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Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

Economics and NKS

A recent long essay at the Red Nova website mentions NKS in a discussion of fundamental issues in modern macroeconomic theory. The essay is entitled "Value and Exchange" and can be found here -

http://www.rednova.com/news/display/?id=124822

The basic claim is that mathematical general equilibrium theory, understood as "the value paradigm" and fundamentally dependent on the assumption of achieved equilibrium, is an inadequate economic theory. The writer contrasts it with "the exchange paradigm", as a bottom up description that incorporates real dynamics, information, and institutions.

NKS does not figure too heavily in the essay. It is mostly brought in to show that the issue is not limited to economics but is of more general, within all of science. Or otherwise put, that the math envy that prompted the edifice of calculus-based general equilibrium theory is not actually justified by the ability of simple equations to describe real complex systems.

While I think some of the author's opinions about where such a bottom up analysis of dynamics of real economies might lead, are hasty and based on limited knowledge of what people may eventually find, I think the criticism of equilibrium thinking in economics is spot on. Since it is a subject that has come up here before, I thought others might be interested in the essay.

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Old Post 02-07-2005 04:24 PM
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Gunnar Tomasson


Registered: Oct 2003
Posts: 69

Thanks, Jason, for posting this - here are my two-cents' worth on the following:

The Impasse in Economic Theory

To understand the current difficulties of economic theory, we need to understand the goals of the research program that guides it. That program has its origins in the work of two great economists- Paul Samuelson and John Hicks-and its goals grew out of theirs.

Samuelson's goal was to reformulate economic theory in the language of mathematics (Samuelson 1947). He believed that this would promote greater clarity and precision. And he hoped that mathematization would lead to a formal unification of the whole of economic theory. He believed this possible because he thought that all of economics could be formalized using essentially the same mathematical approach.

While Samuelson's goal was formal unification, Hicks's goal was substantive unification. Hicks believed that much of economics could be understood in terms of the theory of value-the part of economics that seeks to explain the pattern of relative prices in an economy and the resulting allocation of resources (Hicks 1939). The construction and refinement of the theory of value had been the principal project of economics since Ricardo, and its major components were largely in place by the time of the marginalist revolution of the 1870s. Its most ambitious formulation was the general equilibrium theory of Walras and Pareto that addressed simultaneously all of the markets of an economy and their interconnections. It was within this Walrasian framework that Hicks hoped to unify much of economic theory.1

Samuelson's goal and Hicks's, while different, proved highly complementary. Samuelson's approach was to reformulate a piece of economic theory as a set of equations that jointly determined the economic variables of interest. It was essential to his method that this set of equations could be interpreted as describing an equilibrium of the system in question. The theory of value was especially amenable to this method because the concept of equilibrium was at its very core. Given the relative ease of mathematizing the theory of value, it was then only natural to attempt to mathematize other parts of economic theory by reformulating them as extensions of the theory of value. It turned out that advancing Hicks's goal was a natural way to advance Samuelson's.

Comment:

Let me make two brief - and purposely provocative! - points for the consideration of fellow economists on the NKS Forum.

1. It's a stretch to identify the ignominy of the Hicks-Samuelson approach, long-recognized but purposely ignored, with "an impasse in economic theory" - it takes more than PR work to transform a mathematical plaything into "economic theory".

In the Hicks-Samuelson case - and more so for S than for H, who had come to his senses by the 1970s - the root cause of the problem resided in the phenomenon noted by Pascal in another context.

Namely, the inability of the mathematical mind, when divorced from the intuitive faculty, to see what is in front of it - for, while the mathematical mind may excel in drawing correct conclusions from sets of GIVEN premises, it is easily led astray when divorced from the intuitive faculty.

2. Which brings me to the second point - the pinning of the Walrasian label to the Hicks-Samuelson approach.

Admittedly, it was only late in his life that Walras went on record to state the obvious - that, insofar as they may be said to apply to real-world market economies, the conditions of General Equilibrium must be held to apply at ALL points in time.

That is the OBVIOUS implications of the Laplacian construction of Newtonian mechanics, whereby a single particle of matter is held to interact gravitationally with all other particles of matter in the universe at all points in time.

It is not exactly rocket science to see, as did the Swedish economist Gustav Cassell, that this implies that ALL our observations of real-world exchange transactions are POINT observations.

