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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.
Posted by Tyler Cowen on March 2, 2009 at 12:58 PM in Economics | Permalink
Comments
For the interested: an 2007 essay on physics-based approaches to economics in general.
Not necessarily related, but interesting.
Posted by: david at Mar 2, 2009 2:13:22 PM
Gloryosky, not another econophysicist who thinks
he has discoverd "the answer," although at least
Smolin is deriving his arguments from an econ Ph.D.
thesis from 1996 that somehow has never managed to
get published. Hmmm.
So, the original interpretation of gauge invariance
in GET would be that one is dealing with relative prices
only. I presume that is why Tyler mentions Frank Hahn,
since he was one of the earliest and loudest to complain
about the lack of money in GET, although many have suggested
that Walras's Law allows for dropping out one good to be a
numeraire of value, if not necessarily fulfilling all the
functions of money.
So, in this version we get each person getting to do their
own scaling, heightening the emphasis on individual agents,
which is fine with me, but then making what appear to be
baseless claims about introducing multiple monies. As it is
we already have that in econ, they are general equilibrium
models of foreign exchange rates, although indeed such models
tend to have multiple equilibria, indeed infinite numbers of them.
There are some outright errors in the paper. Thus it is claimed
that Arrow-Debreu does not allow for time or space or contingent
markets. Sure it can, although one can argue that its way of
doing so is annoyingly trivial. Just create new goods that are
indexed by location or time, as with futures markets or insurance
markets. As for dealing with uncertainty a la Talebesque black
swan events, I do not see how this gauge invariance approach
helps with that at all. Just so much handwaving and trying to
be "relevant."
The paper announces rather breathlessly that it has discovered
a "statistical economics." Baloney. Lots of SFI-related and
other econophysicists have been playing this game for some time.
Go look at papers in Physica A or Quantitative Finance, ones by
Eugene Stanley or Jean-Philippe Bouchaud or Joseph McCauley or
Victor Yakovenko, who has spoken on the George Mason campus. This
lit is huge, and Smolin makes himself look silly not being aware
of it. To make matters even more ridiculous, economists beat the
physicists to the punch with such physics-based models of statistical
equilibria, as in the 1974 paper in the Journal of Mathematical
Economics by Hans Follmer or the even better paper in 1993
in JET by Duncan Foley, with an improved followup last year in
JEDC, with Foley having been someone back in the 1960s who was
worrying about the problem of how does money fit into GET. That
Foley hangs out at SFI and knew Per Bak makes Smolin look even
sillier and more ignorant.
A final comment is that the real crime in terms of naming is that
it should be called Arrow-Debreu-MacKenzie GET. Roy Weintraub has
been making this point for years, while not getting anywhere.
The fixed point theorem proof used in the Smolin paper looks more
like the MacKenzie proof, also published the same year independently
as the Arrow-Debreu paper, and is the approach one finds in Hal
Varian's text, which is what has been taught at MIT for decades,
ever since it was introduced into the curriculum there by....
Duncan Foley.
Bah humbug.
Posted by: Barkley Rosser at Mar 2, 2009 2:25:12 PM
Another very clear introduction to gauge theory can be found on Tao's blog
http://terrytao.wordpress.com/2008/09/27/what-is-a-gauge/
Posted by: tomrus at Mar 2, 2009 2:25:53 PM
Another very clear introduction to gauge theory can be found on Tao's blog
http://terrytao.wordpress.com/2008/09/27/what-is-a-gauge/
Posted by: tomrus at Mar 2, 2009 2:27:38 PM
David,
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.
Posted by: Barkley Rosser at Mar 2, 2009 2:30:06 PM
One major purpose of the paper is to start a theory of "disequilibrum," that is, how the economy evolves towards equilibrium when in an out of equilibrium state. This is why gauge invariance is necessary, since gauge invariant quantities characterize the actors' behavior outside of equilibrium. For example, even out of equilibrium, an actor can scale all his (subjective) prices by some constant factor with no difference to his behavior.
Yet it's not clear how it would be possible to model the process by which arbitrage, for example, leads to equilibrium from a disequilibrium state. Such a process seems to depend on the speed at which market participants react to violations of the law of one price and how quickly the fact that markets are out of equilibrium propagates to participants. How could these be modeled without adding tons of new parameters like the intelligence of the actors and social networks between them?
Posted by: Tom Powers at Mar 2, 2009 2:35:33 PM
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.
