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Mathematical modelling in economics

from Lars Syll

 

Tony Lawson has written an extremely interesting paper — What is this ‘School’ Called Neoclassical Economics? — that will be coming out in the September issue of the Cambridge Journal of Economics.

 

The main issue raised in the paper is the meaning of the term “neoclassical” in economics (here for my own take on it), a term that according to Lawson tends to be associated with substantive and policy views when used in criticism, which tends to detract from what Lawson conceives as the central problem of the discipline — an inappropriate reliance on methods of mathematical modelling:

 

Ever since the Enlightenment various economists had been seeking to mathematise the study of the economy. In this, at least prior to the early years of the twentieth century, economists keen to mathematise their discipline felt constrained in numerous ways, and not least by pressures by (non-social) natural scientists and influential peers to conform to the ‘standards’ and procedures of (non-social) natural science, and thereby abandon any idea of constructing an autonomous tradition of mathematical economics. Especially influential, in due course, was the classical reductionist programme, the idea that all mathematical disciplines should be reduced to or based on the model of physics, in particular on the strictly deterministic approach of mechanics, with its emphasis on methods of infinitesimal calculus …

Cora-Ratto-de-SadoskyHowever, in the early part of the twentieth century changes occurred in the interpretation of the very nature of mathematics, changes that caused the classical reductionist programme itself to fall into disarray. With the development of relativity theory and especially quantum theory, the image of nature as continuous came to be re-examined in particular, and the role of infinitesimal calculus, which had previously been regarded as having almost ubiquitous relevance within physics, came to be re-examined even within that domain.

The outcome, in effect, was a switch away from the long-standing emphasis on mathematics as an attempt to apply the physics model, and specifically the mechanics metaphor, to an emphasis on mathematics for its own sake.

Mathematics, especially through the work of David Hilbert, became increasingly viewed as a discipline properly concerned with providing a pool of frameworks for possible realities. No longer was mathematics seen as the language of (non-social) nature, abstracted from the study of the latter. Rather, it was conceived as a practice concerned with formulating systems comprising sets of axioms and their deductive consequences, with these systems in effect taking on a life of their own. The task of finding applications was henceforth regarded as being of secondary importance at best, and not of immediate concern.

This emergence of the axiomatic method removed at a stroke various hitherto insurmountable constraints facing those who would mathematise the discipline of economics. Researchers involved with mathematical projects in economics could, for the time being at least, postpone the day of interpreting their preferred axioms and assumptions. There was no longer any need to seek the blessing of mathematicians and physicists or of other economists who might insist that the relevance of metaphors and analogies be established at the outset. In particular it was no longer regarded as necessary, or even relevant, to economic model construction to consider the nature of social reality, at least for the time being. Nor, it seemed, was it possible for anyone to insist with any legitimacy that the formulations of economists conform to any specific model already found to be successful elsewhere (such as the mechanics model in physics). Indeed, the very idea of fixed metaphors or even interpretations, came to be rejected by some economic ‘modellers’ (albeit never in any really plausible manner).

The result was that in due course deductivism in economics, through morphing into mathematical deductivism on the back of developments within the discipline of mathematics, came to acquire a new lease of life, with practitioners (once more) potentially oblivious to any inconsistency between the ontological presuppositions of adopting a mathematical modelling emphasis and the nature of social reality. The consequent rise of mathematical deductivism has culminated in the situation we find today.

Lawson’s conclusion vis-à-vis the term “neoclassical” is that we should abandon its use. On that issue I will have to return

  1. September 2, 2013 at 5:42 pm

    unfortunately it is not mathematics per se that is the problem — it is the axioms underlying classical and neo classical mathematical economics — namely (1) neutrality of money axiom, (2) gross substitution axiom, and (3) the ergodic axiom in stochastic models [ or the ordering axiom in deterministic models].

    Mathematics is merely the messenger carrying the logical messages that follow from the classical axioms! Do not blame the messenger for the message! Blame those who claim these axioms are universal truths that do not have to be proven to be applicable to the real world of experience!

    • Paul Schächterle
      September 3, 2013 at 12:43 pm

      I agree that Mathematics is merely a messenger.
      But additional to the use of false assumptions (“axioms”) in their models, many economists are IMHO too focused on the use of mathematical models while they do not have their basic concepts and categories carefully thought through.
      Before one can make a mathematical model one has to observe, analyse and find the right concepts. Mathematical models based on flawed concepts are not helpful.