Samuelson, whose approach is predicated on the idea that it is SOUND scientific procedure to draw imaginary supply and demand CURVES through such point observations, took note of and expressly DISMISSED Cassell's as "naive" - as I recall it - in a paper on Consumer Behavior in the 1950s.

Naive, yes!

Cassell?

No!

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Old Post 02-09-2005 10:14 PM
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Fiona Maclachlan
Manhattan College
Riverdale, NY

Registered: Oct 2003
Posts: 11

It's encouraging to see NKS entering the economics meme-stream but I found it odd that the article doesn't mention anything about the growing body of work in experimental and computational economics.

For a different perspective on contemporary economics see David Colander's "New Millennium Economics" in the Journal of Economic Perspectives (14:1, Winter 2000). It's a clever, whimsical piece ostensibly reporting on the state of economics in the year 2050.

Colander is optimistic that economics is getting out of its theorem-proof, pseudo-OKS rut and that the reason is mainly advances in computer technology. He predicts more simulation modelling and computer experimentation, and a fading away of the now dominant culture in economic theorizing.

~~~~
"The other thing was an open problem: What does economics really look like when you recognize it as a prototype of a new kind of science of complex phenomena, which could no longer employ the simple model of mechanics in physics, but had to deal with what then I described as 'mere pattern predictions,' certain limited predictions? That was so much more fascinating as an intellectual problem."
-- F.A. Hayek

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Old Post 02-12-2005 02:32 AM
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Gunnar Tomasson


Registered: Oct 2003
Posts: 69

Re. the following:

"The other thing was an open problem: What does economics really look like when you recognize it as a prototype of a new kind of science of complex phenomena, which could no longer employ the simple model of mechanics in physics, but had to deal with what then I described as 'mere pattern predictions,' certain limited predictions? That was so much more fascinating as an intellectual problem."
-- F.A. Hayek

Comment:

In an essay on methodological aspects of economics, John Stuart Mill wrote that its boundaries were the very last thing to be established in the development of any given branch of science.

Now, a few centuries after its 'birth', the boundaries of economic science remain to be established.

But life is short - and young economists have no choice but to build their careers on the intellectual foundations acquired under the guidance of their mentors.

Mentors who, as members of one of the many "schools of thought" in economics, have no idea whether they are teaching their students stuff which, one day, may be judged to fall outside the boundaries of economic science.

My own view is that the boundaries of Economic Science are co-extensive with those of Common Sense - an attribute, which in principle cannot be reduced to rigorous mathematical formulæ.

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Old Post 02-14-2005 02:15 PM
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Tmaq
Kellie Kolonies
On The Move

Registered: Jan 2005
Posts: 17

Physics is a subset of economics

Physics is a subset accounting, like economics.

I think Von Mises had it right; information sets the bounds.

You can't know what's in a person's heart...but that's where 'values' ultimately come from, ruining any hope of an objective description, or really, any predictive power at all at the 'individual player' level. Many individuals are notorious for it, in my expereince. Can you even predict what you'll prefer, tomorrow?

Additionally, it's a quantized process; values are expressed by choosing one thing over another. That means 'values' are a misnomer. Life operates on 'priorities,' which, regrettably for economic analysis, constantly change on all scales. Plants are fairly predictable, animals less so, people...?

Exchanges are a result of valuations perpetrated by the players, and in every case, they disagree about the relative values, or it wouldn't happen. Like QM, the only objective nature for 'value' is 'events', the 'actual value' only has meaning in one or the other 'frame of reference' and in between observations, 'value' doesn't 'really' exist.

Von Mises was pretty sharp, producing a QM economic framework.

Anyone can, and many do, create systems of conceptualization based upon 'objective' value, formal or informal, universal or eccentric, and plan their speculations AKA express their values, based upon them.

Process physics is doing exactly that, substituting 'nodes' for 'fields.'

That self-referential nature, operating on all scales, ruins the possibility of any one person knowing they've found the correct accounting strategy...assuming they can formualte it at all, or apply it, once conceived.

However, the more successful that method of prediction (for any economic player), the less meaningful the information gathered from prices, as well. Bill Gates fears the effect on MS stock that his moves with his stock would produce.

Economic measurement limits the powerful, in a 'disturbance' model, which has proven, hsitorically, to operate. The larger the economic force, the more market distortion it's purchases and sales produce, and hence the less it can trust the price information it must use to predict the costs and benefits of various options.

