Lee Smolin on general equilibrium theory

He has written on inflation (ha-ha), so why not Arrow-Hahn-Debreu?  The most interesting part of the paper starts here (p.29):

We can now turn finally to the role of gauge invariance in economics. The proposal that gauge theory is essential for making progress in economics was made by Malaney and Weinstein[8]. I would now like to argue that there are deep and compelling reasons why the extension of economic theory to incorporate out of equilibrium behavior should centrally involve the kinds of gauge invariances they proposed.

Here is a short essay on gauge invariance.  He also endorses agent-based modeling.  I didn’t “get” where this paper is headed (OK, you put in gauge invariance but comparative statics are still hard to predict a priori), but I’m always interested to see how top minds approach the foibles of the economic method.

I thank Michael F. Martin for the pointer.


For the interested: an 2007 essay on physics-based approaches to economics in general.

Not necessarily related, but interesting.

Another very clear introduction to gauge theory can be found on Tao's blog


For discussions of the Gallegati et al debate with others on
econophysics, you can also look at several of my papers on my
website such as "Debating the Role of Econophysics" and
"Econophysics and Economic Complexity," although I did not
cover this topic in my entry on econophysics in the New Palgrave
Dictionary of Economics, 2nd edition, also up on my website at
http://cob.jmu.edu/rosserjb. The first of the papers above has
appeared in Nonlinear Dynamics, Psychology, and Life Sciences,
while the second has appeared in Advances in Complex Systems.

Ironically, I would have discussed this issue briefly in a talk
I was scheduled to give today at the Krasnow Institute for
Advanced Study at George Mason, but will not do so, the talk
having been canceled due to snow. The title of the paper is
"Is a Transdisciplinary Perspective on Economic Complexity Possible?"
an early draft available on my website also.

99.97% of all economists haven't yet figure out how to used a genera equilibrium construct to provide a causal explanations of anything.

There's a vast literature on this failure, unread by most math economists at the top 5 schools. Hayek started writing about this fact over 70 years ago, most fully in his _The Pure Theory of Capital_.

There's a reason everyone recognizes modern economics as a failure. Because it _is_ a failure.

Tom Powers,

There is a vast literature on disequilibrium adjustment in economics,
truly vast, and basically completely uncited by Smolin, whose book on
problems with string theory is rather neat. The gauge invariance
assumption is yet another essentially arbitrary ad hoc assumption that
may help one simplify such models a bit, but is there any reason to
believe that it is any more empirically valid than any of the other "ad
hoc" assumptions that get made in such models? To be more precise, it
looks to me like your idea of people someow phase matching their
consumption preferences with production with production preference of
other agents looks like a seriously ad hoc assumption with zero empricial
validity, and simply assumed because it fits some nice concept used in
physics, the very essence of the complaint by Gallegati et al about
"worrying trends in econophysics."


Well, there are people who do computable general equilibrium models that
supposedly tell us the effects of changing trade tariffs or tax rates, as
well as the proliferation of dynamic stochastic general equilibrium (DSGE)
models that get used in places like the basement of the Board of Governors
of the Federal Reserve. I would tend to agree with you that these models
have serious problems, especially the DSGE ones, which get wildly oversold,
but their advocates would disagree, some of them quite strongly. In any case,
I think those advocating these models would argue that they do provide
causal explanations, and these advocates are probably more than 0.3% of the
economics profession, even if they are misguided.

Got me interested, and the comments are interesting. I need time to read.

Michael F. Martin,

Sorry about conflating my reply to you with that to Tom Powers.

Alex (Tabarrok?),

Well, one can argue endlessly about what is a quality paper and what is not.
I have never been much of a fan of either the tatonnement literature (although
reportedly the London gold market uses it) or the way-oversold search literature,
although the latter is not completely worthless sometimes. There is much more
out there besides those, such as the Malinvaud-Benassy approach. There is also
another rather large literature, some of it strictly from more heterodox economics
and some of it based on physics models (e.g. Prigogine and Haken) that operates
in permanent disequilibrium without any adjustment occurring to equilibrium. I
find much of that quite interesting, certainly more so than tatonnement models.

