income is an attribute of?
In what sense do you mean that utility is potential energy and income kinetic energy? I can’t make the four concepts line up at all.
Tracy W 09.18.07 at 11:33 am
Actually Robert – do you think the comparison is that kinetic energy can be converted into potential energy (albeit with some losses), and income can be converted into utility?
But if so, then any other sort of energy can be converted into potential energy, so why single out kinetic energy?
And, while potential energy can be converted into kinetic energy, utility cannot be converted into income in anything like a similar sense. For a start, the concept of applying units to utility is making my head hurt, while I’m quite happy with measuring potential energy in joules.
notsneaky 09.18.07 at 5:20 pm
“standard form for utility functions”
Quasi-linear
u(m,x) = m + f(x) where f’>0, f”X and/or y>Y are more likely to be binding due to low income.
Translog, or the Deaton-Muel….bouwer? utility function – the bane of all first year econ grad students everywhere. Here’s a production function version of it:
http://www.egwald.com/economics/translogproduction.php
just replace K,L and M with x, y, and z to get u(x,y,z). Very general but annoying.
Those are the main ones basically. Then you’ve got the ones that are essentially versions of the above tailored for inter temporal or uncertainty frameworks. Then you twink’em in certain ways to get the behavioral “not-rational” ones, or include altruism in, or status effects or whatever.
notsneaky 09.18.07 at 5:22 pm
html messed with the formulas. sorry.
u(m,x) = m + f(x) where f’>0, f” negative.
not very good empirically but makes some interpretations easier in terms of the numeraire (m – money) and ok if there’s no or small income effects.
CES (constant elasticity of substitution) family
u(x,y) = (x^a+y^a)^(1/a) for a between -inf and 1. 1 is linear perfect substitutes. 0 is Cobb Douglas, imperfect complements. -inf is Leontief, perfect complements.
Stone Geary Linear Expenditure system
u(x,y) = ((x-X)^a)((y-Y)^b) (can generalize this CES style) where X and Y are “subsistence levels” of goods x and y. Often used in development economics where the x greater than X and/or y>Y are more likely to be binding due to low income.
Translog, or the Deaton-Muel….bouwer? utility function – the bane of all first year econ grad students everywhere. Here’s a production function version of it:
http://www.egwald.com/economics/translogproduction.php
just replace K,L and M with x, y, and z to get u(x,y,z). Very general but annoying.
Those are the main ones basically. Then you’ve got the ones that are essentially versions of the above tailored for inter temporal or uncertainty frameworks. Then you twink’em in certain ways to get the behavioral “not-rational” ones, or include altruism in, or status effects or whatever.
Robert 09.18.07 at 8:31 pm
“Do you think the comparison is that kinetic energy can be converted into potential energy (albeit with some losses), and income can be converted into utility?”
Yes, that is part of the analogy Mirowski sees.
I talk about kinetic energy because in a mechanical system without friction, the sum of potential and kinetic energy is conserved. Economists model utility with a conservative vector field. Yet where do you see them discuss what is conserved?
Mirowski’s work is brilliant, and his discussion is much better than I can provide. For more exploration of the mathematics, instead of the history, see:
D. Wade Hands (1993). “More Light on Integrability, Symmetry, and Utility as Potential Energy in Mirowski’s Critical Historyâ€, in “Non-Natural Social Science: Reflecting on the Enterprise of ‘More Heat than Light’†(ed. by Neil De Marchi), Duke University Press.
If mainstream economics were a person, all his memories would be repressed.
Chris Edmond 09.18.07 at 10:12 pm
Anyone who thinks that Mirowski is convincing on utility theory and its relationship (if any) with mechanics should read Hal Varian’s eviscerating review of “More Heat Than Light” in the Journal of Economic Literature (1991, volume 29 issue 2).
Robert 09.18.07 at 10:45 pm
Sorry, Chris, I’m not impressed by Varian. I asked Varian what he made of Mirowski’s appendix in Mirowski (1989). As I recall, he just did not understand the point about how constraints are accounted for in the mathematics of Hamiltonians. A reviewer on Amazon (U.S.) is equally unimpressed.
I think Mirowski writes about history. I gave that Hands’ reference deliberately.
