Comments (23)

• Trevor

  A well written piece (as Mises Daily Articles usually are) but it seems to overlook a simple reply: that continuum assumptions, while obviously unrealistic, serve a purpose. An assumption of a continuum number of agents allows one to use integrals rather than long discrete summations. Results don't change (normally) but the calculations are simplified.

  I recall an EconTalk interview of Vernon Smith (nobel laureate in economics at GMU) where he points out that it only takes a small number (read: half dozen) traders to closely approximate the results of a perfectly competitive model. Thus, assuming a perfectly competitive situation *isn't* claiming that one needs an infinite number of agents to arrive at an equilibrium... just a small number can do it... but the model is simpler to work with in order to make the predictions.

  All this being said, I completely agree with many of the critiques of mathematical economics versus the deductive approach of von Mises but pointing out unrealistic *technical* assumptions takes our focus away from attacking the unrealistic *behavioural* assumptions.

  Published: August 23, 2007 9:14 AM

• David Turner

  I found this article very confused in its arguments. It is valid to attack a model by attacking its hypotheses, and an assumption of a "continuum of traders" might be worthy of attack, but not on the grounds that the concept of the continuum is itself flawed, and certainly not by pointing out a number of (possibly counterintuitive) properties of the continuum that many of us happily accept.

  "Such a theory has nothing important to say about the way things really are, and should be treated as the joke it actually is."

  By the same argument, the usual model regarding the properties of steel girders has nothing important to say about building bridges. Steel girders are made out of finitely many molecues, but you wouldn't bother trying to model each particle individually when you've got a decent model that ignores that fact and treats the steel as if it were continuous.

  Or, similarly, the theorems of thermodynamics say nothing useful, because they're trying to describe the behaviour of large, but finite, collections of particles; and yet we have cars and power stations and all manner of things that were designed using this continuum model. Models are supposed to say things about the real world, but they're also useless unless they're simple enough to work with.

  It's also disingenuous to assert that the real numbers don't exist, as if it matters: they're a useful model, with good predictive power, that's a whole lot easier to deal with than the alternatives. That's why they get used, not because it matters whether you think that they exist or not (nomenclature notwithstanding).

  The following argument is also fallacious:

  "Mathematically speaking, if a set is uncountable, then uncountably many elements can be subtracted from it leaving still no less than uncountably many! What's more, this procedure can be repeated over and over again without significantly decreasing the "size" of the original stock of goods. (Think, for example, of removing "odd" unit intervals — (0,1), (2,3), (4,5), etc. — from the real line; there still remain the "even" ones, each being uncountably infinite.)

  What does that mean in economic terms? It can mean only one thing: that the fact that a single individual consumes a unit of a good does not reduce the total available supply of goods, which implies in turn that the postulated model assumes away the most fundamental fact of economic inquiry, namely, scarcity!"

  The model of the real line fails to demonstrate 'scarcity' because it is unbounded, not because it is uncountable. For example, if my good were the integers, I could sell all the even ones and have no fewer than I started with, and yet there aren't uncountably many integers; if on the other hand my good were the (uncountably many) real numbers from 0 to 1 and I could sell sections of this line, the price could be determined by the length of the section sold because the total length available is scarce: imagine a gold bar that was infinitely divisible (the author accepts infinite divisibility as an assumption).

  Published: August 23, 2007 10:59 AM

• N. Joseph Potts

  If you can't describe your economic proposition by use of mathematics, it may be invalid.

  If you can't describe your economic proposition without use of mathematics, it may be irrelevant.

  Published: August 23, 2007 11:30 AM

• Michael

  I have not read the book that Mr. Jablecki uses to justify his assertion that "the concept of multiple infinities... leads to inconsistencies and contradictions in mathematical theory itself." But the claim is simply not true, as Mr. Jablecki would know if he had talked to any reputable mathematicians before making his uninformed attack.

  Mr. Jablecki may have confused the concept of "multiple infinities," as he calls them, with the axiom of choice. There are indeed mathematicians (though a distinct minority of them) who do not assume the axiom of choice in their work due to counter-intuitive results that one can obtain with it.

  But even then it would be incorrect to say that the axiom of choice causes "inconsistencies and contradictions" in mathematics. ZFC (the standard model of mathematics with the axiom of choice) certainly has not been shown to be inconsistent-- none of the axioms contradicts the others, as far as we know. Mathematics is a rigorous discipline, and if a set of axioms causes contradictions then one or more of those axioms is simply not used.