F.A.Hayek avoided criticism on hyper-rational grounds with recourse to 'evolution,' but Mises recognized the limiting condition; price information, and how much you could predict with it. The economist seeks patterns in the operation of the players who make *their* predictions on the same basis. No wonder positive feedback occurs so easily and often in economics. No wonder it's the 'dismal science;' it's rarely more likely to predict any one outcome than the same method used by 'the man in the steet,' but you don't actually risk anything, aka, make yourself useful or a profit.

A lack of useful economic measurement (AKA, free prices) is what dooms totalitarian societies, even on top of the effect of decreased incentives, hence initiative, for the players.

-Tom

__________________
-Tom McWilliams

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Old Post 02-15-2005 11:05 PM
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Gunnar Tomasson


Registered: Oct 2003
Posts: 69

Tom,

I like your approach!

Here are off-the-cuff comments on the following:

Physics is a subset accounting, like economics.

Agree - out goes TOE.

I think Von Mises had it right; information sets the bounds.

Not sure - the concept of "information" must relate to some given frame of reference or else it is meaningless.

You can't know what's in a person's heart...but that's where 'values' ultimately come from, ruining any hope of an objective description, or really, any predictive power at all at the 'individual player' level. Many individuals are notorious for it, in my experience. Can you even predict what you'll prefer, tomorrow?

Agree.

Additionally, it's a quantized process; values are expressed by choosing one thing over another. That means 'values' are a misnomer. Life operates on 'priorities,' which, regrettably for economic analysis, constantly change on all scales. Plants are fairly predictable, animals less so, people...?

Agree - Samuelson invented the concept of "revealed preference" in an attempt to overcome this objection. The concept cannot withstand a moment's scrutiny, but mainstream economists embraced it out of dire necessity - discard it and you stand exposed as a dilettante playing at economic "science".

Exchanges are a result of valuations perpetrated by the players, and in every case, they disagree about the relative values, or it wouldn't happen. Like QM, the only objective nature for 'value' is 'events', the 'actual value' only has meaning in one or the other 'frame of reference' and in between observations, 'value' doesn't 'really' exist.

Comment:

I think this is not the half of it - for, as Gustav Cassell noted, ALL our observations of exchange transactions reduce to POINT observations.

In the field of Solar System Mechanics, this would not have precluded Newton from deriving his equations GIVEN the stability of lunar/planetary orbits over time.

Absent "revealed preference" - as in the observed "preference" of the Moon and the Planets to move along their orbital paths - the FACTS of the matter would have aborted Samuelson's mainstream economics at the creation.

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Old Post 02-15-2005 11:58 PM
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Tmaq
Kellie Kolonies
On The Move

Registered: Jan 2005
Posts: 17

Hi Gunnar.

Careful! Assuming you meant 'theories of everything' there is still a possibility; an accounting system which works in all realms. And 'completeness' might not be a concern until you interpret the resulting quantities, if 'consistent' and 'comprehensive' both apply.

'Information sets the limits' was pretty vague. I'm not familiar with Samuelson, so I'll have to check him out, but I think any effort to save 'values' in any absolute or continuous-dimension sense is doomed. Only because of opportunity cost does any price matter, and that must be the fundament of their meaning in economic theory, to remain consistent.

If we didn't *have* to 'pay,' whether with effort, time, thought, or a trade-off...who would choose to?

I'm curious what you mean about being considered a dillitante if you discard 'continuous valuation' - the Austrian School is pretty mainstream, and Rothbard aside, it's starts from value=subjective desire-abating potential.

In some regard, it's already the conventional wisdom; free prices are the best way of getting up-to-date information about human desires and the practical means for fulfilling them...so any individual's opinion about others' desires are essentially meaningless for a discussion of the function of prices, and Samuelson's choice of a criteria other than 'what price got paid' is as subjective as the formulation of value he evidently tried to replace.

How did Samuelson attempt to save 'value' as a dimension? I know there are all sorts of 'conversion' attempts, all akin to the technocrats measuring 'normal human input,' or that other freak who tried to boil it all down to 'hours of labor' as if digging holes for an hour is just as useful as doing heart surgery for an hour.

Both attempts were made by people Mises referred to as 'the would-be breeders of men;' they, in their unconscious evaluations, forgot that all people are constantly making evaluations.

Indeed, I believe it was Von Mises who first pointed out why objective value is impossible. People only trade when they disagree about items on their prioirty lists. If I think $2 is less valuable than a latte, and Starbucks disagrees...then, and only then, does an observable trade occur.

