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Mario is right about the thrust of Hayek's analysis being a challenge to the very core of macroeconomic theory.

This was understood, for example, by Mark Blaug. In his book on, "The Methodology of Economics," he explicitly rejected the Austrian critique. He said that if taken seriously it would mean "goodbye" to virtually all macro thinking since Keynes, and this seemed impossible to him to accept.

Because, then, how do you analyze and explain (and try to correct for) economy-wide fluctuations in output, employment and prices?

That it might be possible to construct a micro-market process approach instead of traditional macro-analysis seemed outside of Blaug's thinking.

Furthermore, what does such a micro-process focus lead to as part of its possible policy implications? To return to sustainable re-coordination of interdependent markets, it may be necessary to accept a degree and a period of unemployment; money (and real) wages may have to adjust downwards (through appropriate relative price and resource allocation adaptations; some banks may fail, and depositors lose part or all of their savings; reductions in both government spending and taxing may be necessary (including on entitlement programs); etc., etc.

This msy require a return to -- oh, no! -- real competitive free markets, the rugged individualism that Ohama attacked in his speech yesterday as a "failed" theory that is the opposite of "fairness" and "social justice."

Economic analysis of the "is" -- how logically and historically did the boom come about and why a recession followed -- may lead to an "ought" -- given the micro-economic interconnections this is what may be required to assure sustainable and real re-coordinaton -- that is implicitly and/or explicitly unacceptable to those with various ideological biases, or special interests that wish the government to protect them from "negative" change.

This is the deeper Hayek vs. Keynes debate beyond "just" the Austrian economist's micro vs. the Keynesian macro debate.

Richard Ebeling

But if the thrust of Hayek's analysis was a challenge to the very core of macroeconomic theory, and macroeconomic theory has by and large ignored this challenge... wouldn't it be entirely correct to say that Hayek did not have a significant impact on macroeconomics?

Look, you can't both have that Hayek was an embraced leader of the field and that Hayek was a revolutionary whose insights were ignored.

I love me some Mario Rizzo.

Still, I think this excerpt is more a response to Keynesian economics rather than the economics of Keynes (do Austrians understand the difference??). After all, it was Ludwig Lachmann who noted that Keynes was a more complete subjectivist than Hayek (it is true!).

So, there is nothing wrong with debating people like Krugman and DeLong over fiscal policy. But let's not make the mistake of saying this is an accurate representation of the views of Keynes himself. For that, you need to consult the work of the Post-Keynesian school. I still can't understand why Austrians don't do this.

Now -- let the criticisms come! Just how wrong am I this time?!? (:

Question Matt:

What article won the FEE prize for best article in Austrian economics this year? What was the subject matter of that article?

Um, because they don't want to get it right?

Recall that Krugman hadn't even read Ohlin and _brags_ about not ever having been able to bring himself to read any "prose" or pre-1970s economics ...

Matt is a perfect apriorist.

@David,

it can be both. Hayek's contributions to technical economics in the 20's and 30's is - in part - what got him the Nobel. However mid 30's he underwent significant changes in his thinking that led him to conclude that what he rejected about the Keynesian system was the thinking in aggregates.

There are some hints of that in the early 30's, but it is not until economics and knowledge (1937) and the use of knowledge in society (1945) that this other Hayek is starting to see the light. This is the other big part that got him the Nobel.

You're correct to point out the paradox, but as I've hopefully explained now, is that it is truly just an apparent contradiction.

I would cite sources for this, but I think you can find most of this in Caldwell's writing (?).

Martin,

Did Hayek ever reject thinking in aggregates? If you have a cite or something, of course I'll check it out. But I don't think he rejected thinking in aggregates. After all, a demand curve is an aggregate. What he rejected, I think, were the Keynesian aggregates, which hide the relative price movements and resource movements that are the key to his cycle theory.

Dr. Koppl, on a totally unrelated subject, I must say that I really enjoyed your forensic science youtube talk. I can't wait to depose you when I begin practicing! Do you ever appear as a witness in criminal trials? You are the ideal expert witness for criminal defendants.

Heh. You are kind, Matt. I mostly keep myself squirreled away in academia.

Roger,

May I suggest looking at the first few pages of Lecture I in "Prices and Production," where Hayek very explicitly rejects theorizing in terms of macro-aggregates and averages: total output, total employment, a price level.

He makes the same point in his review of Keynes' "Treatise on Money," in which he says Keynes' aggregates hide all the relevant relative price and production relationships that are the basis of all that actually happens in the market.

And this is different from market demand or supply curves for individual goods.

Hayek's point, I would suggest, was that any such "aggregation" cannot meaningfully and usefully go beyond that point at which any coherent understanding of market processes in terms of scarcity, trade-offs, resource allocations among alternative uses (opportunity costs), relative price and wage relationships, etc., are submerged in the "totals."

That type of "aggregation" was surely the basis of Hayek's "discomfort" with Keynes' general approach in the "Treatise on Money," and even more so in "The General Theory."

What meaningful and relevant microeconomic relationships are left in a framework that reduces the analysis to, and submerges everything under, "Aggregate Demand" and "Aggregate Supply" for everything.

Indeed, I would further argue that even to talk about Aggregate Demand for "output as a whole" is meaningless for understanding any causal relationships, because there is no "demand" for output as a whole.

One can speak of the individual and market demands for shoes, hats, bananas, etc. And one can at least talk about the demands for "consumer goods" relative to the demands for "capital goods."

But there is no one or subgroup who "demands" output as a whole, and therefore it is methodologically meaningless for any reasonable and realistic economic analysis.