Posted by: Greg Ransom at Mar 2, 2009 3:20:17 PM
@Tom Powers
I don't know the answer. But one possibility that I find intriguing has to do with the preference functions treated as static in neoclassical theory. Suppose each term in the preference function for each agent had both a characteristic amplitude and frequency, but randomly distributed phase. We might then hypothesize that each agent will seek to phase-match its consumption-reated preferences to the production-related preferences of another agent (and vice versa). If enough of these exchanges occur, we might observe a steady-state equilibrium in which the flux of supply is matched to the flux of demand. But when exchanges are mediated by a decentralized mechanism such as a market price signal, there might be phase-locking, and thus nonequilibrium fluctuations.
There is no psychology here, but rationality is bounded because we're allowing preferences to evolve in time and that kind of time-dependence is assumed away in rational choice theory.
Posted by: Michael F. Martin at Mar 2, 2009 3:44:43 PM
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."
Greg,
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.
Posted by: Barkley Rosser at Mar 2, 2009 4:07:37 PM
Barkley,
Tom didn't write that, I did. Your points about consulting the literature and providing empirical support are well-taken by me, although I'm afraid I won't be able to satisfy you on either score anytime soon.
Posted by: Michael F. Martin at Mar 2, 2009 4:44:46 PM
Got me interested, and the comments are interesting. I need time to read.
Posted by: Mattyoung at Mar 2, 2009 4:46:56 PM
Barkley Rosser wrote:
"There is a vast literature on disequilibrium adjustment in economics,[...]"
No there isn't -- at least if you count quality papers. I don't count tâtonnement adjustment among being of much use, since it does not deal with adjustment in real time. There is a lot of search theory, but I don't know of search theory models that integrate all markets, production and consumption in real time.
Greg is much closer to the truth -- modern economics is a failure.
I would add that what makes this situation more deplorable is that most economists are very complacent about the failure of economics -- with lots of handwaving about the need for simple models and the need to ignore many aspects of the real world. Unfortunately, these points are mostly used as fig leafs for hiding the inadequacy of economics, rather than as a methodology supported by huge successes.
Maybe this apparent complacency is just an image presented to outsiders and funding institutions, but most likely there is also a psychological need of economists to think of economics as in much better shape than it is. I count your quasi-defense of empirical applications of general equilibrium modeling as a symptom of this complacency.
The above does not necessarily defend the physicist approach to economics -- physicists bring with them a lot of logical clarity, which is welcome, and a lot of completely misplaced intuition and a lot of ignorance, which is not so welcome.
Economists have a much better intuition about where the improvements in economists should be -- but nevertheless, economics does not seem to be in any acceptable shape today.
Posted by: Alex at Mar 2, 2009 5:07:22 PM
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, :-).
Posted by: Barkley Rosser at Mar 2, 2009 5:56:56 PM
Perhaps economists are reaching too high.
Consider the travails of ecology, a rather similar discipline. You can look at energy flows or material flows etc. But there's no assumption that every plant and animal is behaving as efficiently as possible. It's enough that they satisfice, that they each defend their ecological niche.
Consider the sequoyah forest. The trees spend a whole lot of their energy pumping water upward. They get nothing from doing it that way except that when each tree grows as high as it can it doesn't get shaded out as badly as if it grew lower. So they grow to the point they can hardly grow any higher, because of they produce barely enough energy to get the water to grow. Meanwhile each year they produce lots of old needles and twigs and bark, which piles up on the ground and is highly toxic to the seedlings of any competitor (plus their own seeds can't germinate in it, those seeds need mineral soil.) In dry years the debris can burn, but the hot fires which destroy competing plants don't burn through the bark of established trees. Almost all the production of the mature sequoyah forest is devoted to maintaining themselves in a sort of status quo and fending off competition. And in the particular environment where they are most successful, where there is plenty of water from fog and the right temperatures, nothing has challenged them except man. There is no purpose except to sequester resources away from others and to create seeds (which have no chance to survive until a mature tree dies).
And yet, ecosystems that have been mostly stable for thousands or even tens of thousands of years can fall apart when an invader arrives that can fill a niche that has been unfilled before. I read a story on the net recently about northern forests that did not have earthworms. The glaciers killed off the earthworms and the forests adapted. And now earthworms got introduced and are digesting the topsoil and the forests suffer. For all I know it might be a parody, but that sort of thing does happen. If ecologists started out with theories about how ecosystems made sure that every niche got filled and how something-or-other got maximised or optimised or whatever....
Wouldn't it make sense to start out like naturalists? Observe particular industries and see what's going on, and notice what conclusions you can draw from them. Look at monopolies and figure out what it is that lets them survive in the niches where they do survive. Look at industries that have a lot of stability and ask how they maintain that stability. How do they limit competition to familiar areas? How do they create barriers to entry and how expensive is it to do that? How do competitors avoid too many free riders when they pay to limit competition?
Get entry-level jobs or if possible mid-level jobs to obtain access to the informtion needed to study companies. Whatever it takes to actually observe real companies in real economies.