I do not disagre that much of modern economics is a failure, although Greg and
I have some disagreements about the details of what is involved in that, even
as we have more agreement than many observers might suspect, :-).

FYI, Alex is different than Alex Tabarrok.


Instead of physics as a model for economics what about biology. What is your opinion of evolutionary game theory as applied to economics? In his recent book, Sam Bowles essential argues for a reconstruction of micro along evolutionary (stochastic and non-stochastic) lines.

This discussion is making me wonder whether I should try to finish reading Vermeij's Nature: An Economic History. People here may be interested in its discussion of similarities between biology and economics.

"For example, although redwoods may be killing off their competition, I haven't heard of anybody calling for redwood forests to be chopped down for that reason."

Michael Martin, a lot of ecology is descriptive. When it comes to prescriptions, they usually seem to come in two varieties.

First, when humans are harvesting, there's the question how to get the best long-term yield. Try too hard to increase productivity and it gets too hard to keep the reliability up. Large stands of productive monoculture are liable to epidemics, etc. There's some thought to replacing less-productive ecosystems with more-productive ones. So for example the edges of forests tend to produce lots of deer, rabbits, and quail -- animals people like to hunt. Deep interior forests produce small numbers of exotic animals and a lot of beetles. So it's only natural that we would arrange our logging to produce forests that are all edges and not much interior.

The second approach says that we don't understand ecosystems very well, and they've evolved over tens or hundreds of thousands of years (or sometimes much longer), and we should understand how they work before we damage them too much. The systems that are the most stable tend to be the least productive. They spend their energy on preventing change rather than make things for humans to cart away. Old-growth sequoyahs are not very productive at all, but young stands of sequoyahs grow fast. If what we cared about was to maximise our production of redwood lumber we'd cut down the old trees and replant with younger ones. Apart from setting aside preserves, we should try to avoid importing new species. Every new import *might* disrupt a functioning system.

That's one way that ecological thinking has varied from economic thinking. Economists tend to figure that if a corporation comes up with a new successful business model then it should usually just go ahead. If it's more efficient than its competitors then it should outcompete them and everybody (except the competitors) is better off. Ecologists look at things like kudzu and australian rabbits and think short-term ecological efficiency is not always ideal for human beings.

One difference is that evolution is often slow, while human innovation is fast. I don't know what conclusion to draw from that.

Hi Barkley,

Thanks so much for extending a hand. I will be happy to reciprocate in kind.

There are a number of sophisticated outsiders who have thought that this line of gauge theoretic reasoning might be a major opportunity for a new relationship between math, economics and physics. But this sort of hope has now been claimed many more times than it has occurred, and it is therefore impossible to know if this is the case without help from our friends in economics proper. This is one of the reasons we are organizing a scientific meeting on the state of economics as a science at the Perimeter Institute in May:


I just spoke to Lee (who is not an econophysicist but more an econophysicist-skeptic); he has looked at both your comments and Foley's work with great interest and will respond tomorrow. Duncan (and the New School more generally) represent a particularly open attitude within the field which, frankly, we hope will grow during this period of crisis.

I would be delighted to talk about this offline. Lee and I are both mindful that newcomers to economics should acknowledge the impressive body of work assembled in the field. Foley's output certainly fits that bill.

However, I don't think it is always clear to social scientists how disturbing it can be to deal with the economist's corner of what is ultimately supposed to be a *shared* scientific literature. The reason the original work was never heard by the community outside of Harvard wasn't because it lost a fair fight in the market place of ideas as it seemed you initially might have guessed. Rather, it lost a definitive bloody battle to extremely aggressive senior economists working as consultants outside of any scientific or peer-reviewed norms. How bad was it? I actually had no idea until one of them chose to boast about it years later as I would be too embarrased to accuse anyone of what is claimed at:


To the best of my knowledge there is no specific discussion of this incredible document where the claim is made that the 'CPI overstatement' started from a 1.1% target and went looking for a rationalization to deny entitlement spending. If you wish to see for yourself, skip to page 8 and be amazed. There is a reason self-respecting scientists aren't eager to deal with a literature like this.