  2. September 2, 2013 at 6:10 pm

    Another economist (TL) has missed the point. Where mathematicians see mathematics is going is completely irrelevant to the use of mathematics in economics. Mathematics is a tool of symbolic logic for economics. Neoclassical economics has the strength that it has a logic that one can follow, which is more than can be said for other economics.

    There is a shame that the logic is founded on false axioms and that the conclusions contradict reality. The unscientific nature of neoclassical economics consists of (a) not accepting the contradictions are serious and (b) not revising the set of axioms as required. That is, neoclassical economics has not accepted that it has been empirically falsified and therefore its theory has not been modified, as required by the scientific method.

    Mathematics and science have been faked or practiced poorly in economics. But it is ridiculous to conclude that mathematics or science is not relevant for economics or that economics is only rhetoric! Without a single, truly scientific economic paradigm, economics continues to be fractured into many different sets of contradicting opinions. There can be no other way forward for economics except to stop pretending and to start following the arduous road of science, which is a difficult process of building theoretical consensus based on hard facts.

    P.S. After writing this, I see Paul Davidson said something similar.

    • September 2, 2013 at 6:47 pm

      Neither Tony Lawson, nor I, says that “mathematics or science is not relevant for economics or that economics is only rhetoric”. Vis-à-vis Paul Davidson’s question of what is the message and who is the messenger, there is rather ample evidence from the history of economic thought, that in the case of “neoclassical” economics they are intricately intertwined. And please notice that Lawson is certainly not — at least to my reading of his oeuvre — critical of mathematics per se, but rather of the rather monomaniac insistence that to be scientific economics has to be mathematically formalized — and more specifically — that it embraces an axiomatic-deductivist methodology.

      • September 2, 2013 at 8:09 pm

        Lars:

        If you are going to have any economic theory that is logical, then you must start with some axioms and then follow the logic to reach conclusions Therefore the axiomatic –deductive approach is essential for any logical theoretical science whether it be economics or seismology, etc. Without axioms and deductions you are JUST ENCOURAGING PEOPLE to tell stories

        .

        [Even the story telling Bible has an axiom –namely there is a God who created heaven and earth and can interfere with how people behave , if She does not like what people are doing — remember Sodom and Gomorrah]

        The question should be what axioms are relevant for an economic theory that is relevant to the entrepreneurial capitalist system that we operate under!

        Keynes clearly told us what classical axioms to throw out –but he still accepted the classical axioms that people were motivated by self-interest. Although self-interest decisions in an uncertain [nonergodic] system that commits resources could go way wrong; therefore even self-interested decision makers may try to postpone decisions involving the commitment of resources when they fear an uncertain (nonergodic) future.

        Accordingly people in an entrepreneurial system had invented the institution of money contracts to organize production and exchange decisions and help them try to deal with an uncertain future — and even to permit postponement of committing real resources by demanding liquidity.]

      • September 3, 2013 at 1:30 am

        What you did say was: “Lawson conceives as the central problem of the discipline — an inappropriate reliance on methods of mathematical modelling”. Doesn’t this say: reliance on the methods of mathematical modelling is inappropriate?

        Neoclassical economics has attracted support precisely because of it has “an axiomatic-deductivist methodology”, providing a level of clarity which is hard to match with story-telling.

        Formalization is essential in making economics a science, for the sake of clarity. Mathematics is formal for that reason. Formalization of economics does not have to be in terms of mathematics, e.g. could be formalized in propositional logic, although some mathematical formalization would be natural due to a substantial quantitative content in economics.

        Neoclassical economics is a bad craftsman who uses his limited set of mathematical tools badly. Economics needs to overcome the restricting set of neoclassical axioms and to formalize a new set of axioms. As a result of this new set of axioms, economics will need a greatly expanded set of mathematical tools. The resulting new economic paradigm will have a much better chance of explaining observations.

      • September 3, 2013 at 9:16 am

        lyonwiss

        I really don’t think that its fair to interpret “an inappropriate reliance on methods of mathematical modelling” to mean that any mathematics in economics is faulty; just that it may not be as appropriate as some people think.

        As to it providing clarity I entirely disagree. Most applications of mathematical modelling lack clarity completely. Your average econometric study is borderline unreadable and trying to pick through its various assumptions and why certain lags were chosen rather than others is, as Keynes said of Tinbergen’s work, “like living with a nightmare”.