  Published: August 23, 2007 12:33 PM

• Alex MacMillan

  David Turner:

  Well, having studied some college mathematics but far from being a mathermatician, I would guess that the number of real numbers over the interval 0 to 2 is twice the number of real numbers over the interval 0 to 1. Perhaps you can prove this statement to be incorrect.

  But if my above proposition is correct and I removed the interval 1 to 2, leaving only the interval 0 to 1, I would presume that the infinity of real numbers remaining is only half the number of real numbers that I began with.

  So if your good were the set of integers, how would removal of some of them not decrease the number you had left?

  I have attended a number of seminars at which the late Harry Johnson, the well-respected international economist, was present. At one such seminar, the speaker differentiated this and that, took integrals here and there, considered bordered Hessians, and the like. The speaker never faced the audience until he was finished his presentation, since his blackboard scribbling took up all of his time.

  At the end of it all, as the speaker turned to look at the audience, Harry Johnson, sitting in the first row, asked the following question: "Can you tell me a story about what you've just gone through? You know, in everday English." The speaker stumbled as best he could with the story behind his mathematics. When he'd finished, no-one was impressed."

  The economy is made up of human beings,trundling around, making decisions on this and that, whether individually, in business, or in government. If in simple English, a model reflects what such actors are doing, the model is valuable; if it doesn't, it behooves the model builder to explain in simple English why there are insights may be gained from the model.

  
  

  Published: August 23, 2007 1:05 PM

• georges lane

  I found that the text by Juliusz Jablecki was really very interesting.

  However, may be he should think about the notion of "present infinite" - my translation in english of french "infini actuel".
  What is that ? The heart of the debate between Henri Poincaré et Georg Cantor. Poincaré described his position in his book "Science and Method" :
  * in chapter 3 :
  "Cantor a entrepris d’introduire en mathématiques un infini actuel, c’est-à-dire une quantité qui n’est pas seulement susceptible de dépasser toutes les limites, mais qui est regardée comme les ayant déjà dépassées. Il s’est posé des questions telles que celles-ci : Y a-t-il plus de points dans l’espace que de nombres entiers ? Y a-t-il plus de points dans l’espace que de points dans un plan ? etc.
  Et alors le nombre des nombres entiers, celui des points dans l’espace, etc., constitue ce qu’il appelle un nombre cardinal transfini, c’est-à-dire un nombre cardinal plus grand que tous les nombres cardinaux ordinaires. Et il s’est amusé à comparer ces nombres cardinaux transfinis ; en rangeant dans un ordre convenable les éléments d’un ensemble qui en contient une infinité, il a imaginé aussi ce qu’il appelle des nombres ordinaux transfinis sur lesquels je n’insisterai pas.
  De nombreux mathématiciens se sont lancés sur ses traces et se sont posé une série de questions de même genre. Ils se sont tellement familiarisés avec les nombres transfinis qu’ils en sont arrivés à faire dépendre la théorie des nombres finis de celle des nombres cardinaux de Cantor. A leurs yeux, pour enseigner l’arithmétique d’une façon vraiment logique, on devrait commencer par établir les propriétés générales des nombres cardinaux transfinis, puis distinguer parmi eux une toute petite classe, celle des nombres entiers ordinaires. Grâce à ce détour on pourrait arriver à démontrer toutes les propositions relatives à cette petite classe (c’est-à-dire toute notre arithmétique et notre algèbre) sans se servir d’aucun principe étranger à la logique.
  Cette méthode est évidemment contraire à toute saine psychologie ; ce n’est certainement pas comme cela que l’esprit humain a procédé pour construire les mathématiques ; aussi ses auteurs ne songent-ils pas, je pense, à l’introduire dans l’enseignement secondaire. Mais est-elle du moins logique, ou pour mieux dire est-elle correcte ? Il est permis d’en douter.
  Les géomètres qui l’ont employée sont cependant fort nombreux. Ils ont accumulé les formules et ils ont cru s’affranchir de ce qui n’était pas la logique pure en écrivant des mémoires où les formules n’alternent plus avec le discours explicatif comme dans les livres de mathématiques ordinaires, mais où ce discours a complètement disparu.
  Malheureusement, ils sont arrivés à des résultats contradictoires, c’est ce qu’on appelle les antinomies cantoriennes, sur lesquelles nous aurons l’occasion de revenir. Ces contradictions ne les ont pas découragés et ils se sont efforcés de modifier leurs règles de façon à faire disparaître celles qui s’étaient déjà manifestées, sans être assurés pour cela qu’il ne s’en manifesterait plus de nouvelles.
  Il est temps de faire justice de ces exagérations. Je n’espère pas les convaincre ; car ils ont trop longtemps vécu dans cette atmosphère. D’ailleurs, quand on a réfuté une de leurs démonstrations, on est sûr de la voir renaître avec des changements insignifiants, et quelques-unes d’entre elles sont déjà ressorties plusieurs fois de leurs cendres. Telle autrefois l’hydre de Lerne avec ses fameuses têtes qui repoussaient toujours. Hercule s’en est tiré parce que son hydre n’avait que neuf têtes, à moins que ce ne soit onze ; mais ici il y en a trop, il y en a en Angleterre, en Allemagne, en Italie, en France, et il devrait renoncer à la partie. Je ne fais donc appel qu’aux hommes de bon sens sans parti pris."

