"Utility theory is purely ordinal in nature and there is no unambiguously right way to quantify utility changes."
Monday, October 24, 2011
Who said it?
"A utility function is often a very convenient way to describe preferences, but it should not be given any psychological interpretation. The only relevant feature of a utility function is its ordinal character", and
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William Stanley Jevons for both quotes? What about F.Y. Edgeworth?
ReplyDeleteSurely not Bentham?
ReplyDeleteThis is fun. Neither of you are in the right century. Any more guesses?
ReplyDeleteThe focus on the ordinal nature of utility is of particular interest to our Austrian friends - which is also why the identity of the speaker is so interesting.
I would guess Hicks?
ReplyDeleteIf not Hicks (who surely said comparable things) then Samuelson.
ReplyDeleteHal Varian???
ReplyDeleteWas someone using the Google machine?
ReplyDeleteYes - Hal Varian. Who, coincidentally, is the chief economist at Google.
He's also the author of two very famous "mainstream" neoclassical micro textbooks.
I think the key point here is that cardinal utility functions are "a very convenient" way to do microeconomics and talk about microeconomics, even if they aren't "right". They're a reasonable model if you keep in mind exactly what they are: functional representations of ordinal preference relations. A lot of ordinal utility boosters like to act like this is lost on people. I don't think that's true at all.
The only really important place where ordinal utility introduces a problem is in welfare analysis. That's really where we get into talking about total utility (marginal cardinal utility talk is on much firmer ground that total cardinal utility talk).
I think this is a good reason to recognize a few things: (1.) welfare analysis is more like advanced moral philosophy rather than economic science, (2.) making intelligible statements with welfare analysis requires making implicit or explicit decisions about weighting, ranking, or simply "giving standing" to agents, and (3.) we should not be afraid to do #2 as a matter of practice.
The alternative - which has some truth to it - is to eschew microeconomics for its lack of realism. I think within bounds this is a very reasonable position to take, but to paraphrase Rothbard I would not throw utility out with the cardinality bathwater. To quote my math econ professor: "useful abstractions are useful".
"Was someone using the Google machine?"
ReplyDeleteYes and no. I remembered his name from when I was transitioning from Neo-classicalism to Austrianism, so I just tossed it out there. I did then go to google to verify.
Does anybody agree with me when I say that critics of neoclassical economics wrongly assume that neoclassical economists actually take their theoretical ideas to the absurd conclusions they are accused of taking?
ReplyDeleteOften, we see that neoclassical textbook authors themselves have caveats on the purely theoretical tools of analysis in their economics; not even such authors really seem to believe "price = marginal cost" like it is some law of gravity, or take rational expectations to be the Bible.
Daniel, do you know where that quote is from? I know that I have owned his textbook 'Microeconomic Analysis', but for some reason it isn't on my bookshelf.... So, I can't verify.
ReplyDeleteYa - it's that one. The first quote is at the beginning of the chapter on consumer theory. The second is in the discussion of compensating variation and equivalent variation in the consumer surplus chapter.
ReplyDeleteCool, thank you.
ReplyDeleteBTW Daniel if you're bored try skimming this. Another "Who said it?" moment perhaps.
ReplyDelete"Utility theory is purely ordinal in nature and there is no unambiguously right way to quantify utility changes."
ReplyDeleteSo any attempt to calculate compensating or variation and equivalent variation is a necessary imprecision and a task doomed to failure? You don't say!
I would normally not be sarcastic when we agree on economic theory but I'm afraid I have to be glib when so much emphasis is placed in microeconomics on indifference analysis, which carries with it partially differentiable cobb-douglas utility functions.
Mattheus -
ReplyDeleteNecessary imprecision - obviously.
Doomed to failure - not at all.
I am still a proponent of indifference curves and partially differentiable cobb douglas utility functions.
What I am not doing is making a claim for some Platonic reality to a specific specification of a cardinal utility.
And as I said in the comment above - making assertions about marginal utilities and prices is on considerably firmer ground than making claims about total utilities.
Daniel-
ReplyDeleteSure it's doomed to failure. The goal of compensating variation - and Hicksian demand curves - are to illustrate how we can rectify changes in income and prices to achieve an original indifference curve. If utility is purely ordinal, that throws out all linear, continuous indifference curves as well as utility functions.
It all comes down to ordinal preferences between goods! How can you have partially differentiable Cobb douglas utility functions if we can only describe utility in x>y format?
OK you need to review the entire discussion of convenient description and useful abstraction Mattheus.
ReplyDeleteIf you want to think about this discretely that's fine. You can talk about optimization discretely. And then you can say "well, the math after we make the useful assumption of continuity is more workable and gives us the same insight, so let's use that". We do this all the time in science.
So even though the professionals in the field recognize the approach is (your favorite word) epistemologically incoherent - aka, we can't possibly know what we purport to know - it's desirable and advantageous to use?