Surely, this was the basis, for instance, of Ludwig Lachmann's analysis of complementarity and substitutability among and for capital goods in the articles he first wrote in the 1940s, leading up to his book, "Capital and Its Structure." All those relationships relevant for understanding changes in the microeconomic processes were lost in Keynes' aggregates," such as the "marginal efficiency of capital" curve under which all capital was implicitly viewed as perfectly homogeneous and interchangeable.

Certainly it is also part of the reason for Hayek's analysis in his 1937 article, on "Investment that Raises the Demand for Capital." And for his (and Fritz Machlup's) rejection of Frank Knight's restatement of J.B. Clark's conception of capital as a homogeneous, self-perpetuating "fund."

"Capital" is the sum of the market value of a group of capital goods and related assets. But capital goods are individual goods that are created, used in various complementary production sequences through time, and then must be replaced (if the market decision-maker so chooses on the basis of his estimate of profitability of possible alternative production plans).

This was the theme in Hayek's exchange with A. C. Pigou over the meaning and nature of "maintaining capital" intact.

All such discussion loses its meaning if the analysis is reduced to Keynesian macro-aggregates.

Richard Ebeling

Richard,

I looked in P&P. I must admit his language is stronger than I had recalled. But I don't think he said aggregates cannot enter our reasoning. It's that aggregates do not act directly on one another, which is true IMHO. (He says maybe *averages* have to go, but averages are not aggregates.) Again, the demand for shoes is an aggregate. It lumps together thee and me. And it lumps together sling backs and wing tips. We think we know, however, what we're saying about who does what when we manipulate the aggregates labeled "supply of shoes" and "demand for shoes." As far as I can tell, then, it is not that aggregates must be purged or something. Rather, we want aggregates that let us unpack who does what. And we do not want aggregates that mask the relative price movements central to our theory. Now, if H really did slam aggregates as such, I'd have to say he erred. But my scan of that bit of P&P didn't support that reading of Hayek.

As I commented at TM, some of Hayek's contributions (neutral money, rational expectations) have been incorporated into modern macroeconomics. I doubt 1% of economists know where the ideas came from.

Both Roger Garrison and I have frequently made a similar point. There are macro phenomena, but sound analysis must be microeconomic. The question is the appropriate level of aggregation. Macro aggregates are too aggregated for causal reasoning (Hayek, Prices and Production).

Roger,

Hayek argues, in that passage in "Prices and Production," that all of our knowledge of economic relationships are derived from the development of our "individualistic" (microeconomic) approach.

That was the point of the remainder of my comment (which I gather you generally agree with), that the degree of aggregation should be no greater than one that submerges the structures of relative prices, wages, production uses and relationships through which we can grasp the logic of the market process that generates the patterns of resource uses and causal interconnections between the choices of individuals and groups of individuals in society.

Furthermore, I do not believe that the way the "demand" for or "supply" of a good is normally defined or understood in micro-analysis is compatible with how notions of "aggregate demand" or "aggegate supply" for output as a whole as used in macro-theory.

Richard Ebeling

In the Counter-Revolution of Science Hayek makes a distinction between constitutive ideas and speculative ideas. The first are ideas that motivate actors within the economic system. Speculative ideas are those that analysts have and find useful in analyzing complex phenomena.

I think we can apply this to the issue of macro-aggregation. The constructs of the theory the analyst uses should not obscure the factors (ideas) that generate the behavior of the economic actors. The constructs should not conceal the changes that are taking place which affect the plans and actions that ultimately constitute the business cycle.

The key for me is the claim that aggregates cannot directly causally affect other aggregates. The causal links must be microeconomic. After all, Mises accepted the basic truth of the Quantity Theory, but had a damn fine explanation of the micro process by which changes in money affected "the price level" via individual money balances and prices.

Steve, regarding your last comment, I think I can contribute something.

I am both a mathematician and a fluid dynamicist, and dipped my toe in econ on an amateur level when the financial crisis hit, largely due to my desire to understand things. As such, it always puzzled me how economists (whom I later learned were Keynesians) put aggregates in causal relationships to each other. This puzzled me because "aggregate" is just a non-technical word for "integral."

Frankly, I don't know how much math the typical economist takes, so I have no idea if I'm talking down to you or talking over your head. But bear with me here.

In just about any system of equations with enough complexity to be interesting, integrals ("aggregates") are important, but they are intrinsically information-destroying. For example, if I have a differential equation describing the way the distribution of some quantity on a square evolves in time, if all I know about the system are some aggregates, I very likely do not have enough information to know how even those aggregates evolve in time!

But you might. Perhaps the economy is just luckily one of those systems.

What I learned from fluid dynamics, however, is that when your system is nonlinear, once you average ("aggregate") all the terms in the system, you no longer have a closed system. In other words, you have more variables than you have equations. You can see this in the derivation of the RANS equations here:

http://en.wikipedia.org/wiki/Reynolds-averaged_Navier%E2%80%93Stokes_equations

That's not to say means and various statistical moments are either useless or uninteresting. It's quite obvious, for example, that there's a lot CPI doesn't tell us about the value of money. But it is also quite obvious that when CPI inflation is 150%, life is really hard. There's a reason regression forecasting is a thing.

Now it seems quite obvious to me that the monetary goings-on of the world are a great deal more complex than water flowing through a pipe. So if someone even could come up with differential equations completely describing the system, such equations would certainly be nonlinear. And that being the case, the Keynesian approach--the search for well-defined functional relationships between aggregates--is simply doomed to fail again and again and again. Assuming nonlinearity in the equations, it is actually fairly easy to prove this.