  And in Chapter 5 :
  "C’est la croyance à l’existence de l’infini actuel qui a donné naissance à ces définitions non prédicatives. Je m’explique : dans ces définitions figure le mot tous, ainsi qu’on le voit dans les exemples cités plus haut. Le mot tous a un sens bien net quand il s’agit d’un nombre fini d’objets ; pour qu’il en eût encore un, quand les objets sont en nombre infini, il faudrait qu’il y eût un infini actuel. Autrement tous ces objets ne pourront pas être conçus comme posés antérieurement à leur définition et alors si la définition d’une notion N dépend de tous les objets A, elle peut être entachée de cercle vicieux, si parmi les objets A il y en a qu’on ne peut définir sans faire intervenir la notion N elle-même.
  Les règles de la logique formelle expriment simplement les propriétés de toutes les classifications possibles. Mais pour qu’elles soient applicables, il faut que ces classifications soient immuables et qu’on n’ait pas à les modifier dans le cours du raisonnement. Si l’on a à classer qu’un nombre fini d’objets, il est facile de conserver ses classifications ses classifications sans changement. Si les objets sont en nombre indéfini, c’est-à-dire si on est sans cesse exposé à voir surgir des objets nouveaux et imprévus, il peut arriver que l’apparition d’un objet nouveau oblige à modifier la classification, et c’est ainsi qu’on est exposé aux antinomies.
  Il n’y a pas d’infini actuel ; les Cantoriens l’ont oublié, et ils sont tombés dans la contradiction. Il est vrai que le Cantorisme a rendu des services, mais c’était quand on l’appliquait à un vrai problème, dont les termes étaient nettement définis, et alors on pouvait marcher sans crainte.
  Les logisticiens l’ont oublié comme les Cantoriens et ils ont rencontré les mêmes difficultés. Mais il s’agit de savoir s’ils se sont engagés dans cette voie par accident, ou si c’était pour eux une nécessité.
  Pour moi, la question n’est pas douteuse ; la croyance à l’infini actuel est essentielle dans la logistique russelienne. C’est justement ce qui la distingue de la logistique hilbertienne. Hilbert se place au point de vue de l’extension, précisément afin d’éviter les antinomies cantoriennes ; Russell se place au point de vue de la compréhension. Par conséquent le genre est pour lui antérieur à l’espèce, et le summum genus est antérieur à tout. Cela n’aurait pas d’inconvénient si le summum genus était fini ; mais s’il est infini, il faut poser l’infini avant le fini, c’est-à-dire regarder l’infini comme actuel.
  Et nous n’avons pas seulement des classes infinies ; quand nous passons du genre à l’espèce en restreignant le concept par des conditions nouvelles, ces conditions sont encore en nombre infini. Car elles expriment généralement que l’objet envisagé présente telle ou telle relation avec tous les objets d’une classe infinie.
  Mais cela, c’est de l’histoire ancienne. M. Russell a aperçu le péril et il va aviser. Il va tout changer ; et qu’on s’entende bien : il ne s’apprête pas seulement à introduire de nouveaux principes qui permettront des opérations autrefois interdites ; il s’apprête à interdire des opérations qu’il jugeait autrefois légitimes. Il ne se contente pas d’adorer ce qu’il a brûlé ; il va brûler ce qu’il a adoré, ce qui est plus grave. Il n’ajoute pas une nouvelle aile au bâtiment, il en sape les fondations.
  L’ancienne Logistique est morte, si bien que la zigzag-theory et la no classes theory se disputent déjà sa succession. Pour juger la nouvelle, nous attendrons qu’elle existe."