ReplyDeleteWhat other science works that way? What other science admits of its own methodological faults and yet continues in spite of - and sometimes because of - its deficiencies? Friedman embodied the height of this ridiculousness when he argued that economic models should deliberately be unrealistic! Am I talking Greek here, Daniel? Why is my pursuit of a methodologically coherent approach to economics greeted with such hand-waiving and sometimes open hostility?
Man A can be equally indifferent towards certain ratios of goods X and Y. He might have no preference versus 10X and 5 Y or 9X and 6Y. He may be unable to choose one or the other given his belief that they yield equal satisfaction. This much we can talk about and be correct. But to take a truism like this and construct these sweeping curves that imply 1) continuity and 2) measurement is WRONG.
I don't see how this is so unorthodox. Man does not appraise goods in infinitesimally small increments but in discrete units. The equilibrium price and quantity of butter cannot emerge on the basis of millionths of pounds and cents. The construction of larger or smaller indifference curves also implies some type of measurement between goods, dollars, and value. But no such measurement is possible. I doubt I'd be able to draw an indifference curve for myself let alone for anyone else.
You gesture and soothe these concerns with concessions that it's "not perfect" but rather good enough - but isn't the point of science to advance our understanding of certain phenomena? What scientist is satisfied with "good enough?"
well, the math after we make the useful assumption of continuity is more workable and gives us the same insight, so let's use that
But it doesn't, Daniel, that's the whole point. A standard undergraduate course in microeconomics is fraught with fallacy and mistake. And these mistakes go back to the 19th century with Marshall and Walras, they aren't new. You'll have to forgive me if I'm not terribly pleased spending years of my life studying models that will, by definition, be fallacious.
re: "So even though the professionals in the field recognize the approach is (your favorite word) epistemologically incoherent - aka, we can't possibly know what we purport to know - it's desirable and advantageous to use?"
ReplyDeleteEpistemology is for the philosophers. Actually, because of my philosophical predilections I would say that epistemologically coherent statements simply cannot be made by anyone, but that's not particularly relevant here. Philosophers - whether they can make epistemologically coherent statements - are the ones who worry about it.
re: "What other science works that way?"
All of them.
re: "What other science admits of its own methodological faults and yet continues in spite of - and sometimes because of - its deficiencies?"
No. Now you are being sloppy Mattheus. You are jumping from epistemology to methodology. Noting epistemological incoherence (which I still maintain is the fate of all us mortals) is NOT THE SAME as defining - much less demonstrating - methodological faultiness.
re: "Friedman embodied the height of this ridiculousness"
The height that Friedman embodied was the practice of economic science - and only a few have matched him.
re: "Why is my pursuit of a methodologically coherent approach to economics greeted with such hand-waiving and sometimes open hostility?"
Not hostility - and again, you are confusing methodological coherence with epistemological coherence. I am a big proponent of methodological coherence on here. I'm not all that interested in epistemology - coherent or otherwise.
re: "But to take a truism like this and construct these sweeping curves that imply 1) continuity and 2) measurement is WRONG."
ReplyDeleteDefine "wrong". If you mean "not real" I agree. If you mean "not a useful explanation of the world", I disagree.
re: "I don't see how this is so unorthodox."
A lot of it is implicit. People will praise science for talking about what we really know. Because they do that, denunciations of epistemological incoherence may not sound all that unorthodox. But if you start peeling back the layers of any science you begin to see that "reality" has little to do with science, and that we're mostly dealing with explanations of experience. Why do we classify species? Why do we talk about particles that are actually potentially bunches of strings?
re: "I doubt I'd be able to draw an indifference curve for myself let alone for anyone else."
I know I couldn't. But I also know that describing my preference relations as complete and transitive is a fairly reasonable first cut, and I can build from those two properties A LOT of behavior that we observe in the real world. That advances my understanding of the economic action of highly evolved primates tremendously - so you bet I'm going to go with that.
re: "You gesture and soothe these concerns with concessions that it's "not perfect" but rather good enough - but isn't the point of science to advance our understanding of certain phenomena? What scientist is satisfied with "good enough?""
I am very glad you think that science is about advancing our understanding of certain phenomena. But I would word the rest of it differently. I would not say that I think it's "good enough". I would say that I think it's "better than any alterantive". You seem to be saying that because it's not perfect on one dimension we cannot use it. That seems wrong to me. If you come up with a more useful way of talking about preferences that DOESN'T rely on these assumptions I'm all ears. But your current offering is distinctly less useful.
re: "A standard undergraduate course in microeconomics is fraught with fallacy and mistake. And these mistakes go back to the 19th century with Marshall and Walras, they aren't new. You'll have to forgive me if I'm not terribly pleased spending years of my life studying models that will, by definition, be fallacious."
OK, then don't. I'm finding that it's paying huge dividends in my understanding of the world.
Sorry this is so long. You don’t have to respond. This was as much for my own sake as for yours.
ReplyDeleteActually, because of my philosophical predilections I would say that epistemologically coherent statements simply cannot be made by anyone, but that's not particularly relevant here.