In my work as a fluid dynamicist, I have seen this take shape in the fact that regression correlations can be built for aggregates as long as the system doesn't change--i.e., if you don't tip your airfoil too far, or speed up the flow too fast, or, even worse, switch from airfoils to flapping wings. Again, it seems evident to me that these econometric models must all have the same problem--the most exhaustively, carefully built regression correlation will break if the system changes, say, if there's a major labor dislocation, or some formerly foundational technology is rendered obsolete.

Finally, a note on Hayek. I have read Pure Theory of Capital, and the more I think on it, the more I think Hayek was not up to the task for much the same reason as Muslim mathematicians were not up to the task of inventing caclulus. It was not a deficit of intellect, but of language. Calculus was much easier to invent once the Cartesian plane and symbolic algebra were invented, neither of which Islamic scholars had. It seems to me that the language Hayek was using to describe something he could almost grasp--and seemed to know he was almost grasping--was woefully inadequate to the task.

Someone should develop the intellectual tools necessary to actually do economics at the level Hayek was attempting to reach.

Josh S,

I agree completely. As far as I can tell, economists are competent at a certain kind of calculus-based proof, but outside of that limited scope they are really quite limited and ignorant. At the very least, nothing like your RANS equation seems to occur. The Journal of Economic Theory, for example, reads more like philosophical proofs than physical ones. I am similarly convinced that information economics is sometimes in defiance of the laws of physics.

I agree about your comment on Hayek as well. He struggled to explain social evolution too, it seemed, possibly because the English language isn't well-geared for it.

Although, it has always seemed to me that Keynesian economists might be enamored by their aggregate and monetary macroeconomics because it does SEEM like a physical system (not that they are deliberately copying physics) in that there are a limited number of objects which obey simple cause-and-effect rules, making it possible to effectively solve the system. That this may well be in defiance of mathematical law due to the underlying aggregate nature of the seemingly simple objects is a fairly entertaining possibility.

Richard,

I do generally agree with the substance of your earlier comment. Mostly, I think it is a mistake to describe such a view as somehow opposed to aggregates. Again, the demand for shoes is an aggregate. (BTW: I’m just trying to channel Alfred Schutz, who somewhere [Economica?] explained it all very nicely IMHO.)

You said, “One can speak of the individual and market demands for shoes, hats, bananas, etc. And one can at least talk about the demands for ‘consumer goods’ relative to the demands for ‘capital goods.’” Indeed. And when you do that, you are manipulating “aggregates.” You also say, “But there is no one or subgroup who ‘demands’ output as a whole, and therefore it is methodologically meaningless for any reasonable and realistic economic analysis.” But no one demands “shoes as a whole” either. Thus, I don’t think that I would personally introduce the notion that certain aggregates are “methodologically meaningless.” I would just argue in relevant cases that this or that set of aggregates masked vital relative price movements, vital resources reallocations, or whatever. Or I would argue in relevant cases that the aggregate(s) in use obscure who is doing what.

I might quibble with you over a few minor points, but, again, I think our substantive positions are pretty similar. It’s just that I don’t want us to bash “aggregates” as such. That just seems to expose us to justified criticism and to divert attention from the two key issues: 1) Does the aggregate in use mask relevant changes in less aggregated variables such as relative prices? 2) Does the aggregate in question obscure relevant questions of who does what?

Josh S & Calvin: Traditionally economists have used classical analysis, about which von Neumann and Morgenstern complained justly. The dominant thing was Boubakian real analysis. (I think Wade Hands may have been the first to put his finger on this point.) Beginning about 1980,however, things began to change. Game theory became more widely used, and technical game theory matured. And the complexity revolution changed the tools economists use. Hayek was an early complexity theorist, actually, who approached both Prigogine and Hakken, as Barkley Rosser notes in his JEP survey of complexity economics. I like both developments. I have been pushing "computable economics," which is a branch of complexity economics. Computable economics takes Goedel and Turing seriously. IMHO that's a math that lets us take our ignorance more seriously.

"In my work as a fluid dynamicist"

Josh, what do you know about systems where the dynamics become mathematically intractable?

And do the "models" fit every exemplar of the phenomena?

According to Nancy Cartwright, only small parts of nature actually fit the brittle "models" given to us by physicists -- most of nature is not captured adequately according to the demands of these constructs.

Does that insight apply to fluid dynamics?

"Computable economics takes Goedel and Turing seriously. IMHO that's a math that lets us take our ignorance more seriously."

At what point to the economists take Witggenstein & Kuhn seriously?

It's a human science, for gods sake.

What unites us in coordinated behavior is common ways of going on together and learning processes which allow rivalrous understandings to come into closer coordination.

NONE of this involves sets of "givens" and "given relations" as you find in a formal construct or a computational construct.

Wittgenstein, not Godel.

Kuhn, not Carnap.

Hayek, not Arrow or Lucas or Rosser.

It's what is on the other side of Carnap, Godel, Arrow, Rosser, etc. that capture how symbols have any significance or how humans manage to coordinate their behavior using shared public items, which become "givens" to ONE mind when ONE person builds a formal system.

No formal system takes open ended learning seriously.

No formal system takes conceptual growth and change seriously.

No formal system takes Kuhn or Wittgenstein or Hayek seriously.

No formal system takes the background of shared goings on together / language use seriously, the stuff which makes the uses of shared public symbols possible.

No formal system takes the background of training and paradigmatic problem solving under the guidance of teacher/scientist seriously.

Roger writes,

"Computable economics takes Goedel and Turing seriously. IMHO that's a math that lets us take our ignorance more seriously."

In order to take ignorance seriously, you have to see how formal systems have no room for the core dimensions of ignorance -- all of the stuff involved in open ended learning, conceptual change & going beyond a prior "given" set of "information".

Roger writes,

"Computable economics takes Goedel and Turing seriously. IMHO that's a math that lets us take our ignorance more seriously."