If you start with observing reality, it will lead to interesting questions to try to answer about how things actually happen.
This is the way physics started out, believe it or not.
Posted by: J Thomas at Mar 2, 2009 6:19:47 PM
FYI, Alex is different than Alex Tabarrok.
Posted by: Alex Tabarrok at Mar 2, 2009 6:43:14 PM
@J Thomas
Your analogy to ecology is interesting for several reasons. Economics, like ecology, may rely ultimately on some aesthetic considerations so long as we have an incomplete understanding of the dynamics of the entire system. 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.
But another reason is the truth that the richness of any theory should be driven by observations, not aesthetic considerations alone. Although such a truth would counsel in favor of modesty in the application of any theory to a phenomena as complex as a market, I don't believe that uninformed observation alone will lead us to deeper understanding. Learning requires an active comparison of observation against the predictions made by theory, and revision or recreation of theory where the predictions are off. For better or worse, the mental economic model most lawyers, policymakers, and lawmakers have in mind right now is neoclassical. These people ought to be aware at least of the limits to the model. Where other models are available to provide better (albeit also incomplete) predictions, then those should be used in addition or instead.
As for the suggestion for accessing the relevant information to test new models, this is a pretty bad time for anybody to be moving around, and I don't know of any entry-level or even mid-level jobs that permit access to this kind of information in my career. But perhaps the same companies would make the information available for academic study with the suitable constraints on disclosure certain information. Or perhaps there are historical databases available to economics professionals that include similar information. Regardless the evidence will come out eventually.
Posted by: Michael F. Martin at Mar 2, 2009 7:14:37 PM
Barkley,
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.
Posted by: Dan in Euroland at Mar 2, 2009 7:16:18 PM
Dear Dr. Rosser,
Thank you for the interest in our work, although I don’t know you, and have no idea why any economist would want to inhibit a potentially interesting interdisciplinary conversation with a catty ‘Hmmm’ garnished with a ‘Bah Humbug’. I think you will find that Lee’s take is but one approach to introducing Gauge Theory into economics. There are others if this is not to your taste.
Cowen’s point about comparative statics is an astute one however and may be more helpful to you. What you will find is that there are certain persistent artificial limitations in economic theory which require gauge theory to be handled properly. Malaney and I showed for example that gauge theory allows welfare comparisons without the Beckerian empahsis on artificial assumptions of static preferences.
Try this:
http://pirsa.org/06050010/
and see if you don’t see more of what Lee is seeing as the potential for really meaningful interactions between fields.
Simply put: It seems an amazing fact that economic theory (or more specifically marginal economics) is a natural occurring gauge theory. Why a few prominent economists wished to pretend otherwise rather than opening the field to new results is actually kind of interesting, but hardly a dis-proof of the interest value in the discovery. It's not like we simply forgot to publish the work: this was the subject of a fairly serious dispute between mathematicians and economists. If we're wrong, that's fine, but if we're right it's sure going to be a story worth telling.
If you think this is all old hat or cranky econophysics you could help a mathematician out by pointing me in the literature to the formula for the extension of the Konus cost-of-living index to changing ordinal preferences. It seems a central issue in the theory of welfare and should be given in the talk above if memory serves. I’ve been talking about it with economists for over a decade. I agree with you that I should cite it if it is well known, but all I have are either impossibility arguments (Frank Fisher and Karl Shell, The Fed: http://www.federalreserve.gov/pubs/feds/2007/200704/200704pap.pdf) or interesting but incomplete results (http://papers.ssrn.com/sol3/papers.cfm?abstract_id=771904). In fact no one from Arrow to Samuelson to Maskin seems to know the reference. The Fed's Travis Nesmith gave the clearest explanation we've heard:
"[A] time varying objective function generally cannot be tracked by an economic index."
so we had been under the impression that the work might be novel and welcome. But I'm happy to cite if we are simply talking to the wrong people.
Thanks in advance!
Regards,
Eric R. Weinstein
Posted by: Eric Weinstein at Mar 2, 2009 7:59:08 PM
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.
Posted by: Curt Fischer at Mar 2, 2009 9:08:20 PM
J Thomas,
Well, for some time now ecological theorists have modeled ecological communities by borrowing the
general equilibrium framework from economics, although as you note, generally without any assumption
of optimization. So, a "community matrix" as studied by Eugene Odum is really an input-output matrix,
and Walter Isard, who coined the term "ecologic-economic" in 1971, looked at combined ecologic-economic
input-output matrices. People like Robert May and Daniel Ludwig and C.S. Holling have studied the
dynamics and stability or instability of ecosystems in ways that look like similar studies of economic
dynamics.