  May be Juliusz Jablecki should also read - if he had not until now - the book of Donald O'Shea (2007), "The Poincaré Conjecture - In search of the universe", Walker Publishing Company, Inc.

  Nothing gives the right to economists like Aumann to choose set theory rather than other mathematical theories for developing an assumed economic theory.

  Juliusz Jablecki wrote :
  "Following Aumann's example, Rudiger Dornbusch, Stanley Fischer, and Paul A. Samuelson set out to develop a generalization of Ricardo's classical international trade analysis by assuming that the number of goods is uncountably infinite. Obviously, as Ludwig von Mises observes, not every generalization is a sensible one."

  I totally agree. A real generalization would be for example to introduce uncertainty. And if you do so, you find many problems ! (cf. Murray Kemp (1976), "Three Topics in The Theory of International Trade", (Studies in international economics), North-Holland/American Elsevier.

  Best regards

  Published: August 23, 2007 1:36 PM

• Eric

  I don't know much about mathematical economics, but I do know computers and models in particular. Here are some of my initial knee-jerks:

  1. Computer models are too complex to be proven correctly programmed using mathematical analysis.

  2. Computers don't use real numbers, they use integer approximations - called floating point numbers. In chaos theory, a rather small change can lead to a large difference down the road, so if there's any chaos theory at play (I don't know what these models contain) then just the round off error of floating point numbers could invalidate some models.

  3. Because of point 1, only testing can determine if a model is correctly programmed and that says nothing about its validity. Perhaps a model, could help to stimulate some thinking, but to use it for predictions, especially for public policy is absurb.

  4. One can repeat the above argument for global warming models as well.

  However, models, especially computer models are especially useful for getting funding and especially politically generated funding. You see with computers, you can also have lots of very attractive graphic displays. And this is the best way to bamboozle a politician with stolen money who might just give you a piece of the action.

  Published: August 23, 2007 3:16 PM

• PJ

  An interesting article. Who cannot but be sympathetic to the claim that much mathematical economics is just a game.

  But to argue this a priori from the assumptions?

  Think about the physics case, since it is used here. Physics uses quantum mechanics with even more strange assumptions to great and powerful real world effect.

  Ultimately scientific theories are valued by whether they 'deliver the goods' now or at least sometime in the future. Some very weird mathematics has turned out to be very useful - much to the surprise of the original creators.

  
  

  Published: August 23, 2007 3:40 PM

• Alex MacMillan

  PJ makes the valid point that the proof of the pudding is in the eating. We should seek to list or elicit the listing of a dozen or so insights that have been provided to economics from the years of mathematical economics research and mathematical economic model building.

  Published: August 23, 2007 5:20 PM

• Anthony

  "If you can't describe your economic proposition by use of mathematics, it may be invalid.

  If you can't describe your economic proposition without use of mathematics, it may be irrelevant."

  And the good thing is that Austrianism is both good economics and also capable of being mathematically expressed.

  Published: August 23, 2007 7:08 PM

• Niccolò

  I must say, I agree with David Turner, but at the same time... Its this type of stuff that really makes me hate math, even though I'm relatively good at it.

  Who cares?

  Published: August 24, 2007 2:48 AM

• David Turner

  Well, having studied some college mathematics but far from being a mathermatician, I would guess that the number of real numbers over the interval 0 to 2 is twice the number of real numbers over the interval 0 to 1. Perhaps you can prove this statement to be incorrect.

  Yes, as long as you agree that two collections contain the same number of things if there's a function that goes between the collections which has an inverse. That's a standard definition, from which you get uncountability, and is what the original author was using. Search Wikipedia for 'Cardinality' if you want more information or examples. Then the function f(x)=2*x demonstrates that (0,1) and (0,2) are actually the same size.

  It's counterintuitive, and I don't pretend that it's a *useful* observation in this situation. Here, it's much more likely that one would like to 'measure' the intervals, and the branch of maths called 'measure theory' indeed does this. The 'length' of (0,1) is certainly half that of (0,2). You don't, strictly, even need the continuum to do measure theory (but it helps).