Is that absolutely true? [/sarcasm]
Epistemologically coherent statements are those statements that cannot be denied because a denial would entail a performative contradiction. Blah blah we've been over this. I'm not about to explain Kant and Mises again, suffice to say that it doesn't make any logical sense to believe that utility is subjective and psychological, and also make models suggesting we can measure and compare it. That's what I'm talking about when I say epistemologically incoherent. If we take it as a basic axiom that utility is subjective, then a lot of neoclassical babies need to go out with the bathwater.
Philosophers - whether they can make epistemologically coherent statements - are the ones who worry about it.
Philosophy doesn't do much good if other sciences do not incorporate its findings. I'm sorry you're not interested in philosophy. But someone as intelligent as you should be able to see how an error in epistemology will lead to larger errors in all "applied philosophies" (science). Hume's work on induction shaped the modern scientific method. There's a great example of why philosophy is important to scientists.
Noting epistemological incoherence is NOT THE SAME as defining methodological faultiness.
Fine, then we can't complain that the shaman who prays to fairies dancing around his head has a faulty methodology? It's clearly his epistemology that's faulty, but I wouldn't begrudge the skeptic who blames his method of inquiry. I see what you're saying, but I guess I just don't make a distinction in this case.
The height that Friedman embodied was the practice of economic science - and only a few have matched him.
The height of current economic science. Don't you dare think that Friedman represents some pinnacle of methodological inquiry. The Whig theory of history was never true. You should know the dangers of positivism better than anyone.
Define "wrong". If you mean "not real" I agree. If you mean "not a useful explanation of the world", I disagree.
ReplyDeleteThis is some equivocation! Since when did "wrong" mean "not useful?" Is this a legitimate question? I've always been taught that truth is a function of objective reality, not human concerns. Modeling continuous indifference curves as a representation of utility is wrong. Period. I didn't address whether it was helpful or not (although the admission that it is NOT TRUE should shed some light on that as well).
But if you start peeling back the layers of any science you begin to see that "reality" has little to do with science, and that we're mostly dealing with explanations of experience.
Now we're Humeans? I think your approach of science is too constricted. I would categorize mathematics and geometry as sciences. The point is that rationalism has a place in science and I seriously think it must be more included in economics if we are to have reality line up with science.
That advances my understanding of the economic action of highly evolved primates tremendously - so you bet I'm going to go with that.
Versus deductions made on unassailable axioms? Action is action, primate or not. Praxeological inquiry can have lots to say about even very primitive animals. The trick is about what we're asking. Are we asking about concretes (What will this gorilla eat?) or categories (What must logically be the case if he chooses pie?).
You seem to be saying that because it's not perfect on one dimension we cannot use it.
If I could understand biological processes on the basis of rational deduction, I would throw out induction in this as well. I'd rather take what I know from logic over what I speculate from experience. And there are logical relations at work in economics. You can’t prove the law of diminishing marginal utility from experience but through praxeology. Proofs, after all, are the domain of logic.
That seems wrong to me. If you come up with a more useful way of talking about preferences that DOESN'T rely on these assumptions I'm all ears. But your current offering is distinctly less useful.
This isn't a question on praxeology versus induction. We're not arguing if rationalism or empiricism should reign on economic science. It's a question of which theory. There are theories out there (I promise) that don’t make assumptions at all.
I'm finding that it's paying huge dividends in my understanding of the world.
It can't pay you dividends in your understanding if it's wrong. Neoclassical microeconomic theory implicitly endorses cost-of-production theory of prices; it implicitly (and explicitly) endorses cardinal utility functions and production functions; it implicitly makes egregious interpersonal utility comparisons; and on and on ad infinitum. It seems the only reason you accept these really questionable conclusions is because you aren’t familiar with more correct (and therefore accurate) approaches. That’s the point of Austrian economics. I’m glad you’re with us on a few points, Daniel, but the real difference in theory isn’t whether capital can be stretched or fallacies of composition exist, but a difference in methodology.
re: "Epistemologically coherent statements are those statements that cannot be denied because a denial would entail a performative contradiction"
ReplyDeleteYou are confusing logical coherence (predicated on certain assumptions about this performance) with epistemological coherence. Logical coherence is very useful, but it doesn't give us any roadmap to true knowledge.
re: "Philosophy doesn't do much good if other sciences do not incorporate its findings. I'm sorry you're not interested in philosophy."
I am interested in philosophy. I never said I wasn't interested in philosophy. I am not particularly interested in epistemology. I thought I was quite clear about that. That's not entirely true, though. I'm interested in epistemology insofar as I find making the point that it is largely useless a good one to make.
re: "There's a great example of why philosophy is important to scientists."
I wouldn't claim it wasn't.
re: "This is some equivocation! Since when did "wrong" mean "not useful?" Is this a legitimate question?"
Well I just want to make clear the sense in which I say "I accept this wrong claim". Utility functions are wrong in the sense that Newton was wrong. I feel like if I'm going to accept a thing that you and I both agree is wrong I should have the freedom to clarify in what sense I am accepting a wrong claim.