I'm guessing that Samuelson, like many economists, imagined some kind of information he'd prefer to have other than prices paid, and set about developing or deriving some act of measurment for 'value' independent of current prices, which is to say, independent of individual human capriciousness.

The fundamental error in the conceptualization of the 'real' value, is the expression of values in the attempt at 'conversion.' When we *pay* attention, that counts as a revealed preference, a move that was doubtlessly overlooked in Samuelson's attempt...as it must always be overlooked, to make the attempt at all. His focus on any specific criteria is an expression of the very 'value' he was attempting to observe, poisoning the attempt. The only way to make the attempt while accounting for the bias is to use all criteria, or even prefer those you *don't* like, a contradiction in terms, if not emperically. Neither option makes the attempt tenable.

That same 'revealed preference' is why science is not 'value-free'; you can't pay attention to everything, so your 'values' are revealed by what you do, in fact, pay attention to, even if the discoveries are 'value-free,' or the researcher really is disinterested in the 'answer' she seeks.

Regarding point observations; Unity is Plural, and at minimum, Two.

Every 'point' observation always requires (at least) two elements. Trades, obviously, have 4 or more. 2(+) players, 2(+) items traded. Even you weren't aware of yourself before you were aware of someone else, first.

In terms of science, every fact also comes with a 'confidence level,' 'chi-squared correlation' or 'error-bar,' which sometimes counts as the more informative aspect of the data; a measure of the resolution of the observation - how 'fuzzy' it is, which is to say, how much it is *unlike* a point.

Put it all together, and 'point' is a wholly inadequate metaphor for observations. Even metaphors have (at least) 4 parts. I suggest 'event' instead.

Are you aware of anyone attempting a representation of Von Mises work along systems-theory lines? He's got a very systematic approach, and it would combine quite nicely with Feynman's 'least action' approach. It was only in the realm of Physics that we were surprised to discover that all the ways something could happen each contribute to determining what *does* occur. Economists recognized such a mechanism ages ago; opportunity costs, aka, prices = the cost of using an alterntaive instead. When there aren't alternatives, prices go up.

I'll have to check out Cassel, nevertheless.

BTW, Kepler and Galileo did all the work for solar system mechanics. They developed the specific-case relations which Newton generalized into "F=ma" - Newton could have done his work on Venus with a force-table.

So this is excellent; I was looking for some insights into 'NKS.' You've given me two leads already.

Thanks,

-Tom

__________________
-Tom McWilliams

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Old Post 02-17-2005 07:35 AM
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Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

While I find your (Tmaq) review of Mises argument more or less accurate, that argument was decidedly weak and unconvincing even as fully elaborated by Mises himself. Mises wanted to argue against planning. There are many good arguments against planning and he found not a few of them. But among them he counted the unknowability of initial valuations, and this argument is quite weak. In fact he considered it his strongest argument, when it is one of his weakest. It is instructive to look at why.

Essentially it is an "unknowable initial conditions" argument. It is analogous to chaos theory enthusiasts who reason "some things are sensitive to initials, arbitrarily small initials are unknowable, everything is connected to everything else, ergo nothing is knowable". This is a complete fallacy.

There are some minor quibbles with it, that one often hears but that do not touch the real fallacy involved. I mention them to get them out of the way. One, not everything is relevantly connected. Two, most impacts of initials are damped outside of narrow regions. Three, the actual sensitivity does not extend to arbitrarily small levels. (At a small enough scale all the relevant systems become discrete etc).

The more basic problem is that unknowability of a logical or empirical prior does not entail unknowability of a later resultant of that prior, especially not when the scale of aggregation has been changed. Inability to measure the position and velocity of every molecule in a gas does not imply inability to measure temperature. Inability to predict all disease does not imply inability to profitably sell life insurance. One might readily predict aggregated demands without knowing diddly about exactly which individuals will choose which schedule of preferences. In fine, inability to know everything in no way implies inability to know anything.

Mises was partially motivated by the analogy of QM, no doubt. (Popper advanced similar arguments in favor of indeterminism). He was also motivated by his Weberian philosophic background, which taught him that the sphere of values was inherently unknowable because unscientific because subjective. Which is a philosophic error in its own right - the fallacy that there are no subjective facts. Not an error any economic practitioner actually makes. Find me the retailer who reasons "my customers' desires are subjective, so I have no way of influencing or even knowing them, so I might as well put whatever I dream up on my shelves as just as likely to be wanted as anything else". Of course subjective facts remain facts and not opinions. That is why economic constraints are real, and cannot be altered by make believe.