  So if your good were the set of integers, how would removal of some of them not decrease the number you had left?

  Again, the function f(x)=2*x shows that there are as many even integers as there are integers. Implicitly, we're assuming that the integers are fungible. Thus I could take my remaining stock of even integers and divide them all by two and I would get a pile containing all the numbers again, and continue to sell them.

  Of course that's silly too: you can't sell an integer, and I only brought that up because the original author's argument about the lack of scarcity in the continuum also applies to the integers, so cannot be taken as an argument against the continuum.

  The speaker never faced the audience until he was finished his presentation, since his blackboard scribbling took up all of his time.

  I don't make any pretence that mathematicians are good communicators. Some of them are; some non-mathematicians are bad communicators too. Using mathematics to obfuscate a simple point is bad form, but so is using any jargon, and 'literary' academic economic writing is guilty of this too.

  The economy is made up of human beings,trundling around, making decisions on this and that, whether individually, in business, or in government. If in simple English, a model reflects what such actors are doing, the model is valuable; if it doesn't, it behooves the model builder to explain in simple English why there are insights may be gained from the model.

  I couldn't agree more.

  Eric:

  1. Computer models are too complex to be proven correctly programmed using mathematical analysis.

  3. Because of point 1, only testing can determine if a model is correctly programmed and that says nothing about its validity. ... To use it for predictions ... is absurd

  I think the author was talking about all mathematical models, not just computer ones. What is the point of making a model if not ultimately to make predictions?

  Published: August 24, 2007 3:44 AM

• MJ

  Interesting, generally it was pretty good. However, I would have been more impressed with the article had he quoted Benjamin Graham's classic statements about how academic market-economists and their econmetric equations which are supposed to simulate markets. Graham claimed that every time they substituted letters for numbers they were in fact "substituting letters for experience." Warren Buffett and Charles Munger, annually have fun at poking holes into the absurdities of academic economic theories.

  If anyone wants to read a really good article on the methodology of modern economic theory, and it's errors read Alan Musgrave's "Unreal Assumptions in Economic Theory: The F-Twist Untwisted" Kyklos Vol.34, 1981, p.377. It is really good for students who are struggling with writing economics essays, trust me!

  Published: August 24, 2007 6:22 AM

• MJ

  Interesting, generally it was pretty good. However, I would have been more impressed with the article had he quoted Benjamin Graham's classic statements about how academic market-economists and their econmetric equations which are supposed to simulate markets. Graham claimed that every time they substituted letters for numbers they were in fact "substituting letters for experience." Warren Buffett and Charles Munger, annually have fun at poking holes into the absurdities of academic economic theories.

  If anyone wants to read a really good article on the methodology of modern economic theory, and it's errors read Alan Musgrave's "Unreal Assumptions in Economic Theory: The F-Twist Untwisted" Kyklos Vol.34, 1981, p.377. It is really good for students who are struggling with writing economics essays, trust me!

  Published: August 24, 2007 6:24 AM

• Anthony

  David, out of curiosity, what would you consider the best critiques against mathematical economics?

  Published: August 24, 2007 8:20 AM

• Alex MacMillan

  David: I checked the Wikepedia reference concerning infinite sets, uncountability, etc. Thanks.

  Certainly, by using the mathematical definitions of uncountable sets, of which the sets of real numbers over the intervals (0 to 1) and (0 to 2) are two examples, each set has the same cardinality (number of elements). Also, by mathematical definition, I agree that the number of elements of the set of integers is unchanged by the subtraction of any number of elements (say, by eliminating the even integers).

  The question then is: What relevance do such mathematical definitions and mathematical relations that follow from such definitions have for economics?

  In the real world there may be lots of goods, lots of competitors and consumers in a market, but there are never uncountable infinities of these things. Whenever inputs or outputs, or competitors or consumers are removed, there are fewer inputs, outputs, competitors or consumers remaining. Therefore, if the economic implications of an economic argument (or model) would not hold (even approximately) if such infinite assumptions are false, then the argument or model is not useful (except by chance). If, however, the infinite assumptions merely are used to approximate "lots" for mathematical simplicity (being able to differentiate this and that, etc.), and the results of the model would approximately hold in the absence of such approximations, then such approximations may be economically useful. Again, though, it is up to the model builder to show that such approximations are not critical for the model's results.