I should also say:

Gerald Edelman's Darwinian global brain science, not Hayek's "connectionist relations between givens" global brain science.

Edelman allows for open-ended learning/discovery, conceptual change and genuine ignorance in ways Hayek's "how possible" mechanism fails to allow for.

Greg, check out my contribution to the December 2010 JEBO and then tell me whether "formal systems have no room for the core dimensions of ignorance." What do you make of Markose's "Type IV dynamics" or the game theory results of Alain Lewis and of Tsuji et al.?

Greg, I'm not sure how to answer you other than to say that my point is that even in a system where the dynamics are mathematically tractable, the kind of aggregation economists do destroys so much information as to render the system unsolvable. So it's silly to not expect macroeconomics to have the same problem.

Will do.

"Greg, check out my contribution to the December 2010 JEBO and then tell me whether "formal systems have no room for the core dimensions of ignorance." What do you make of Markose's "Type IV dynamics" or the game theory results of Alain Lewis and of Tsuji et al.?"

My understanding is that without simplifications Navier-Stokes equations are mathematically intractable and that at some dimensions fluid dynamic problems cannot be simplified in a satisfying way to make the math tractable.

But that's just what the scientific literature is saying, this is not my field.


Roger, formal systems can display different types of ignorance, e.g. even the Greeks came up with formal results revealing aspects of human ignorance, e.g. our unknowable ignorance of the next number in the pi series in the absence of cranking out the next step in the series.

This sort of thing -- beginning with a set of formal "givens" -- only takes you so far.

So you would reject the Tsuji, Da Costa, & Doria argument on socialist calculation, Greg?

Let me read it first. On what grounds you you guess I would reject it?

"So you would reject the Tsuji, Da Costa, & Doria argument on socialist calculation, Greg?"

Markose, of course, looks interesting ...

The literature on computability & complexity, incompleteness & the infinite is very difficult: I've been reading Gregory Chaitin on the topic & I need to read it very slowly to wrap my head around it.

But if your are Hayek or Blaug, it's not that important -- it's clear that equilibrium constructs have a tenuous link to real people learning in the market.

This stuff is important to explain the inapplicability of these formal systems to the real world to people who the career system have made into formal system robots.

But for non-robots, not so significant, but extremely interesting even for that.

Roger a few years ago wrote:

"These recent results show that computability issue crop up in contexts we had thought of as “finite,” because our vague descriptions allow an infinite variety of finite games to fit the description. Thus, you get computability problems cropping up in contexts we had thought immune to them. In a forthcoming JEBO article, Prasad says, “Even for games with computable equilibrium points, best responses of the players may not be computable.”

Computability problems are ubiquitous. I think that matters for economics. It matters for discussions of creativity. It matters for the socialist calculation debate. It matters for policy analysis."

Well, you seem to reject anything that smacks of "formal systems" as somehow inadequate to any "Austrian" discussion of ignorance. I really don't get that at all. I figure we need to move to some specific analyses to avoid Tis! vs. Tisn't! The cites are in the JEBO paper I flagged.

Doesn't it matter if the multiplier is .5 or 2.0, or under what circumstances it might be one or the other?

Ah! So you think it's about equilibrium? This literature does end up using equilibrium notions along the way, but it is not asking whether, like, economies are in equilibrium or something. Rather, the question is what agents in the system can and cannot know about each other and about the system and it's about what imaginary external observers could know about the system. Equilibrium is a tool for such inquiries, but not the point of them.

Well, I don't reject it.

In fact, I used the problem of the sensitivity to initial conditions of non-linear phenomena oin mechanics and the mathematical intractability problem in dynamics to illustrate & convey aspects of Hayek's knowledge problem.

It has pedagogic, explanatory purposes, but does not fully capture the issues involved.

Roger writes,

"Well, you seem to reject anything that smacks of "formal systems" as somehow inadequate to any "Austrian" discussion of ignorance."

Well, in a deep sense and a complete sense, it is radically inadequte.

But for explanatory and pedagogic purposes, and to capture parts of what are involved, its has its role.


"Well, you seem to reject anything that smacks of "formal systems" as somehow inadequate to any "Austrian" discussion of ignorance."

Roger,

As you know, I applaud your efforts, but ultimately I do side with Greg here (as you also know). It is not publicly available yet due to publisher issues, but I have a paper coming out on moving beyond close-ended models of choice, and single-exit theories of equilibrium --- which makes the argument that Greg is sort of pointing to with respect to economics as a HUMAN science. Dick Wagner's book is outstanding on this --- see Mind, Society and Human Action.

I just gave this talk to our philosophy department here at GMU a week ago and we had a good conversation. Also see my paper on "Anarchism and Austrian Economics" which was my Cuhel Lecture and in that I try to make the case that in order to shift the focus to institutional analysis you have to have an open-ended model of choice.

Roger's computability economics shows the limits --- it proves a negative very rigorously. He and I disagree on the impact of that proof. I do think it is a very "smart" approach, I just always agree it is as "good" as Roger believes. Still, I encourage ALL to read Koppl, and to also read his SDAE Presidential address, which is one of the core readings I will start my advanced topics in Austrian economics seminar with next term.

I get this, Roger. Here's the Kuhn point -- how do we "model" different and rival understandings of the world using a univocal logical construct made out of stipulated "givens" known to each mind reading an academoc paper?

I get that a formal construct with univocal givens can show us or hint at aspects of our ignorance or limitations on our knowledge.

But this is pail stuff compared to the Kuhn point about different understanding of the world that can't be limned in a formal syntax & stilulated semantics.