Anyways, Mirowski is always intriguing. I like to think I prefer a minimalist writing style, and that certainly doesn’t describe Mirowski. But in an ideal world Mirowski would certainly be a part of the conversation about economics and physics.
notsneaky 09.18.07 at 11:18 pm
Re Amazon reviewer; After SK got published there I’m having a very hard time taking anyone who gets published in Physica A seriously. That second review by that guy actually tends to confirm this bias of mine.
Personally I don’t give a flip where economic ideas originated except as interesting history. It really has nothing to do with the validity or usefulness of these ideas.
Chris Edmond 09.18.07 at 11:55 pm
Sorry, Robert, I’m not impressed by Mirowski. He seems to neither understand utility theory nor classical mechanics. And he writes badly.
John Quiggin 09.19.07 at 2:09 am
While I’ve had my disgreements with Varian, he seems to have made the right assessment of Mirowski.
In essence, Mirowski correctly observes that
(i) lots of economists, mostly pre-1950, made loose analogies between economics and physics, for example between energy and utility
(ii) these analogies don’t work well
From this, most economists appear to have drawn the inference that we should develop utility theory from ordinal preference rankings independent of any physical analogy. Mirowski wants to claim that, having relied on unsound analogies, economics is fundamentally unsound.
As notsneaky says, the history of an idea has at most a glancing relationship to its validity.
Chris Edmond 09.19.07 at 3:27 am
John,
It would seem that we UQ economists are as one when it comes to Mirowski.
Tracy W 09.19.07 at 3:53 pm
Notsneaky – those functions you list for utility functions strike me as extremely different to the functions I gave for potential energy. The functions for potential energy are well-defined and cover all the available things affecting the relevant form of potential energy. I can plug them in and calculate the gravitational potential energy of a bicycle at the top of a steep hill.
But I can’t do the same with the equations you give to calculate utility. Plus you have so far given three different equations for utility – but there’s no reason to think that solving one equation would give you an answer to plug into another equation for utility.
And as for your equating the concepts, I still don’t follow. I think you are mixing up two different concepts. “Energy is conserved” has a different meaning to that of a “conservative vector field”. A “conservative vector field” is a statement about the mathematical properties of that field. I am reaching the limits of my knowledge of vector calculus here, but I presume when you say a conservative vector field you mean the standard economic assumption that if a person has a utility function of the form u(x) then u'(x) > 0 and u”(x)
notsneaky 09.19.07 at 5:53 pm
tracy w., I’m not the one who’s saying there’s an analogy between economics and physics or utility and energy. That’d be Mirowski as channeled by Robert. In fact, even though my knowledge of physics is pretty limited, I don’t see the link at all. I think you’re just saying the same thing but with a lot more knowledge of physics.
Robert 09.19.07 at 8:45 pm
Tracy, as far as I can see none of the equations you or notsneaky have set out are particularly relevant to the topic. The mathematics needed here is that of div, grads, and curls. I don’t know that I’m inclined to explain further.
Robert 09.19.07 at 8:47 pm
Given John’s first clause in the 3rd comment, the 25th comment seems odd to me.
It also seems odd that the second paragraph in the 23rd comment is answered in the text referring to Hands in the 20th and 22nd comment.
I find that a reviewer at Barnes and Nobel says, “Varian’s Review a Gross Injustice. Hal Varian has never tried actually addressing a single issue raised by Dr. Mirowski. Instead, Dr. Varian ignored a footnote and appendix in order to pretend Mirowski was ignorant of a trivial mathematical point. But what most needs to be said here doesn’t concern Mirowski’s critique of neoclassical economics — brilliant, scathing, hilarious though it be…” — Dave Tarpley
Tracy W 09.19.07 at 11:13 pm
Oops, sorry notsneaky. The effort of trying to remember vector calculus clearly overwhelmed both my brain cells so they fell down completely on keeping track of names. Please accept my apologies.
Robert – somehow I’m not surprised that you don’t feel inclined to explain further.
Chris Edmond 09.20.07 at 1:39 am
Robert,
Varian’s review points out that Mirowski’s argument is fallacious. Why don’t you try explaining in your own words why Varian is wrong. I’m not sure what standing I should give to Amazon or Barnes & Noble reviewers who don’t actually provide any counter-arguments themselves.