Even at the level of pure theory, the first time I heard something like 'Gauge theory is unnecessary since agent preferences can now be assumed stable and homogeneous by the work of Stigler and Becker' from a leading economist I thought I was hearing an inside joke. It took someone reading the famous and inane 'Rocky Mountains' quote for me to realize that many leaders in the field were prepared to use fiat to avoid risking an exciting and productive revolution.

There is a world of difference between asking outsiders to submit to peer review which requires them to cite solid and often counterintuitive results and forcing them to salute plain ideology and lousy work backed by nothing more than appeals to credentialism.

Happily, I don't think that Foley presents any such problem.


Eric R Weinstein

lee smolin, a top mind? hahaha

I just want to thank you for this post. The paper is way above my pay grade, but that hasn't stopped me from thinking about it since you posted it, to the detriment to my other reading. I was going to post a comment on your F/F post, but I was still thinking about this post. I have a human agency approach to these problems, akin to behavioral approaches, so I'm going to try and use this approach for my own benefit. I hope that you do more of this. Take care, Don

@ J Thomas

Ecologists look at things like kudzu and australian rabbits and think short-term ecological efficiency is not always ideal for human beings.

There are many relevant differences between ecological efficiency and economic efficiency. As I said before, in the end, many judgments about what is efficient will reflect aesthetic considerations.

On this question of aesthetics I defer to Aristotle, who identified happiness as a worthy goal for society:

Presumably, however, to say that happiness is the chief good seems a platitude, and a clearer account of what it is still desired. This might perhaps be given, if we could first ascertain the function of man. For just as for a flute-player, a sculptor, or an artist, and, in general, for all things that have a function or activity, the good and the 'well' is thought to reside in the function, so would it seem to be for man, if he has a function. Have the carpenter, then, and the tanner certain functions or activities, and has man none? Is he born without a function? Or as eye, hand, foot, and in general each of the parts evidently has a function, may one lay it down that man similarly has a function apart from all these? What then can this be? Life seems to be common even to plants, but we are seeking what is peculiar to man. Let us exclude, therefore, the life of nutrition and growth. Next there would be a life of perception, but it also seems to be common even to the horse, the ox, and every animal. There remains, then, an active life of the element that has a rational principle; of this, one part has such a principle in the sense of being obedient to one, the other in the sense of possessing one and exercising thought. And, as 'life of the rational element' also has two meanings, we must state that life in the sense of activity is what we mean; for this seems to be the more proper sense of the term.

In more concrete terms, maybe we as a culture of reason should start measuring more with financial statements than simply time-averaged costs and costs of sales. Even with no additional money spent on recording information, adding one additional measurement -- average turnover in dollars per unit time -- to each balance sheet account might both deter some opportunistic behavior by accountants and make it easier to see a rate of growth or decay. Many of the failures we are suffering from right now did not result from an inability to see into the future, but from a refusal to learn from the past.

What a shame that Smolin abandons String theory due to the dead end it has led physics after 30 years.

And then launches straight into Equilibrium theory.

Isn’t the saying; fool me once shame on you, fool me twice shame on me...


Above is a presentation which is quite clear.

Here's where I came across it:

" For an introduction into the topic, I recommend Eric Weinstein's talk on “Gauge Theory and Inflation,† that you can find at PIRSA: 06050010."


Dr. Smolin,

Gauge invariance has instrumental value in economic theory as it applies to accouting rules. The format for financial statements (balance sheet = snapshot in time, income/cash-flow statements = time-integrated sum of revenues and expenses) is predicated on neoclassical theory to the extent that it treats scale-dependent measurements of the accounts (in dollars) as observables.

Accountants and investors know the problems with this instinctively -- that's why ratios are so often used to assess the financial health of a company. But there is a lot of room for improvement.

For years the debate over accounting reform has focused on corporate governance issues. Valuation has more recently become an issue because of Financial Accounting Standard 157, which asks accountants to mark the value of assets held (even without any immediate plans for sale) to current market value. FAS 157 is clearly predicated on neoclassical concepts.


There is a new Theory of Everything Breakthrough. It exposes the flaws in both Quantum Theory and String Theory. Please see: Theory of Super Relativity at Super Relativity.org
Einstein was right!