"Ah! So you think it's about equilibrium? This literature does end up using equilibrium notions along the way, but it is not asking whether, like, economies are in equilibrium or something. Rather, the question is what agents in the system can and cannot know about each other and about the system and it's about what imaginary external observers could know about the system. Equilibrium is a tool for such inquiries, but not the point of them."

Thanks for the plug, Pete.

We've been having the same fight for decades now! I do know and admire Dick's recent book. I will have a comment in the SIEO symposium on it. In that comment, i try to connect computability theory to the physics metaphors in Dick's book. In my 2010 JEBO paper I argue for literary methods and I get there by a kind of computability path. So, as you know but others may not, the formal tools I like do not crowd out literary methods. They create room for literary methods.

Jonathan,

"Doesn't it matter if the multiplier is .5 or 2.0, or under what circumstances it might be one or the other?"

What my statement means is that this is not a good way to look at the economic system. The "multiplier" is not real; it is a theoretical construction. It depends on the constancy of expectations. It ignores the sustainability of expenditure. It ignores the need to re-allocate labor and capital.

It is a simple tool for the wrong problem.

@david

"Look, you can't both have that Hayek was an embraced leader of the field and that Hayek was a revolutionary whose insights were ignored."

Hayek was an ignored revolutionary in some aspects (capital theory, method), and a leader in others (informational and institutional economics). But this has nothing to do with what Krugman is saying. Krugman is not saying that Hayek is not an important figure today; he's saying that Hayek was NEVER an important figure in economics. This is, without a doubt, simply incorrect.

Josh,

There are economists, mostly non-Austrians, who are using fluid dynamics equations in modeling economic systems. I am not aware that it is necessarily the case that introducing nonlinearities into a linear closed system opens it.

To Greg and Roger,

Sheesh, you guys have to drag me into this? So, Greg thinks I am a bad guy in there with Arrow and Lucas. I doubt I can convince him otherwise.

Then there is Roger mentioning me, and it must be noted that I was the editor who accepted his paper for publication in JEBO, as well as having coauthored with him on this computability stuff. But I am really more into dynamic complexity, even if Roger says that such in Hayek comes from his analysis of computability. As it is, my thoughts on this are incomplete, and I am having trouble fully computing them.

I don't say or believe that anyone is a "bad guy" .... or that math constructs dom't have centrally important purposes, Barkley.

I'm just broadly gesturing at examplars to illustrate a distinction.

OK, Greg. I'll accept that I am merely an exemplar of something that you disapprove of rather than being an actual bad guy. Makes my day.

And, Josh and others, I have long argued in numerous publications and papers, many of them on my website, that nonlinearities in the economy leading to dynamic complexity and sometimes related to computational complexity as well, are a source of fundamental uncertainty in the economy.

Greg,

Now it just seems like you're saying no model captures everything, which no one disputes. Recall that I objected to your remark that "formal systems have no room for the core dimensions of ignorance." That seemed to say that you're totally missing the point if you use mathematical symbols to run your argument. But I think Markose's discussion of "Type IV dynamics" and the game theory results of Alain Lewis and of Tsuji et al. give us some pretty "Austrian" results about our ignorance. So, again, maybe we should restrict our attention to those arguments to keep the discussion focused. Otherwise it just seems like we're stuck saying "Is so!" "Is not!" back and forth.

Josh, interesting post. My brother-in-law is an electrical engineer. I showed him a graph of business cycles from 1790 to 1950 which showed the deviation from mean output during each cycle. He said it looked like a graph of an out-of-control system. I asked him why such a system would be out of control and he said that the feed back loop is too long to correct the system so you get large oscillations. I think that describes our macro economy pretty well. The lags between policy changes and their effects are too long for bureaucrats to control the system. Some can’t even make the connection.

I’m not sure what you think Hayek was attempting in “Pure Theory” that he wasn’t up to the task. He wasn’t trying to come up with equations to model the economy. His purpose was to provide sound capital theory for economics, which is the main problem with mainstream econ and part of the reason their equations don’t work.

As he writes in the preface, Hayek wanted to extend capital theory from static to dynamic theory, but the approaching war forced him to rush his book into publication. Still, he did a pretty good job of laying a foundation for dynamic theory which others have built on.

Read Hayek’s Nobel Prize address and you’ll see that he doesn’t consider math models of the economy to be possible because the necessary data simply doesn’t exist and probably will never exist. Models based on existing data are nothing but the fallacy of looking for your keys under the street lamp.

No, I'm saying it fails to capture of the main things, including the core of learning /causation in the domain at explanatory interest.

"Now it just seems like you're saying no model captures everything."

Roger, I can mark open ended learning with a public symbol and put it in a formalism.

O = opened ended learning

There, I've done it.

Now I can load that into a formal equilibrium system .....

Can you see the magicians shell game here?

Is not!

We can aggregate individual demands for a single good, to get market demand for shoes. We can even aggregate the demands for all consumer goods and services, to get consumer good. But we cannot add together the demands for consumer goods and capital goods?

Isn't it obvious that the trade off relevant to the demand for all output is money? People demand less output and more money or vice versa?

And scarcity of all output is what aggregate supply is all about. That is why long run aggregate supply is vertical.

Why is this so different than the trade off between huge aggregates like all consumer goods and all capital goods?


My critique of Hayek isn't the lack of equations; far from it. I simply think the formal language he was using was not up to clearly capturing the phenomena he wanted to describe.

Barkley, it's not that nonlinearities make systems open; it's that integral equations are open. In other words, suppose I have a function over time and "space" (in economics, I suppose our "space" is all people and businesses in the economy).

u(t,x) = f(u,u) + g(u)

where f is a nonlinear operator and g is linear, and u is a vector of variables of interest. Define U(t) to be the integral of u(t,x) over x. What Keynesian economists want is for there to be an equation

U(t) = h(U,U)

where g may or may not be nonlinear. We'll denote integration over x by I_x. The problem happens when we integrate the original equation.