And don’t sneer about div, grad, curl and all that. It’s pathetic.
Robert 09.20.07 at 6:35 am
Apparently, Chris misreads an allusion:
http://www.amazon.com/Div-Grad-Curl-All-That/dp/0393969975
as a “sneer”.
The B&N reviewer and myself have already pointed out text in Mirowski’s book, ignored by Varian, that demonstrates Varian to be incorrect.
notsneaky 09.20.07 at 2:11 pm
Robert I’m assuming that when you say that Varian ignored some of Mirowski’s text you’re referring to the part of his review where he’s talking about the integrability conditions for inverse demand functions. I don’t have Mirowski’s book so I don’t know if this is true or not though I guess given Mirowski’s style of exposition I can understand how someone could miss a footnote. But yeah, a necessary condition here is the symmetry of the Sltusky matrix.
But again. So what? Even granted that Varian missed some footnote I think the broader jist of Varian’s review is correct. Just because both physics and economics have gradients in it, don’t mean that economics proceeds by stealing inappropriate ideas from physics.
I wouldn’t take personal correspondence or conversation – as referenced in 22 – to be an adequate basis for judging whether or not Varian understands Hamiltonian constraints either, unless it was quite extensive. It’s quite possible that you two talked past each other or that he misunderstood you (hmm…). Without more details and context it’s hard to give any weight to your claim.
Also when I used the adjective “interesting” in 23, I wasn’t referring to Mirowski in particular but to the field of HET in general.
Finally, this is just obviously part of your nefarious plot to ban calculus from economics and replace it with tedious linear algebra of corn and iron matrices. Isn’t that stolen from somewhere too?
Chris Edmond 09.20.07 at 3:38 pm
OK Robert:
I *introduced* the allusion to Schey’s book by writing “div, grad, curl and all that”. I don’t need to look it up on Amazon, I have it sitting on my shelf right next to Spivak on manifolds.
You just said “The mathematics needed here is that of div, grads, and curls. I don’t know that I’m inclined to explain further” in a way that pissed me off. If I tried to exclude you from a discussion about general equilibrium or game theory by suggesting you don’t know enough about topology or measure theory, you’d be pissed off too.
Varian’s critique of the Mirowski can be boiled down these paragraphs, both from page 595 of his review:
“Much of Mirowski’s argument about the defects
of the neoclassical formulation of utility
has the following form: “A neoclassical economist
says X. A natural extension of this is Y.
But Y is ridiculous. Therefore, X is ridiculous.”
However, in most cases, a more accurate conclusion
from this argument is that Mirowski’s
“natural extension” is ridiculous.”
and
“Mirowski’s claim that neoclassical economics
is “incoherent” because of the misappropriation
of the energy concept is alrnost entirely based
on this sort of argument. Over and over again
he claims that conservation of energy is an inherent
aspect of the physical concept of energy,
and that this sort of conservation principle is
not valid for utility. To Mirowski, this implies
that utility is not an intellectually coherent concept.
To anyone who understands neoclassical
economics this simply shows that utility is not
energy.”
The discussion about integrability conditions arises later when Varian is pointing out Mirowskis’s general cluelessness about neoclassical economics. Irrespective of the merits of his particular criticisms of Mirowski’s presentation of integrability theory, I think Varian’s general criticism of the whole enterprise stands. The online reviews by customers at Amazon and Barnes & Nobel simply do not address Varian’s general criticism.
And finally, I first read Wade Hand’s article on Mirowski as an undergraduate in the early 1990s shortly after the Duke conference volume was published. I didn’t need you to draw it to my attention.
notsneaky 09.20.07 at 5:41 pm
As an aside, this whole “Integrability problem” thing IS related to the usefulness/truthfulness of the “rationality” assumption which this post was originally about.
