Tuesday, June 10, 2008

What Is Apathy? I Don't Care.

As far as I can see, Varian implies in the following combination of quotations that the student need not care about vast chunks of his textbook:
"...we show that the theory of utility-maximization implies certain testable restrictions on the observed choices of consumers. Such restrictions have several sorts of uses. For example, one can use these observed restrictions to test the model against actual behavior of economic units. Given some data, one can ask if it could have been generated by a maximizing unit..." -- Hal R. Varian (1978) Microeconomic Analysis, Second Edition, W. W. Norton & Company, p. 2
"...the utility maximization hypothesis imposes certain observable restrictions on consumer behavior. In particular, we know that the matrix of substitution terms... must be a symmetric, negative semidefinite matrix." -- Hal R. Varian (1978) Microeconomic Analysis, Second Edition, W. W. Norton & Company, p. 135-136
"It can be shown that any continuous function that satisfies Walras' law is an excess demand function for some economy; i.e., the utility maximization hypothesis places no restrictions on aggregate demand behavior... Thus, any dynamical system on the price sphere can arise from our model of economic behavior." -- Hal R. Varian (1978) Microeconomic Analysis, Second Edition, W. W. Norton & Company, p. 246
In other words, the empirical content of the "utility maximization hypothesis" on the level of the theory of markets is close to empty.

24 comments:

Gabriel said...

That depends on the interests of the respective students. Why assume that they only care about the aggregate?

All models, made sufficiently generic or left with enough degrees of freedom, will be able to rationalize any observation.

In applied work, i.e. working with data, you invariably use (more) restricted models but applied analysis is informed by the generic results of more general theory. So where's the beef?

Anonymous said...

There is absolutely no reason why the socially constructed organization of the data into "aggregate demand(s)" should be the only kind of data relevant for judging the falsifiability of a model.

Pace Solow, there is no evidence that God intended to make life easy for economists, and thus make aggregate demands sufficient for testing models.


The problem with general equilibrium is that it is false, not that it is unfalsifiable.

Hahn claims somewhere that Joan Robinson didn't grasp the fact that the constancy of utility functions through time is what gives empirical content to utility based theories. Given that the falsifiability of the utility maximization hypothesis transfers just fine into the (strong) falsifiability of GE models, you seem dangerously close to making the same mistake.

Alex

YouNotSneaky! said...

There's two ways to go here.

You can either construct a model where demand doesn't play a role, and in that way side step the whole problem of aggregation. Personally I think this way of dealing with what Alex and Solow refer to as God not making life easy for the economists leaves a lot to be desired.

Or you can still try to do some kind of "macro" while at the same time recognizing that this problem is common to ALL macro theories where demand plays a role. It's there in the "Bastard Keynesian" approach. It's there in AD approach with the SMD theorem. And of course it's there with the DSGE approach in regards to the representative agent. I mean, there is that "general" in "general equilibrium" after all.

(I guess a third way would be too stick with plain old accounting based on input/output tables. But then you got no reasons to make any kind of policy recommendations or predictions)

Michael Greinecker said...

I don't think consumer theory is that important for general equilibrium models. It´s mainly needed for welfare analysis. Pretty much every behavior not violating the budget constraint gives, when aggregated over enough consumers, something sufficiently continuous and convex to do existence proofs.

If you want to make statements about aggregate behavior, make assumptions on the distribution on behavior. Werner Hildenbrand for example used the assumption that demand is more dispersed with higher income on average. This he used for deriving the law of demand in a GE framework.

Mike Beggs said...

To be fair to Varian, the intro to his textbook does explicitly invite students to ignore large chunks of it. :)

walt said...

It's also not actually illegal to do economic research where the unit of observation is a single consumer.

Robert Vienneau said...

I see lots to disagree with above, some more batable than others. Don't some of you disagree with each other?

Anyways, I will register why I bracketed out the implications of utility maximization for individual behavior. It seems to me that experimental economists have shown, often against their desire, that people are not utility maximizers.

The empirical grounding of many of the propositions of orthodox economics is an enigma.

Ian Wright said...

>All models, made sufficiently generic
>or left with enough degrees of freedom,
>will be able to rationalize any
>observation.

That's why parsimony in science is so important. General equilibrium is not parsimonious.