I_x (u(t,x)) = I_x(f(u,u)) + I_x(g(u))

The problem is that integration does not commute with nonlinear operators. So you get

U(t) = I_x(f(u,u)) + g(U)

You might think it's a good idea to decompose u using u = U + u'. And you might be able to massage the equations to get:

U(t) = f(U,U) + g(U) + h(u',u').

But now your system isn't closed. What you want is a system that predicts the time evolution of integrals in terms of other integrals alone. Of course, the reality is that in economics, you don't even have the original nonlinear equation. This is all hypothetical reasoning--my hypothesis being that even if you could find an equation to describe the entire economy down to every individual transaction, it would be nonlinear, so once you integrated it to get an equation relating aggregates, you would have an open system.

Ergo, the Keynesian quest of finding a reliable equation to predict aggregates is doomed to failure.

This reminds me of what Skousen wrote in his “Structure of Production” about people who follow principles of Austrian econ even if they don’t know about Austrian economics. Austrian economics attracts the worker bees of the economy, such as financial experts and business owners, because they have learned the same truths through experience.

Who pays attention to mainstream economists? The answer is other mainstream economists, politicians and socialist professors in the arts and humanities. Why does Krugman write a political column instead of a financial advice column? Because he doesn’t know anything of any practical value.

The Austrian business cycle theory has enormous practical value for investors and businessmen. So why would anyone care that Hayek had not influence on a field that is as worthless as tits on boar?

It is interesting that formal systems in one of the areas I know about -- axiomatic consumer choice theory -- has rendered the subject, including welfare economics, a conceptual mess that has almost no application to anything vaguely real.

Of course, this does not mean that all formal systems in economics are doomed to this fate but it does give one pause. The formalist mind-set is generally in a world unrelated to the kinds of questions and answers that people who are interested in real social problems either ask or accept as answers.

I am not personally interested in pie-in-the-sky formal-system possibilities that will make up for all of the harm actual formal systems have done to the relevance of economics.

I know I understand the world much better than the overwhelming majority of formalist economists. And that is that.

be undertaken and what form it should assume.

In short, he does not want to focus on aggregate

IMO calculus and algebra are the wrong tools for modeling economies anyway. I think a lot could be done with cellular automata. I think it would not be too difficult to encode certain behavior rules with some randomization, using the subjective theory of value, marginal utility and a few other things, and watch how the system evolves with time.

Josh, I have occasionally thought that calculus and algebra were not up to the task, too. Have you checked out agent based modeling? Boettke has written about it some. It seems to hold some promise.

However, I'm not quite ready to give up on econometrics. The real problem with mainstream econ is not their use of math, but the theory behind their math. I'm confident that econometrics done with Austrian theory would be a major improvement in modeling.

It may be kind of late to add to this thread, but I would like to say a word about "formal systems." I think there may be some confusion here. I think perhaps we normally think of "formal systems" as expressing the "Cartesian esprit geometrique" that Hayek opposed. But when we move to computability theory, almost the opposite is true. It all starts with Goedel, who showed that Hilbert's idea to basically compress all of math into a set of axioms wouldn't work, if I may be allowed to speak loosely. So Hilbert wanted to squeeze all of math into the model of Euclidean geometry. But Goedel showed that you would not be able to prove all true theorems within such an axiom system. Turing basically showed that there is no way out; *any* consistent axiom system that gives you "a certain amount of finitary number theory" (in Goedel's words) is incomplete. So computability theory is all about how we cannot, in some sense, squeeze even formal systems down to a set of axioms and then expect those axioms to generate all the mathematical truths expressible in the system. It's about how the Cartesian esprit geometrique that Hayek opposed is, indeed, a bust.

There are at least two interesting aspects to this. First, we might be able to use this stuff to show that the Laplacean dreams of economists are incoherent and must be given up. Second, we can move down to the system level, enter the system as it were, and show that agents within the system have limits of knowledge unimagined in more standard versions of "formal" economics.

At the root of all of this computability stuff is the problem of self-reference, which comes in two interesting ways. First, there is the liar's paradox. "I am lying." Second, there is the infinite regress of "I think that you think," which Morgenstern explored in the context of Holmes vs. Moriarty. The infinite regress of "I think that you think" arises naturally in economics, as Morgenstern emphasized. In particular, it arises in the policy context and, therefore, in macroeconomics. It's a big job to work out a "positive" macroeconomics that takes self reference seriously, but I think it is something worth doing.

Josh S,

Your recent comment reminds me of this:

http://xkcd.com/793/

@Roger,

On your last point. You may recall that Andy Schotter, Roman Frydman and I co-authored an SEJ article extending Morgenstern's insight (as "Newcomb's Problem") to show the impossibility of a rational expectation of policy.

Josh S,

Philip Mirowski wrote a very good book you might want to take a look at, More Heat than Light: Economics as Social Physics, Physics as Nature's Economics (Cambridge U. Press, 1989> A paperback ed. was published in 1991.
In Chap. 7, "The Ironies of Physics Envy," he has a great discussion of "Paul Samuelson, scientist."
PAS has a lot to answer for.

Jerry,

Thanks for that reminder. I confess, the last time I read the paper (until just now) was in WP form in 1980 or 1981. I don't think I understood it at the time. It is a powerful argument IMHO that deserves to be renewed and discussed at this time of change in macroeconomics.