I confess that this statement of yours is not just jumping out at me as
screamingly obvious. Would you care to elaborate for us ignoranti,

Of course the folks like Weinstein, Malaney, and Smolin who have given us a formalism for the Coase Theorem have made a very useful contribution. I think it's especially useful for what it points out about the treatement of time in neoclassical theory. Economists need to learn how to look at time-series in frequency space.

It is interesting to note also that Coase came up with his theorem after spending time actually observing work inside firms. He didn't come up with his theorem analyzing stock prices.

Perhaps I wasn't clear enough. Gauge invariance of the sort identified in Smolin's paper implies the Coase Theorem. It implies a lot more than that too. I have to think more about the Goldstone modes that should be associated with dynamic spontaneous symmetry breaking here. Dissipative forces, however, can play a role in breaking symmetries. And transactions coats play a dissipative role in neoclassical theory.

1) Barkley (and maybe Michael): General Equilibrium Theory, I believe, claims in both its neo-classical and even more New Classical work --- rational expectations, perfect information (no asymmetries, presumably, between agents), no agent-principal problems (like investment banks undertaking high-risk gambles with repackaged mortgage securities and seeking to pass the risk down the line to some one else), and equilibrium in all markets unless exogenous shocks occur --- that the problems of time-change and future estimates are essentially risks. As such, they can be made calculated with a certain degree of statistically valid probability estimates, given past-economic behavior . . . micro or macro (or both).

If that is true, then how in your views can or could major economic agents --- say, financial institutions --- cope with the problems not of risk, but uncertainty. The latter can be any major random change --- usually an unfavorable shock, though not always --- that dislocates the economy in totally unforeseen ways, no? How would any formal econometric or game-theory model --- whether using gauge invariance, DSGE, Bayesian methods or what have you --- deal with uncertainty of this sort.


Think here, if it helps, of the use of formal computer models by mortgage brokers and bankers and hedge funds and insurance-agencies of housing prices that never, in the past, even fell noticeably on a nation-wide level in the US before until 2005 or 2006. There was always some risk they might, but it was considered negligible, right? So much so that it was not even introduced into the models. And hence the steep decline in prices that hit the mortgage market was an uncertainty-shock that has resulted in a global system-wide crisis for financial institutions and the real economy everywhere.


2) Enter Ronald Coase's work.

What Michael and others referring to it overlook is that Coase is also regarded as the father of New Institutionalism, . . . though Barkley hints at this when he refers to Coase as the father of the field of Law and Economics. True, Douglass North has been the most prominent theorist in the field, but Coase's work in law and property rights and transactions costs was very likely a big inspiration for North's work.


Needless to say, the importance of institutions is multiple in economic life, even if neo-classical and New Classical and for that matter Old and New Keynesians as well as Austrian economists tend to discount or ignore it. And they’re doubly relevant to this question of using some new or advanced modeling technique for dealing with GET or, conceivably, a disequilibrium theory that is at most temporary until some sort of either private-market or government-policy spurs initiatives to resume a path leading to equilibrium again.

This faith in modeling techniques follows, it seem, from the concept of an ergodic economic world that a post of Tyler’s deal with last week. That assumption seems pervasive in virtually all economic theorizing today. In which case, no matter what the “risks† of major “shocks† to the economy may be --- endogenous or exogenously inflicted --- these shocks are treated as essentially random and stochastic. And so no matter what the initial or intervening conditions that dislocate an economy and cause it to misallocate resources --- including less than fully employed labor at the natural rate in a recession --- the economy will supposedly return, sooner or later, to a general equilibrium condition, no?


4) There seems to be one exception to these preferences for formal and abstract modeling in economics: New Institutionalism (though conceivably behavioral economics is another).

In particular, New Institutionalists --- and as a political scientist I naturally gravitate to this theoretical view of the economy --- seem to be the minority of economists of note who break with notions of an ergodic world and apply stochastic views of persistency of market equilibrium in the long run, whatever the temporary shocks of a random sort. Instead, they focus on continued change. These changes are bound at certain times to be major and disruptive. They initiate periods of flux and turbulence when old theoretical guides no longer apply as effective guides to action, whether in the public or private realms.

