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There is a paper over at Real World Economics Review which is creating a bit of a kerfuffle. The paper is “The giant blunder at the heart of General Equilibrium Theory” by Philip George. I hope Blair Fix has read it or can read it soon. It is only a few pages long but it appears to be making an elegant and profound point. If it is correct, it really does torpedo GET (General Equilibrium Theory) and DSGE (dynamic stochastic general equilibrium), at least in the eyes of scientific thinkers. I think assessing this paper for math and science validity would play precisely into one of Blain Fix’s strong suits. Here is the link to George’s paper.
http://www.paecon.net/PAEReview/issue101/George101.pdf
The paper by George is of real interest and deserves to be taken seriously, in my opinion. This is whether or not it offends certain research program sensibilities, which seems to be the focus of the kerfuffle on the RWER blog. There, at least one respondent and maybe two are “heterodox” (maybe?) and yet clearly buy into GET and/or DSGE theory. At least one of them appears worried about heterodox economics’ respectability in the eyes of orthodox economics. I for one don’t think heterodox economics should care about conventional economic sensibilities. I also don’t think Philip George’s argument can be easily dismissed when I consider it from a philosophy of science point of view. Economics is a wicked problem. What are we dealing with when we deal with wicked problems even in the hard sciences? Modern Complex Systems science recognizes the seemingly irreducible complexity of the world. Here is an interesting view of the matter from the angle of the philosophy of science and complex systems.
“One aspect of the variability (of complex systems theories and models) is the variety of complex systems phenomena engaged: in one application it may be counter-intuitive dynamics — such as the survival of cooperation in a sea of cutthroat competition — in another, self-organisation — such as rhythmic entrainment among food-stressed slime mould amoebae — in still another the onset of chaos — such as in local climate fluctuations — and so on. Another aspect of the variability is that characterising complex system principles is often a ‘wicked’ problem where the key dynamics generating a phenomenon is itself a function of the application conditions.
To take a simple example, traffic jams on expressways may be caused by any of entry/exit rates, truck/car proportions, flow density, driver pathway correlations, etc. Moreover, the dynamics of jam formation for each of these conditions is significantly different. For instance, truck/car speed differential is important near lane-change originated jams but less important for high density braking-originated jams, and
unimportant for pathway convergence jams. So there is no usefully generalisable, detailed dynamical rules for traffic jam formation.” – “Introduction to philosophy of complex systems: A” by Cliff Hooker in the volume “Philosophy of Complex Systems” – Edited by Cliff Hooker.If the formation of traffic jams is so complex how much more complex are economies? We can consider how traffic jams and general congestion affect economies, along with a myriad of other factors. We can note that we haven’t solved the problem of preventing traffic jams and their inefficiencies via conventional economics. Is not conventional economics supposed to be about the efficient use of resources? Well, we haven’t priced traffic jams correctly. Why? Maybe negative externalities are an endless set and at some point (usually very early because of special interest pleading) we stop pricing negative externalities. Is the DSGE theory right and we simply haven’t applied it because of capital as power? Is the DSGE theory wrong and we haven’t applied it anyway because of… capital as power!
To think that price theory alone and equilibriating with prices (as market fundamentalism) can control for such problems is an heroic assumption. But the greater heroic assumption is to think that an economy (in its entirety as a socioeconomy and in its aspect as a dissipative thermodynamic system out of equilibrium with its environment) can be described by an equilibrium model. It cannot validly be so described or modelled. When conventional economics began fully adopting GET or DSGE theory circa the 1970s , mainly as academic theoretic exercises, it was already the case that physics and especially the biological sciences were abandoning the equilibrium paradigm outside the classical “simple” physics arena. Conventional economics and GET/DSGE with their pretensions to scientific status were really wholly called into doubt as a superseded paradigm, even if nobody said so at the time.