Basically what it says is that if you observe a demand function in the real world which has certain properties then there is some preferences which “rationalize” (again, in the economic sense of the word, so “purposeful” would probably be better for the sake of semantics) it. Or in other words, even if the individual isn’t truly rational (purposeful) but instead behaves according to some heuristics or whatever, from the modeling stand point she is equivalent to some other person, who is rational, with some preferences. Which means that you can still make predictions and all that. So a lot of “irrational” behavior is not really a problem for economic theory. In other words as long as there’s method in madness we’re good to go.
Robert 09.20.07 at 8:19 pm
I thank Chris Edmond for an explanation of his reading. It seems he is being pissed off on Tracy W.’s account. This seems odd to me.
I take it, maybe wrongly, Tracy W. is an advanced student. It would not surprise me if he aces all his courses. However, in asking me to explain the connection between 19th century physics and neoclassical utility theory in more detail, he is asking me to do some work. I still don’t feel like doing the work.
I haven’t read it lately, but I consider Varian’s review an embarrassment for Varian. And, yes, I am especially focusing on that part that Chris Edmond does (“Mirowski’s general cluelessness”) and does not (“Irrespective of”) say he wants to argue about.
I take it that Mirowski demonstrated that the structure of utility theory is taken from physics. Once sensitized by Mirowski, I’ve noticed the claims to physics-like science in, say, Walras myself. (By the way, “Amateurs borrow, professionals steal.” I forget where I am stealing that from.)
Mirowski wrote a history. Any primer in his book on physics and economics is as needed for the history. As I recall, Mirowski says that he abstracts from a transformation in commodity space needed to take account of the income constraint. Whether or not Varian understands Hamiltonians, he (unjustly) failed to note Mirowski’s caveat.
(I thought Mirowski made this point that he was writing history, not theory, somewhere or other. Through Google books, I was only able to locate some mocking of Varian’s textbook in Mirowski’s “The Goalkeeper’s Anxiety at the Penaly Kick” or whatever.)
I think that Mirowski adequately documents that mathematicians and physicists questioned early neoclassicals about integrability and conservation laws. His bit about Gibbs questioning Fisher is admitedly labeled as speculative. Perhaps some day specialists will find documentary evidence on this point.
I find Chris Edmond’s comment about Wade Hands odd. I first brought his paper up in a response focusing on a question from Tracy W. I also cited my mention of it as an answer to “notsneaky”. So once again, Chris Edmond seems to be getting into a dander on the part of others.
Anyways, I take it that Hands has demonstrated that utility theory does contain conservation laws, discussed hardly at all, if ever, by neoclassical economists. Hands clarifies how to account for income effects. Although Hands does also write about history, I take this clarification to be about the structure of the textbook theory, not early history. Chris Edmond does not comment on the substance of Hands’ paper.
Perhaps I ought to point out that nowhere in these comments have I suggested that neoclassical economics ought to be rejected because of the supposed absurdity of these conservation laws. Nor have I said otherwise.
I do find the logical implications of the structure of utility theory in tension with some beliefs and claims of neoclassical economists. (By the way, contrary to the impression one might get from John Quiggin, revealed preference theory failed to live up to Samuelson’s stated goals. At least that is a claim, both Mirowski and Hands accept. They cite a study by Stanley Wong, which I have not properly read.)
Where do Varian or other textbook writers discuss the conceptual structure of utility theory, as it relates to the Slutsky and integrability conditions? (My question in comment 20 remains unanswered.)
Let me re-iterate my major claim: Mirowski is a neccessary part of any current and informed conversation about physics and neoclassical utility theory.
engels 09.21.07 at 1:24 am
Or in other words, even if the individual isn’t truly rational (purposeful) but instead behaves according to some heuristics or whatever, from the modeling stand point she is equivalent to some other person, who is rational, with some preferences. Which means that you can still make predictions and all that.
An ingenious approach. For some reason it reminds me of this.
notsneaky 09.21.07 at 1:53 am
An ingenious approach. For some reason it reminds me of this.
Except it’s nothing like that. Not even remotely comparable. And anyway, anyone who criticizes economic theory reminds of this.
See, we can all play that stupid game. Too bad it has nothing to do with the actual result.
Please take more care when pulling BS analogies out of thin air next time. Like, pick one that’s at least funny or something.
engels 09.21.07 at 3:39 pm
Wow, I guess I must have really hit a raw nerve!
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