This view of unforeseen changes follow from the “path-dependency† view of the world.

In contrast to the ergodic outlook, these disruptive changes --- call them shocks if you want --- throw the economy and its surrounding political-legal-cultural environments off their previous business-as-usual operations and hence prevent history from repeating itself. In that case, the economy of, say, the USA won’t return to a similar equilibrium of the sort that prevailed in the past. Far from it, either major institutional adaptations will be made to channel the economy into new and productive ways, or --- the case of most countries in the world that we regard as “backward† --- there won’t be such adaptations and those economies will suffer from long periods of stagnation.


5) By contrast, on the institutional view, if a country’s institutions are flexible and adaptable, then policymakers in the public and private realms that make and apply institutional laws and rules will innovate under the pressure of these unforeseen challenges . . . and thus help, guide, and channel business and financial enterprises to change in efficient ways too. And the same applies to new knowledge created by scientists, inventors, and others as well as encourage new entrepreneurs to exploit these opportunities that our “artifact† world provides.

This institutional view of the economy --- embedded in a wider political, social, and cultural world continually under change (despite, obviously, some ergodic persistence) --- stands very much in opposition to the formal and abstract modeling efforts in virtually all mainstream economics, does it not?


6) Two brief conclusions follow:

* -- The problem with rational expectations or earlier neo-classical general equilibrium theories of the economy isn’t just the problems of perfect information and strong notions of rationality, but rather the more basic assumption of ergodicity. With only “risks† subject to probability theory calculable in such formal models, and not “uncertainty† produced by fast-moving and wholly unforeseen changes.

* --- And as someone who has done a fair amount of work in the past on comparative economic development across countries, it’s the institutional nature of each that explains largely why some are very rich and advanced, some are growing fairly fast, and most don’t grow much at all . . . those latter dominated by predatory and corrupt elites, whose advancement upon various public and private hierarchies depends not on achievement but rather mutual back-scratching in patron-crony networks largely closed to outsiders. By contrast, good, flexible, and adaptive institutions help us cope with uncertainty by helping us to develop and apply new knowledge to reduce and maybe even master the new challenging changes and reorient our behavior, individual and collective, in new and more effective manner.

Until the next major and unforeseen shocks occur, needless to add.


Oh, one more observation just popped to mind. As Japan’s travails from 1991 until 2004 --- when the booming global economy ended deflation and restored some halfway decent economic growth for 3 years, thanks to a bustling surge in exports --- even a rich and technologically advanced country can fail to adapt its institutions and policies in blatant ways. Come to that, those 3 years seemingly show that nothing really ever changed in Japanese institutions since 1991. Hence the country’s plunge into a downward spiral that is nothing less than breathtaking with the collapse of its export markets abroad since last spring . . . at something like an annualized 14% GDP decline last fall.


Michael Gordon, Aka, the buggy professor


I have just gone back and looked at Lee Smolin's paper again. I see nothing in
it whatsoever that relates directly or indirectly to the Coase Theorem. I think
you are going to have to spell out this argument more clearly, if you wish to
continue maintaining or pursuing it.

Buggy Gordon,

Indeed, it was for father the "new institutionalism" by focusing on the role of
transactions costs that Coase received his Nobel, not for co-fathering the "Law
and Economics" school of thought. The key paper was his "Theory of the Firm"
back in 1937. While North shared the prize with Coase, he is not really Coase's
follower in this regard. The great advocate of the importance of transactions
costs is Oliver Williamson, the most cited economists of all time, according to
Geoffrey Hodgson, but no Nobel for him so far.

"As I said before, in the end, many judgments about what is efficient will reflect aesthetic considerations.

"On this question of aesthetics I defer to Aristotle, who identified happiness as a worthy goal for society"

Many people have noticed that for individual human beings there tends to be a sort of conservation of happiness. Long-run average happiness tends to average out apart from circumstance. A member of the social elite may be utterly shocked at an unexpected snub or a failed flower arrangement. But later in the concentration camp the same person may be exhilarated to successfully steal a cabbage leaf.

So assuming we can even measure happiness well, it may not be a good economic indicator.