        Mathematics can be used to promote clarity in some limited circumstances. But it can also be thrown up like a fog around bad quality work and poorly interpreted data.

        paul davidson

        I think that Keynes was fairly clear that most mathematical modelling was entirely undesirable. There are many points in the General Theory where he expresses this opinion and there are also relevant quotes in his letters to Harrod on Champernowne. Of course the most relevant quote remains the most famous:

        “The object of our analysis is, not to provide a machine, or method of blind manipulation, which will furnish an infallible answer, but to provide ourselves with an organised and orderly method of thinking out particular problems; and, after we have reached a provisional conclusion by isolating the complicating factors one by one, we then have to go back on ourselves and allow, as well as we can, for the probable interactions of the factors amongst themselves. This is the nature of economic thinking. Any other way of applying our formal principles of thought (without which, however, we shall be lost in the wood) will lead us into error. It is a great fault of symbolic pseudo-mathematical methods of formalising a system of economic analysis that they expressly assume strict independence between the factors involved and lose all their cogency and authority if this hypothesis is disallowed; whereas, in ordinary discourse, where we are not blindly manipulating but know all the time what we are doing and what the words mean, we can keep “at the back of our heads” the necessary reserves and qualifications and the adjustments which we shall have to make later on, in a way in which we cannot keep complicated partial differentials “at the back” of several pages of algebra which assume that they all vanish. Too large a proportion of recent “mathematical” economics are mere concoctions, as imprecise as the initial assumptions they rest on, which allow the author to lose sight of the complexities and interdependencies of the real world in a maze of pretentious and unhelpful symbols.” (GT, Chapter 21)

      • September 3, 2013 at 12:10 pm

        pilkingtonphil

        You are referring to the mathematical gibberish in journals, which are ugly and often done to hide ignorance. This can be a problem, particularly when most economists are poor in mathematics (as
        evident in curricula and research papers).

        Economics is far from ready to produce great deductive insights, simply because there is currently no set of useful axioms which are sufficiently consistent, realistic and powerful to build valid
        and insightful economic propositions.

        All elaborate economic or econometric models currently in existence rest on unproven assumptions. Apart from accounting identities, which are tautologies, there is currently no proven economic laws with which to build valid mathematical models for economics.

        The current primitive state of mathematical economics does not prevent charlatans from using overly complicated mathematics to obfuscate and discombobulate readers and to get away with outrageous claims.

        While Keynes clearly understood the pseudo-mathematical scam then and now, I think he own work would have benefited subsequent generations more if he had formalized it, at least to the degree where his assumptions are made explicit.

    • JS
      September 3, 2013 at 12:28 pm

      Why don’t you address what Lawson actually says on things rather than dismissing a caricature. For example in

      http://thetransatlantic.org/2010/03/10/economics-science/

      he argues:

      “Many economists accept that the modern discipline of economics is not in a healthy state (see Lawson, 2003, chapter 1). Indeed with the onset of the recent ‘crisis’ perhaps most now do (see Lawson 2009b). Many even connect the problems of modern economics to the question of science, the topic of this short note. Amongst those who do so, however, there are significant differences. Indeed there are essentially two opposed groups to be distinguished. The first comprises those who think that the problems with the discipline arise just because an economic science is infeasible, that attempts to render economics scientific are misguided; it is the concern to be scientific that leads economists astray. The second group comprises those who, in contrast, think that problems arise just because economics has yet to realize its full scientific potential. I also believe the parlous state of economics is connected to stances taken with regard to the question of whether economics can be a science. But my assessment diverges sharply from those of proponents of both sides of this debate, given the terms in which the latter tends to be cast. For, fundamentally, both groups associate science with the use of mathematical methods. And their contrasting expectations concerning the possibility of an economic science primarily reflect different expectations concerning the possibility of gaining insight using mathematical models. My contrary view is that the use of mathematics is irrelevant to the question of whether a discipline qualifies as science.

      Further, with a revised conception of science to hand, I do argue that a science of economics is entirely feasible, but I also contend that the current emphasis on formalism in modern economics mostly obstructs the potential of economics for realizing its potential as a successful science.

      I thus side with the first group in being optimistic about the possibilities of a successful economic science, but hold a contrasting conception of science. I side with the second group in thinking that the emphasis on formalism is unhelpful in modern economics, but do not suppose that giving up on formalism impedes the possibility of economics being scientific in the sense of natural science. Let me briefly elaborate…..”

      • September 5, 2013 at 3:51 am

        pilkingtonph, I agree broadly with your blog article, provided by the link. But the Basil Moore article you referenced contains common errors which need commenting on.

        Basil Moore wrote more clearly than most, on account of a formal approach to discussion (as you indicated). But his flawed use of econometrics shows a common misunderstanding of regression models: for t-values to indicate statistical significance, the model errors have to be symmetric and normally distributed, which is typically false. Almost no economist bothers to check this condition and therefore most applied econometric claims (from papers I have read) are invalid, (particularly when R-square is less than 90%).