Hayek made much more sophisticated arguments than Mises about the unpredictability of economies. He traced it to the complexity of economies as information processing systems, not to unknowable initials. He noticed that sub patterns of mutual accomodation or coordination of private plans, may not all be compatible with a single future trajectory of prices - creating the potential for "forced errors" - situations from which somebody or other has to be wrong about their predictions and therefore present private expectations must be falsified somewhere. He did not try to shunt possible complexity off into a sphere outside of economics proper and merely fed into economics as data (unknowable "initials" within individuals), but saw how irreducible complexity could arise in the coordination problem itself. Can these initials and those be put together with one set of prices, or not?

Economies are not actually all that unpredictable to begin with. On short time scales, sufficiently aggregated economic variables are readily approximated all the time by actual economic actors. A few subsystems aggregate overall risks and behave in quite unpredictable ways, certainly. But it is not as though an auto company needs to be able to predict the stock market precisely in order to know how many tires to buy this quarter. There is lots of local order. Sufficiently averaged quantities are readily predicted, in practice. On a quarterly time scale GDP is a line and almost a constant - its typical changes are miniscule. Telling an econometrician he can't know such things because values are subjective, is as silly as telling an aeronautical engineer that no plane will ever fly because QM indeterminacy might be magnified by chaotic fluid dynamics.

If one is debating the existence of certainty in a Hume seminar, arguments of a certain tendentiousness are tolerated. But knowledge is a much more robust thing than that, and it occurs. There are excellent questions to be asked about how one knows things and how much one can know, but denying that knowledge occurs (and matters) is denying the evidence, and is simply false.

A more promising track is to follow up Hayek noticing that economies are information processors, and that an ensemble of private plans need not all be compatible with an actual objective state of the world. Either with the one existing, or (for some ensembles of plans) with any possible objective arrangement. And then to view use of information as a process of mutual adjustment of models and assumptions, in addition to and alongside of a means of selecting a distribution of goods. And yes, also an ongoing adjustment of valuations.

(Too many classical economists treated having a sound reason for positing some feedback in some direction, as equivalent to being at an equilibrium resulting from prior repeated action of that feedback. As systems models readily tell us, these aren't remotely the same. The dynamics resulting from the former can be quite complicated, and it should be no surprise that the simplicity of the latter is not always empirically established).

As for the statement (in passing) that trades are generated by disagreements about the value of things traded, it is true in some cases and can be a fair modeling assumption for limited purposes (e.g. where the issue is differing estimates of the amount of the same commodity that a certain contingent claim might eventually represent). But it is a sufficient rather than a necessary condition. There can be gains from diversification, for instance, even where individual valuations are identical. People's budget constraints are over ensembles of goods, not individual goods. The offers of others allow them to navigate to different ensembles, by giving up the marginally least important to them in favor of the marginally most important. There is no a priori reason different individuals would desire the same ensemble.

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Old Post 02-17-2005 05:18 PM
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TEL


Registered: Feb 2005
Posts: 1

That's right.
Any equilibrium matter's most when the optimal;at least defined, expression, is wasted on the fundamental fallacy which mathematics can be used to-co-incidentally, position where the least errors are occuring.
If such things like 'market stability' are confused here, than why should calculus help?
To do basic figure's which market watcher's need almost instantly, get's pretty confusing to the statician whose first excuse of failure, will begin the descent into a post=Darwinian melt-down that hasn't anything less 'marketable' than divining what pure mathmatic's are rally about.
That's a base, and good starting reference when you've many assuming calculus to have already defined how the shapes are laid, but not if there's stability placed ahead of assesing whether profit's in science could assume the totalitarianism which work from the bottom up.
Do you blame other's when markets fail, or improbable's that couldn't prove how they'd worked only perhaps twice in real time.

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Old Post 02-18-2005 10:08 AM
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Jason Cawley
Wolfram Science Group
Phoenix, AZ USA

Registered: Aug 2003
Posts: 712

The most perfidious way of harming a cause consists of defending it with deliberately faulty arguments. - Nietzsche

Or more charitably, maybe it is just a language barrier, I suppose...

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Old Post 02-18-2005 02:54 PM
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