"The impact of SMD theory is quite general … Its chief implication … is that the hypothesis of individual rationality, and the other assumptions made at the micro-level, gives no guidance to an analysis of macro-level phenomena: the assumption of rationality or utility maximization is not enough to talk about social regularities. This is a significant conclusion and brings the microfoundations project in GET [General Equilibrium Theory] to an end. Of course, if one does not want to look for regularities at the macro level, the SMD results pose no problem; but every theorist who wants to argue that a change in some price variable … affects a corresponding quantity aggregate in a definite direction, cannot base this argument on GET."
S. Abu Turab Rizvi in Rizvi, S.A.T., (1994) "The Microfoundations Project in General Equilibrium Theory", Cambridge Journal of Economics, Vol. 18, No. 4, August, pp. 357-377.

Anonymous said...

"That's why parsimony in science is so important. General equilibrium is not parsimonious."

What exactly is your justification for the claim that general equilibrium is not parsimonious?

Do you have an explanation of prices in all markets which uses fewer variables?

Risvi's statements are correct, but they don't support the claims that general equilibrium is unparsimonious or unfalsifiable.

I'm only commenting on this because I think overemphasis of parsimonious explanations in social science is misleading. This is not physics, where we're not sure if various mathematical entities exist or not -- we know that technology, people, their preferences, expectations, and endowments exist. It is rather the explanation which ignores these factors that needs to justify why it does so.

Alex

Anonymous said...

>What exactly is your justification for the claim that general equilibrium is not parsimonious?

Because GET defines a Turing complete virtual machine. You could implement Microsoft Word on GET, as ridiculous as that may sound. But the joke is on neoclassical theory.

So at best GET functions as a "language" for talking about economics. But it has little or no explanatory or predictive content since it says that "anything" may happen.

> we know that technology, people, their
> preferences, expectations, and
> endowments exist. It is rather the
> explanation which ignores these
> factors that needs to justify why it
> does so.

That there are preferences and expectations doesn't imply they are important determinants of macroeconomic phenomena. That begs the question.

The (empirically successful) science of statistical mechanics shows that the macro-level properties of systems with huge numbers of degrees of freedom
are largely independent of the detailed micro-level properties of the constituent particles. Stat. mech. solves "aggregation problems" quite differently. Here's a long quote from one of the founders of stat. mech.:

"Those general laws of mechanics which are used in statistical mechanics
are necessary for any motions of material particles, no matter what are
the forces causing such motions. It is a complete abstraction from the
nature of these forces, that gives to statistical mechanics its specific
features and contributes to its deductions all the necessary flexibility.
... the specific character of the systems studied in statistical mechanics
consists mainly in the enormous number of degrees of freedom which these
systems possess. Methodologically this means that the standpoint of
statistical mechanics is determined not by the mechanical nature, but
by the particle structure of matter. It almost seems as if the purpose
of statistical mechanics is to observe how far reaching are the deductions
made on the basis of the atomic structure of matter, irrespective of the
nature of these atoms and the laws of their interaction."

GET is a pretty fantasy told in terms of antiquated mathematics. There are much better alternatives to GET for moving toward a real understanding of macroeconomic phenomena.

Anonymous said...

"[GE] has little or no explanatory or predictive content since it says that "anything" may happen."

No, it doesn't say this at all. That's a poor interpretation of the SMD results.

"The (empirically successful) science of statistical mechanics shows that the macro-level properties of systems with huge numbers of degrees of freedom are largely independent of the detailed micro-level properties of the constituent particles."

Reasoning by analogy does not get you very far. And this reasoning by analogy fails even in physics: if you want to predict what a billiard ball does at the tenth impact, you need to take into account even the gravitational pull of the persons playing billiard.

At any rate, I said that you need to provide a justification for ignoring expectations and preferences, etc. , not that it is impossible do to so. As an empirical question though, there are plenty of examples where the justifications for ignoring such factors are very poor indeed.


"There are much better alternatives to GET for moving toward a real understanding of macroeconomic phenomena."

Not really -- I would be pleasantly surprised if this were so.

Alex

Anonymous said...

> No, it doesn't say this at all.
> That's a poor interpretation of
> the SMD results.

Tell that to the leading theorists of GET theory. Here's a quick quote from Mas-Collel on the subject:

Except "for the obvious restrictions, (e.g. Walras Law) literally anything can be the excess demand of a well-behaved exchange economy."
Andreu Mas-Collel in Mas-Colell, A., (1989) "Capital Theory Paradoxes: Anything Goes", In Joan Robinson and Modern Economic Theory ed. Feiwel, G.R.; New York University Press, New York, pp. 505-520; p. 506.

By "anything" he really means *anything*. Such destructive consequences of the SMD theorems are not hard to find in the literature.