Regarding the optimization question, this showed up in an older view, especially associated with Herbert Spencer,
who argued for the optimizing element in evolution. Spencer was also an advocate of laissez-faire economics,
and Clements, who originally hypothesized the idea of ecological succession, argued for leaving wilderness
areas alone partly on the basis of Spencerian arguments and analogizing from the arguments for laissez-faire
in economics. Laissez-faire for nature also.
Dan,
I have praised evolutionary game theory from time to time and publish papers on it in the journal that I edit,
Journal of Economic Behavior and Organization. However, there is a lot more to applying biology to economics
than just evolutionary game theory. In fact the central theme of the paper mentioned above that I did not present
today at the Krasnow Institute involves this struggle between econophysics and econobiology.
Eric,
I see that your paper on gauge invariance is still being worked on. I suggest you try submitting it to the journal
I edit I just mentioned above. I am always open to innovative approaches, as those who run this blog can tell you.
My comments were on Smolin's approach. My "bah humbug" was on his claim to have discovered a "statistical economics,"
and more precisely his failure to cite any of the work of Duncan Foley, among others. One of the complaints by Gallegati
et al in their 2006 paper on "Worrying Trends in Econophysics" is precisely this tendency to make half-baked and unjustified
claims of "universality" along with failures to know what has already been done in the economics literature. Smolin is
guilty of both of these "worrying trends" big time.
Regarding the matter of price indices, it may well be that gauge invariance theory has something to offer. I note that
Smolin does cite the Divisia index, which has long been claimed to be an index that does overcome these problems of
relative variations, although it has always been terribly difficult to apply very well in practice.
Curt,
The old term for what we now call ecology, since that term was neologized in the 1860s by Ernst Haeckel, was
"nature's economy."
Posted by: Barkley Rosser at Mar 2, 2009 10:26:33 PM
"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.
Posted by: J Thomas at Mar 2, 2009 11:21:14 PM
What good is introducing gauge invariance or any other high-powered mathematical innovation into economics if you can't conduct objective tests of the damned things? How does one go about devising an empirical test of the proposition in questio?
Math has it best (pure deduction FTW), but the physical and chemical sciences have it easy - they can make predictions about particles in boxes, and then lock up the particles in boxes and see if they actually behave that way. Economics and the social sciences aren't so lucky; they make predictions about people in boxes, but you can't ethically lock people up in boxes and see if they actually behave that way.
Posted by: Neal at Mar 3, 2009 12:41:41 AM
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:
http://www.perimeterinstitute.ca/Events/The_Economic_Crisis_and_Implications_for_Science/The_Economic_Crisis_and_its_Implications_for_The_Science_of_Economics/
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:
http://faculty-web.at.northwestern.edu/economics/gordon/BoskinvsNAS.ppt
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.
Regards,
Eric R Weinstein
Posted by: Eric R Weinstein at Mar 3, 2009 1:10:49 AM
J Thomas,
When humans are harvesting the concern is not to get "the best long term yield" but to maximize the present value of the resource, which means timing the harvesting based on the appropriate discount rate, given the various revenues or benefits of harvesting and the costs. Once upon a time, Irving Fisher said "cut when the growth rate equals the real interest rate." Then it was realized that he was not thinking about replanting, which brings up the concerns you mentioned about how younger trees grow faster than the older ones, and indeed the German, Martin Faustmann, had solved this problem back in the mid-19th century, which did imply cutting sooner than the recommendation of Fisher so as to get those younger trees planted sooner that would grow faster. Then people began to realize that there was more to forests than just timber, with these other benefits exhibiting many different time patterns. Deer hunters like even quicker cutting because the deer really like the edges of former clearcuts that happened about six to ten years ago, while bear hunters would just as soon have no cutting at all as the bears like the large old fallen down tree logs in old growth forests, and so it goes.
Neal,
Of course the proof is ultimately in the empirical pudding, but often a theory must be developed prior to being able to figure out how to use it empirically.
Eric,
Glad you guys are aware of this other work. I wondered when I saw that this stuff has not been published if some sort of shenanigans had been pulled. Sorry there has apparently been a screw job involved here. Imposing an assumption of constant preferences is silly and out of date. I look forward to seeing a comment by your associate here, but eventually this should go offline. I will simply note that JEBO is strongly oriented not only to innovative ideas but also to multidisciplinary, dare I say "transdisciplinary"?, work. Also, Duncan Foley is on my board of editors, as are some other people with such broader interests and knowledge, and I have published work in econophysics as well as a variety of biological applications in economics.
Posted by: Barkley Rosser at Mar 3, 2009 1:50:48 AM
lee smolin, a top mind? hahaha
Posted by: iron pimp hand at Mar 3, 2009 6:07:22 AM