  Published: August 24, 2007 11:38 AM

• Eric

  David:

  This is the second time I've made an assumption that the economists that use models also use a computer to compute their results. This makes it even sillier that these econmists think they can model an economy with only a set of equasions and a slide rule.

  As an old mentor of mine used to say, "I think you give them too much credit".

  Published: August 24, 2007 10:15 PM

• RogerM

  Somebody correct me if I'm wrong, but I think there are two kinds of mathematical economics. One is pure theory, like that in physics, and only concerned with elegant equations. Infinity and infinitely divisible components attract them because that's what calculus works with. The other type is econometric modeling, which is applied statistics. Pure theorists write equations on blackboards and solve them and don't care about data or the real world. Econometricians use historical data and computer software to solve their regression equations, and they're actually trying to understand the real world. Econometrics tries to model and predict the real world.

  Pure mathematical theorists are in danger of counting the number of angels that can dance on the head of a pin. Econometricians have fallen out of favor because their statistical models don't predict very well, but that's not because they're using math. It's because their theory is bad. They're trying to model the real world using neo-Keynesian or neo-classical theory, which doesn't work.

  I may be wrong, but I think this article was aimed at the mathematical purists, not the econometrics econs.

  Austrian econ has the correct theory. If someone could apply that theory to econometric models using good data, I think you would have a killer forecasting tool.

  Published: August 25, 2007 12:06 AM

• Robert

  I think David Turner is mistaken to write about the real numbers as a "model". It is not as if mathematics consists of empirical generalizations about the universe at some abstract level.

  Despite some details of Jablecki's exposition, I think the appropriateness of Aumann's application of the mathematics of the continuum to economics is worth thinking about. I have even recommended, on my blog, considering Georgescu-Roegen's article. (I'm linking this comment, though, to a blog post summarizing Musgrave's article.)

  Eric is not only uninformed about economic theory. His anti-intellectualism extends to software, as well. Edsger Dijkstra has something interesting to says about proofs of correctness of computer code.

  A better application of software concerns to economics might be to ask about the computability of general equilibrium and Nash equilibrium and so on. I find Philip Mirowski worth reading for the history. K. V. Velupillai is another author worth reading here.

  I also find curious Anthony's query for "the best critques against mathematical economics". That's not the kind of thing that can be critiqued, in total. One can object to certain trends in mathematical economics, or the models associated with schools of thought in economics, or sociological trends in economics, etc.

  Likewise, I find curious RogerM's comments about "econometricans hav[ing] fallen out of favor." What, all of them? Including in applications that are not tightly tied to the economy? And, by the way, some aspects of Austrian economic theory are just wrong.

  Published: August 25, 2007 1:14 AM

• Anthony

  I was referring to the derivation of theories from econometric modelling.

  Which aspects of Austrian thinking are wrong?

  RogerM, I agree on all your points.

  Published: August 25, 2007 6:15 AM

• Robert

  The mathematical economic theory that I think of as canonical is not derived from econometric modeling.

  Published: August 25, 2007 8:43 AM

• Alex MacMillan

  Maybe people think I was kidding, but I'm still interested in the "proof of the pudding" argument for the contributions of mathematical economics. I was looking for a dozen insights into economics that mathematical economics (including econometrics) has brought forth. How about a half-dozen, then? I'm not suggesting that someone might know of an entire half-dozen, but maybe someone can start the ball rolling with a single insight. Then someone else might know of another one, etc.

  Published: August 25, 2007 9:24 AM

• RogerM

  Robert: "Likewise, I find curious RogerM's comments about "econometricans hav[ing] fallen out of favor."

  I was referring to econometrics in economics. The development of econometrics gave Schumpeter the confidence to declare the end of free market economics because he was convinced that economists now had the tools in econometrics to direct the economy from above without the messiness of the market. By the 1980's economists nearly worhipped their econometric models. The failures of those models to explain and predict business cycles, or predict anything else worthwhile, has cause a serious tarnishing of their image. That doesn't mean that many economists use them; what else are they going to do? But few people have the confidence in them that they used to have, and for good reason. Economists seriously oversold the capability of those models, often sounding more like used car salesmen than economists.

  Like physics, few theories have been, or can be derived from econometric modeling, but that is not its purpose. Theory should come from the apriori method of the Austrians. Econometric modeling does nothing more than put numbers to that theory so that we can make quantitative predictions instead of just qualitative ones.

  Published: August 25, 2007 3:56 PM