>Reasoning by analogy does not get you >very far. And this reasoning by analogy >fails even in physics: if you want to >predict what a billiard ball does at >the tenth impact, you need to take into >account even the gravitational pull of >the persons playing billiard.

This is an example from classical, not statistical, mechanics. I don't understand the point you are trying to make here. A pool table has a very small number of degrees of freedom compared to the kinds of systems studied in statistical mechanics, and in economics. But even in this case the n-body problem makes it practically impossible to predict the outcome of the "tenth impact".

But doesn't this example point to the enormous conceit of GET? We're supposed to swallow that "you have an explanation of prices in all markets" based on aggregating the heterogeneous expectations and preferences of millions of individuals? Come on, we've got to get real here.

Anonymous said...

"By "anything" he really means *anything*."

It's not at all clear that you're following the discussion. Mas-Collel et. al simply states that that aggregate excess demand functions can not be restricted (meaningfully) a priori. Aggregate excess demand functions are not all there is in the GE model however. If you take into account endowments for instance, you get plenty of restrictions.

Indeed, if I remember correctly, one of the points that Rizvi makes is that you need to take into account distribution in order to make some predictions.

"I don't understand the point you are trying to make here."

Let me put it in a different way, illustrating how reasoning by analogy may fail here.
One reason why statistical mechanics is able to ignore the behavior of small particles is the crucial use of the central limit theorem.

In order to prove the central limit theorem, you need some conditions on the random variables over which you make the sum. Independence of those variable is one assumption that is usually made. Other, less restrictive assumption can be made, but if you sum over highly correlated variables the central limit theorem generally fails.

Now if we talk about expectations, there is plenty of evidence that correlated (and perhaps mistaken) expectations play an important role in the phenomenon of business cycles. At the very least you need a theory about how those expectations behave, because a hand-waving invocation of the central limit theorem will just not do it.

"We're supposed to swallow that "you have an explanation of prices in all markets" based on aggregating the heterogeneous expectations and preferences of millions of individuals?"

I don't see how you can attribute such claims to me if you read my posts above.

I guess you can call me a macro-skeptic -- I don't believe that macroeconomic theories based on few variables are all that likely to provide successful explanations.

Alex

Gabriel said...

Robert,

>> "Anyways, I will register why I bracketed out the implications of utility maximization for individual behavior. It seems to me that experimental economists have shown, often against their desire, that people are not utility maximizers."

The only test I know for utility maximization (only testable empirical restriction) is either WARP or something very similar. (A test on internal consistency, assuming time-invariant preferences).

To test for WARP violations you have to assume that you identified the right model of the world that the agent is using (i.e. the agent might maximize utility but might have a different model of the world than you) and you also need to assume-away measurement error. That would be one point in the defense of utility maximization.

Another point worth making is that even theories which don't past all test all the time can still be useful.

If you want to account for systematic WARP violations (e.g. the endowment effect), it makes sense to extend the baseline framework (prospect theory, kink in u. function) rather than scrap everything.

Anonymous said...

Sure you can "restrict" GET. But here's the rub: since it is so general you can "restrict" GET to fit *any* empirical time-series. How then can GET be falsified?

One cannot falsify a (Turing complete) language since it literally can "say anything".

But a language is not a theory.

You mention "plenty of evidence" that "correlated expectations" play an important role in business cycles. But this begs the question again. Standard macroeconomic models do a very poor job of predicting (not fitting!) empirical phenomena. Fitting, or rather over-fitting, is easy with GET for the reasons given above.

Such fits are not evidence that expectations play an important role in determining macroeconomic variables. (I'm willing to change my mind if you can cite good work out there that shows otherwise.)

SMD theorems are super-destructive to GET. But this point is still not fully appreciated.

Stat. mech. can deal with correlations at the micro-level, but this is a side-issue.

Anonymous said...

"Sure you can "restrict" GET. But here's the rub: since it is so general you can "restrict" GET to fit *any* empirical time-series. How then can GET be falsified?"

You don't restrict it arbitrarily, you restrict it based on given empirical data (distribution).

Alex

Anonymous said...

You'd have a point if the only restrictions placed on GET were based on empirical data. But they're not are they? Many are non-empirical, arbitrary simplifications required in order to get "nice" results.

Anonymous said...

"Many are non-empirical, arbitrary simplifications required in order to get "nice" results."

Yes indeed. But I'm not a defender of current economic practice.