Here is the JSTOR link:

http://www.jstor.org/stable/1058483

testing

Roger,

Wittgenstein showed that no system of formal symbols & relations have any significance for human beings outside of our background of shared ways of going on together in the world and in using the symbols, stuff made possible by our training in a community and from our innate motor control "systems" and the "nature" of our brain, i.e. from our innate humanity.

Kuhn & Hayek developed similar arguments, focusing on the foundational role of training, imitated practices, and unarticulated "traditions", often acquired via the experience with paradigmatic problems and solution networks.

There is a direct parallel between Wittgenstein and Mises.

"Formalists" believe that significance can be grounded in stipulated sets of relations between "given" / univocal entities, sketchable on a sheet of paper and isomorphically re-enacted somewhere in the world or in the head.

In economics, for the formalist, the valuations and prices found in a math construct captures all there is to the significance of valuation and prices for an individual and in the real world of market goods and prices. Valuational and/or price relations can be calculated on the basis of the "given" elements "given" to the economic mathematician, who divines either the utilities in the head of "agents" or real relations in "the economy", which mirrors a math construct and can be build simply by plugging in "given" "data" from the world. And this is taken to be really what the world is like. Paul Samuelson, Abba Lerner and Kenneth Arrow are perhaps the poster boys of this conception.

Mises detonated this view. Mises showed there are no such "entities" or "given data" anywhere.

Later I hope to play out the direct parallel to Wittgenstein and his "private language argument" again Russell, Frege, and Plato, etc.

If you understand Wiggenstein, Godel's destruction of the Hilbert program, etc. becomes a side show, a nail through the heart of a hopelessly confused program that has already been shown to have begun from a fatal mistake, a hopeless confusion.

rules of the game or the parameters of the sub-discipline of modern macroeconomics

Greg, I'm trying to talk about how to use the tools of computability theory in economics and you're talking about the philosophy of mathematics. For the sake of argument, let's say that the philosophy of math doesn't need Goedel once it has Wittgenstein. Okay, but I'm not doing the philosophy of math; I'm an economist. The "computable economics" of Velupillai and others is about economics. It uses notions such as Turing computability and the related tools of metamath to do economics. He's a great example that cites Hayek and everything:

http://eprints.biblio.unitn.it/archive/00000901/01/14_05_Velupilai.pdf
published version here:
http://www.springerlink.com/content/m42581171513k859/

That's not "formalism" in some Hilbertian sense. It's not the "formalism" Lachmann criticized. It's not the "formal systems" approach Mario questions above.

Again, why not read my Dec. 2010 JEBO paper or the Tsuji et al. paper and talk about *that*? Otherwise we have no anchor to our conversation.

The deductive ideal and the formalist project come from the demand for justification.

That's why formalism has any purchase, and it is the impulse that 20th century economists derived from the math/logic group in Vienna and Central Europe.

The deductive ideal is a bust as a model of the growth of understanding/knowledge, as a model of language, as a model even of math.

Mises / Hayek showed it to be a bust in economics.

Isn't the incompleteness / undecidability result just a cherry on top? Even in economics?

Undecidability and incompleteness are formal properties that are produced in the pursuit of a formal project. The grounds of this project go back to Euclid and changed form with the rise of set theory and the new logic of Frege, etc.

Economists in the 20th century adopted this program from the math/logic tradition.

If we aren't clear about the significance of this tradition and what Godel & Turing meant to it in math/logic are we going to be more clear about it in economics?

Perhaps the idea is that economists are going to teach those working in math/logic what it all means.

Nash & von Neumann, of course, were mathematicians, not an economists.

I'm simply suggesting we take a step back and ask ourselves a question we forgot to ask:

What the hell are we trying to do, and why are we trying to do it?

The formalist project is an attempt to satisfy a demand of the deductive ideal for justification that extend to the tradition going back to Euclid.

The deductive idea has been a bust as a model for how our understanding of things grows and as a model of our language use, and much else.

There is no compelling reason to be trapped by it.

If we aren't trapped by it, pathologies internal to the project become less compelling -- because the whole project is less compelling.

Now, if the significance of the FAILURE of the deductive ideal project is what is of interest, the Mises & Hayek are directly relevant, as are are Kuhn and Wittgenstein.

Perhaps incompleteness and undecidability are ladders for folks who are attempting to climb their way out of the fly bottle.

For those of us not in the fly bottle, what is the relevance?


Much of Hayek's progression from the 1920s to the 1980s can be told as the story of a man climbing his way out of the fly bottle of the deductive ideal.

Compare _Monetary Theory and the Trade Cycle_ and all of its references to the deductive ideal, and the rejection of the deductive ideal found in Hayek's _Studies in Philosophy_ or his _The Fatal Conceit_.

The deductive ideal has been a something of a bust even in mathematics (Russell, Godel, Turing, etc.) - why should economists grab hold to it like a drowning man grabbing for a life ring?

There are homogeneous aggregates, which dominate Keynesian thought, and heterogeneous aggregates, which are necessary for any thought.

Greg,
I don't see how to advance the conversation fruitfully at this point. I made the rather mild claim that the technical tools of computability theory might help us make a few "Austrian" points in economics. In response, you tell me how I should give up "the deductive ideal" and get with Goedel and Turing! And you seem to have some phobia about reading either the Tsuji et al. paper or my Dec. 2010 JEBO paper even though I have repeatedly said that without some such conversational anchor we can't really hope to get on the same page. I'm afraid that's it for me. I don't expect to respond to you again on this thread. Frankly, I am rather discouraged from engaging you on computability in the future too. I hope I don't sound petulant or tart or something, but when you seem to "correct" me by pointing to Goedel and Turing . . . Well, I just don't know what to do with that. I have been *invoking* Goedel and Turing not neglecting them. Presumably, I am not getting your point(s) at all, but we seem to be so far from meaningful dialogue that, as I say, I don't see how to advance the conversation fruitfully.