Somehow the here for it.

Michael, AKA, the buggy professor

J Thomas,

There are other measures of ecological efficiency besides being able to
suppress possible successor species short of a major collapse of the
ecosystem, such as biomass production per unit land, energy throughput,
not to mention such useful things as level of biodiversity and resilience
to those major disruptions. Climax ecosystems are often not at all good at
any of those, and there is no singly climax for any given locale, as you
suggest by noting that a succession can get "hijacked along the way."

Thus, where I live in the mid-Atlantic region, in the George Washington
National Forest, deer max out around six to ten years after a clearcut or
a major fire, turkey and quail max out around 25 years, which corresponds
with the peak of biodiversity, with lots of shrubbery and maple trees
growing up under the oaks, and many differenet animals eating the many
different plants. The climax forest, which bears like, appearing at
about 60 years, is majestic and "cathedral-like" in its lack of undergrowth
and species feeding on them, but not at all resilient to disease or fire
or much of anything else, and does not capture much solar energy or
throughput much of it. Not at all efficient and not at all resilient,
the ecologist C.S. Holling having long noted a tradeoff between stability
and resilience of ecosystems, which has its counterpart in economics.

J Thomas,

Your definition of ecological efficiency seems to correspond to what in economics would be
monopoly power, the ability "to suppress competition" as you put it. This is most definitely
not associated with efficiency in economics in general, with the exception of the rare possible
"natural monopoly." But that has been a shrinking category for some time. I see nothing to
get excited about particularly regarding climax ecosystems, unless they contain some rare or
endangered species that needs protecting.

Why the conspicuous silence on the recent Willem Buiter on the sorry state of monetary economics? I'd be interested to hear a rebuttal, if indeed you have one.


Barkley, I don't see Microsoft being so great at nimbly processing energy or producing biomass or diversity, either.

Mostly corporations are good at their core competencies and not as good at other things. General Motors tried to be good at large cars, SUVs and trucks. Not so good at fuel efficiency or predictable repair schedules. Should they stake their future on their ability to compete on somebody else's home ground? They instead hope for good times when americans want big cars.

Microsoft dominates desktop business software and the OS it runs on. Should they redesign themselves as an internet company? Are they successful in their niche because they are nimble, or because they force others to be nimble to stay out of their way?

I contend (maybe wrongly) that in general economic domination does not come from efficiency at processing energy or producing biomass. Domination comes from whatever allows the creation of captive markets.

If you have to compete on price in your home market then you're on the ropes already. And if your company competes on quality then it might get forced into the high-end where you have high margins, and try to expand into the mid-range as you're able. Maybe, as for GM, that's too hard.

Innovation can open up new markets, but most innovations fail. You don't want to depend on innovation for your bread and butter. You want a captive market that will buy what you produce, and use the surplus you get from that to fund your breakouts into new stuff.

When your captive market dissipates before you find a new one, people will accuse you of regidity, lack of innovation and incompetence. But....

I argue that successfully suppressing competition is what it *means* to be efficient. That's the criteria, the only criteria. It's what it means to be successful. Things like "nimbleness" are possible means to that end, that are particularly respected and honored.

But when IBM and later Microsoft etc were consolidating their positions as dinosaurs, it didn't particularly help their competitors to be nimble, unless they used that nimbleness to abandon those markets and do something else. There's a time to be nimble, a time to be quick, and a time to be a successful dinosaur.

Of course successful dinosaurs that later fail tend to go extinct, just like nimble companies that fail only larger.

I feel like we're somehow talking past each other. I don't disagree with what you say, and I don't see that you disagree with me except somehow in emphasis, but you talk as if you disagree.

"...you are trying to use a word, "efficient," in a way unlike anybody else, including ecologists, much less economists."

OK! I didn't think there was anything original there, but maybe there is after all.

I'll probably follow up on that over the next 5 or 10 years, if it isn't already being done. This is an important and useful insight at the fundamental level of economic activity, so somebody ought to spread it.

The Douglass North suggestion by the Buggy Professor was right on the mark. Prof. North has taken to talking about the "non-ergodicity" of economies of late:


Comments for this post are closed