“The (classical science) study of simple physical systems of a few components and of many-component systems at or near stable equilibrium supported the idea that the paradigm of scientific understanding was linear causal analysis and reduction to linear causal mechanisms, with the real as what was invariant under symmetry groups (a formal stability) or invariant to small perturbations (dynamical stability). Paradigm cases
included 2-body solar system dynamics, engineering lever and circuit equations, equilibrium thermodynamics of gases.The philosophy of science evolved compatibly, focusing on determinism, universal a-temporal (hence condition-independent) causal laws, analysis into fundamental constituents then yielding bottom-up mechanical synthesis. To this was added a simple deductive model of explanation and prediction — deduction from theory plus initial conditions gives explanation after the event and prediction before it. Reduction to fundamental laws and separate contingent initial conditions became the basic explanatory requirement. This supports an ideal of scientific method as
logical inference: logical induction from the data to form the most probably correct theory, deduction from theory for prediction and explanation, and deduction from data that conflict with prediction to a falsification of the predicting theory, or other assumptions.” – Cliff Hooker op. cit.Then:
“… by the late 1970’s it is clear in retrospect that science had begun to pull together many of the major ideas and principles that would undermine the hegemony of the simple symmetry/ equilibrium orthodoxy. Instabilities were seen to play crucial roles in many real-life systems — they even conferred sometimes valuable properties on those systems, such as sensitivity to initial conditions and structural lability in response. These instabilities broke symmetries and in doing so produced the only way to achieve more complex dynamical conditions. The phenomenon of deterministic chaos was not only surprising to many, to some extent it pulled apart determinism from analytic solutions, and so also from prediction, and hence also pulled explanation apart from prediction. It also emphasised a principled, as opposed to a merely pragmatic, role for human finitude in understanding the world. The models of phase change especially, but also those of far-from equilibrium dynamical stability, created models of emergence with causal power (‘downward’ causality — see above) and hence difficulty for any straightforward
idea of reduction to components. And, although not appreciated until recently, they created an alternative paradigm for situation or condition-dependent, rather than universal, laws.” – Cliff Hooker op. cit.Notice that hard science was just beginning to fully appreciate, in the 1970s or early 1980s, that “the hegemony of the simple symmetry/ equilibrium orthodoxy” was collapsing, just about the time, roughly, that the Arrow–Debreu model was erected assuming simple symmetry and equilibrium. In my opinion, the problem has to do with “axiomatisation” in science and in quasi-science and in non-science. I can flesh out a simple discussion of this issue if I have piqued any interest.
But to finish here, I will state that I provisionally accept the likely correctness of the thesis in “The giant blunder at the heart of General Equilibrium Theory” by Philip George. The maths argument looks valid to me so far as I can understand it, which is not all the way I admit. I am not sure what Arrow–Debreu are doing in their theoretical dimensioned spaces. However, the considerations of the philosophy of science of Complex Systems which I can understand from Hooker certainly do suggest Arrow–Debreu, and conventional economics generally, are in the wrong paradigm space with respect to hard science let alone with respect to social science.
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Thanks, Rowan, for bringing my attention to this paper. I read it with interest.
First off, I enjoyed the quips from Feynman about adding temperature. Unfortunately, I don’t agree with the author’s criticism of ‘price vectors’. But I’m getting ahead of myself.
Let me start by being clear that I think General Equilibrium Theory is garbage, for many many reasons. That said, this paper focuses on a very specific criticism, which is that GET proposes that prices can be treated as ‘vectors’, when the author claims this is untrue.
On that front, I’ve always found economists’ use of the word ‘vector’ to be utterly pretentious. A price vector is nothing but a list of prices. But clearly economists want it to sound fancy, so they bring in the language of vector physics.
Now to the main claim in the article, which is that price lists do not satisfy the property of ‘vectors’ because they cannot be added. George writes:
Now it is meaningless to add the price of a good on Monday to the price of the good on Tuesday.
I think this is wrong. When I calculate my monthly living expenses, do I not add the price of commodities purchased at different times? And doesn’t everyone consider the resulting cost total valid?
In other words, George’s comparison to temperature is incorrect. No, we cannot add temperatures. Yes, we can add prices … we do it all the time.
None of this is to say that general equilibrium theory has any merit. It does not. But I see no problem in treating prices as an n-dimensional list and then doing mathematics with it. The problem with general equilibrium lies in the name itself, the supposition that you can explain prices in terms of market equilibrium. None of the steps work, as Jonathan Nitzan elegantly shows in this video:
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Blair,
Thanks for reply. This little issue threw up another interesting paper which has real system implications and finance system implications. I admit I didn’t find the paper. Somebody else linked to it. I think you might find it very interesting unless you are already aware of all the concepts involved.
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I’m actually more curious about another part in the referenced Debreu nobel paper: the commodity vector part.
I just don’t understand how a vector emerges, or what the vector space means, when each commodity has a different unit of measure. Is the space (almost) infinitely multidimensional, or…?
Thanks,
Steve
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To reiterate, I think the language of ‘vectors’ is unnecessary. Debreu is just doing basic accounting:
z = an itemized list of the things I’ve sold
p = a price list of these itemsThe value of my sale is the sum of the item quantities times the item price. Really basic stuff dressed up in pompous verbiage to appear profound.
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