Computational methods is what is going to prove to the rest of the economists that the Austrians were right all along.

Oh, I have tried to stay out of this. I am not going to defend "formalism," and indeed have been on record in more than one locale as criticizing at least certain versions of it. But, Greg, when you claim that "Mises showed that there are no such "entities" or "data" anywhere," you really go over the top.

I might have agreed with you once upon a time, oh, maybe 20 years ago or more. But the older I get the more I think there is an objective reality out there, however we label it or interpret it due to our social conditioning and all that. So much wheat has been grown and harvested, however we measure it or how accurately we know it. The price of Brent crude is something definite right now in dollars, even if dollars are a social construct. And, even subjective experiences, including misperceptions of reality, are themselves a part of reality, objective reality.

I suspect that you really did not want to go this far, and I find it amusing that is von Mises rather than Hayek whom you invoke when you do so. You are more careful when you cite FAH.

I doubt that Mises or Greg Ransom or anybody would deny that a certain tonnage of wheat has been grown in any given year or that a certain price was paid for a given commodity at a given time. What Mises pointed out is that there are no determinable, constant relations among economic quantities. In physics we can calculate the acceleration of gravity at the surface of a planet as GM/R^2. Once we measure G in laboratory experiments, we apply the equation with confidence to a multitude of cases. In the realm of human action, the prices change, the elasticities change, preferences change, and entirely new alternatives arise. Sure there's a reality out there, and we do our best to model it. But when it comes to modeling human action, humility is in order.

This isn't the case at all, Roger.

I've said much the _opposite_ -- but then you have implied that acknowledging a role for using these formal results to illustrate some aspects of "Austrian insights" was to to admit that there was NOTHING to my claim that these formal results fail to capture the core of what lies outside of a formal system, i.e. genuine open-ending learning, etc.

I've said I'd much like to read Tsuji et al. and your own paper. I haven't had as yet a chance to do so, much do think I will learn from them.

I have no such phobia.

You _yourself_ have said that the burden is on you to show why this work is of any relevance. I haven't suggested much more.

Roger,

"I don't see how to advance the conversation fruitfully at this point. I made the rather mild claim that the technical tools of computability theory might help us make a few "Austrian" points in economics. In response, you tell me how I should give up "the deductive ideal" and get with Goedel and Turing! And you seem to have some phobia about reading either the Tsuji et al. paper or my Dec. 2010 JEBO paper."

I agree with you on all this Barkley:

"But the older I get the more I think there is an objective reality out there, however we label it or interpret it due to our social conditioning and all that. So much wheat has been grown and harvested, however we measure it or how accurately we know it. The price of Brent crude is something definite right now in dollars, even if dollars are a social construct. And, even subjective experiences, including misperceptions of reality, are themselves a part of reality, objective reality."

Barkley, I really meant only this.

Mises explains that there are no "utils" in the head, no cardinal utilities, no indifference curves, none of Paul Samuelson's pseudo science (see Stanley Wong's great book), attempting to mimic some hybrid "operationalist/Machian" image of science.

And prices and calculation in prices are stuff of the real world, not can't have a real existence in math construct.

That's all I meant.

I've studied under a philosopher of science who believes the only "real" entities in the world are those discussed in particle physics -- and everything else is _eliminated_ as "fictional" talk referring to nothing in existence.

So you don't have to tell me about taking a realist stance toward, say money (as Hayek does in _The Counter-Revolution of Science_).

I've written a paper on the explanatory reality of functional and biological kinds for that Professor, so I know all about what is at stake in various versions of the "Realism" and "Anti-Realism" debate.

I'm a realist about everyday categories, social science categories and biological and physical scientific categories -- a controversial position.

Greg, you know the old saying, "don't tell me, show me". What if you go past telling us that everything has changed since Wittgenstein, Kuhn etc and show us how they add value to the attack on specific problems of theory, policy or methods.

This what I have tried to do with the fallible apriorism (a la Barry Smith and Karl Popper) to provide an alternative to the strong (justificationist) apriorism that puts Austrian economics out of bounds for other economists.

And with the Popperian concept of metaphysical research programs to suggest that the Austrian program is ok according to the state of the art in the philosophy of science.

You also need to respond to Roger's line of argument to show how or why his take on the problem can't work.

I am just trying to figure out how Greg keeps citing an economist who claimed all economics must be deducted from the axiom of human action as the progenitor of the destruction of the "deductive ideal."

Josh, pure economic theory is deduced from the action principle and a few auxiliary assumptions such as the fact of scarcity. But the application to real-world situations requires additional assumptions regarding the actual preferences of individuals and the specific physical and other constraints within which they act, and these assumptions must come from experience -- from data broadly conceived. The problem with seeking quantitative output from mathematical models is that you don't have enduring constants to put in the equations. It's as though, in fluid mechanics, each little fluid element had its own individual viscosity, equation of state, and a host of other parameters, along with a mind of its own to change those parameters, with the fluid itself collaborating to change the shape of the physical constraints on the flow. Your earlier comment about the necessary shortcomings of econometric models is right on target. It may be possible to use mathematical Tinker Toys, as it were, to illustrate various principles or possibilities or effects. What you can't do is expect to measure and determine the parameters, put them into equations, and capture anything reliable about the evolution of a dynamic market economy.

Josh, I was clearly gesturing toward Mises case against common uses of mathematical economics.

Many consider "the action axiom" part of the weaker aspects of Mises re-casting of economics, Mises is still genuflecting to the deductive model and the justificatory paradigm, but this part of Mises didn't really work, did it.

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