I do think that the theoretical point that GE is falsifiable is important and needs to be defended against misinterpretations of the SMD result. This is so because if something better is built out of GE, it may not put more restrictions on prices. (Though it is possible that more restrictions will be available.)

Alex

Michael Greinecker said...

"Because GET defines a Turing complete virtual machine. You could implement Microsoft Word on GET, as ridiculous as that may sound. But the joke is on neoclassical theory."

Of course you can implement Microsoft word in a system described by newtonian mechanics. That doesn't imply that the movement of billard balls may follow Microsoft word- it just means that you need some data to make predictions.
Btw: Can you provide a reference for the claim?

"So at best GET functions as a "language" for talking about economics. But it has little or no explanatory or predictive content since it says that "anything" may happen."

GE without any information about the data of the GE model- preferences, endowments, production technology- ownership structure allows anything to happen by constructing appropriate data. But that data doesn't become real from this. Even quantum mechanics is irrefutable, as shown by FA Muller. But of couse using actual real world dataand common sense, QM has fantastic predictive power.

An example of good empirical work in a GE framework is given by Werner Hildenbrands work on the law of demand.

Anonymous said...

>Of course you can implement Microsoft
>word in a system described by newtonian
>mechanics. That doesn't imply that the
>movement of billard balls may follow
>Microsoft word- it just means that you
>need some data to make predictions.

I agree that GET isn't the only theory that is Turing complete. But the analogy with physics is again instructive. First, the binding of theory to an empirical context in Newtonian mechanics is wholly based on empirical observables. That's not the case in GET. Second, Physicists don't use Newtonian mechanics as a language to talk about *all* physical phenomena.

For example, to understand the behavior of very large systems with huge numbers of degrees of freedom they use statistical, not classical, mechanics.

But economics, in general, tends to take a different tack: it applies GET to *all* economic phenomena, including macroeconomics; despite the lack of empirical success, and despite the acute logical difficulties expressed in the SMD theorems.

What accounts for this difference?

One reason, and certainly not the most important, is that it's uncomfortable to realize one has been sold a scientific dud, especially when "learning the language" required time and effort.

>Btw: Can you provide a reference for
>the claim?

Not without a search, but it follows straightforwardly from SMD. SMD implies any kind of chaotic behavior can occur. Certain classes of chaotic systems are Turing complete. Hence GET is Turing complete.

Thanks for the link to the paper.

YouNotSneaky! said...

"despite the acute logical difficulties expressed in the SMD theorems."

How are these LOGICAL difficulties (never mind the "acute" part)? They are properties of the model. And the properties follow from the general framework that is adopted. If there are wealth effects a lot of crazy stuff can happen. Now, call me crazy too, but I do happen to think that wealth effects matter at least some times in the real world (else, stick with partial equilibrium). And as soon as you let wealth effects into your model, well, you get a lot of kinky stuff, no matter what you call your model. General or particular. Equilibrium or all-kinds-of-wacky. Neoclassical or Post-Neo-Fangled-ThingyMagingy. That's basically what the SMD theorem says. It's a general (there's that word again) theorem in the same sense as Arrow's - it says the real world is complicated and if you, as a researcher, want sharper predictions you better be ready to make some crazy (there's that word too again) assumptions.

What's wrong with multiple equilibria anyway? And relatedly,

"SMD implies any kind of chaotic behavior can occur."

No it doesn't. At least not by itself. In particular Debreu's theorem rules out non regular economies. So comparative statics still apply locally. Unless you have been somehow sitting on an unstable equilibria for a long time, which sort of means that it's not really unstable.

Gabriel said...

The reason that G.E. is used as the framework for macro models is not because of its inherent empirical content (none, as some of you point out all the time), but rather because it allows one to leverage existing theorems proven in the more general case and the knowledge and lore of economists. That, and because it makes it fruitful to talk of welfare, expectations and credibility (within those restrictions!).

Michael Greinecker said...

"No it doesn't. At least not by itself. In particular Debreu's theorem rules out non regular economies."

No. It rules out non-regular equilibria on a set of endowments having full measure. But that also rules out endowments that don't contain anything of some good. It is however possible to modify Debreu´s result in a way that avoids this problem (by varying both endowments and preferences).

YouNotSneaky! said...

Michael,

School year being over I'm away from the office, away from my books and with no jstor access, so I can't remember the exact conditions for the theorem. I do remember however that Debreau's theorem is pretty general.

Note also that Robert's example in the follow up post exploits exactly the "endowments that don't contain anything of some good" aspect.