        When applied to monetary policy, regression models is almost certainly noise and invalid, because of policy asymmetry. Central banks can easily restrict money supply by raising interest rates and increasing capital reserve ratios of banks (potentially causing a recession). But doing the opposite does not lead necessarily to increase money supply in terms of increased commercial lending (potentially causing a boom). Model errors should be asymmetric. This is abundantly evident recently: enormous monetary stimulus has been ineffective in targeting US growth.

        Most mathematics in economics is simply bad mathematics. So may be Tony Lawson is right in this sense: until economists learn mathematics properly, it may be better not to use it at all. So the conclusion is not that mathematics is unimportant, but rather that economists need to be better educated in mathematics. But this opposite conclusion may not be popular.

  3. BFWR
    September 2, 2013 at 7:14 pm

    Money is basically accountancy. Those empirical accounting facts DO expose undeniable mathematical and economic consequences which cannot be abstracted out by theory. Those consequences are the fact that the monetary and economic systems are inextricably intertwined by the conventions of cost accounting. That is, one cannot consider total individual incomes without also considering total costs simultaneously created. They are inevitably linked by the REALITIES found in cost accounting data.

  4. Podargus
    September 2, 2013 at 7:49 pm

    Mathematics is necessary for accountancy.I would hope that economists aspire to cover a wider field.
    Both economics and psychology claim to be sciences. That is a spurious claim as they both are dealing with human thought and behaviour where science is not applicable.But philosophy certainly is.

    Until economists and psychologists get together and climb down from their ivory towers and get with reality on the ground we will continue to see and hear these angels on the head of a pin arguments like in this article.

    • September 2, 2013 at 8:14 pm

      The purpose of theory is to EXPLAIN observable phenomena — Seismology is a science even though it can not predict the date and time the next earthquake will hit California. But it can explain the geological conditions that causes an earthquake.

      Economics can NOT predict the NEXT financial crisis but it can explain the conditions that (psychologically?) cause the financial panic to occur.

    • BFWR
      September 2, 2013 at 10:42 pm

      Yes, and calculus is necessary to understand that accountancy data through time as a flow. That flow will show that in the normal operation of any enterprise’s productive process more in total prices are created than total incomes are simultaneously produced to liquidate them. This economic disequilibrium can be palliated for a time by continuous money injection as is done now, but it cannot be resolved by such injections most especially in the form of loans back into the economy/productive process…because that will merely re-initiate the price inflationary nature of production itself….at least under the current conventions of cost accounting. The velocity of money does not resolve this problem because any money re-circulating, must go through a business and when that occurs the same cost accounting conventions are again, re-initiated. Altering the current rules of cost accounting so that consumption is ALSO financed by an independent credit creating agency mandated to distribute a universal dividend based only on the statistics of the gap between the cost of total production and the total cost of consumption over a given period of time (say monthly) would break up the monopoly on credit creation enjoyed by the current holders of private banking licenses. Couple this policy with a monthly voluntary discount mechanism to consumers and the rebating back of the discounts given by participating merchants and you’ll eliminate both monetary and price inflation. It’s elegant, simple, monetary stock and flow consistent, recognizes the creditary (+,-) nature of the money system….and confronts the actual empirical data found in the cost accounting books of any ongoing economic concern….and their price inflationary economic consequences.

  5. September 2, 2013 at 10:21 pm

    Hi all,

    Just to say that Lawson and I corresponded on this and he asked me to summarise the paper on my blog. Perhaps those on here might be interested as he told me it was a very accurate summary:

    http://fixingtheeconomists.wordpress.com/2013/08/27/what-is-neoclassical-economics-and-are-many-heterodox-economists-actually-neoclassical/

    Phil

  6. September 2, 2013 at 10:52 pm

    Mathematics is not merely the messenger. The theories that are developed have often been shaped by the mathematics used, and that certainly is the case in mainstream economics.

    In earlier stages of economic thought, (political) arithmetic was the only tool used. It proved useful to define some concepts from Petty until Ricardo, such as Ricardo’s differential rent (obtained through a difference), the social surplus (also obtained as a difference between total product and wages), or Quesnay’s Tableau.

    Then came calculus, which shaped the new theories used. Cournot’s use of calculus, which influenced subsequent marginalist analysis (not least Marshall’s analysis, which is driven by mathematics before “burning” it) brought the idea that we can study the variation of one factor in isolation while assuming everything else constant, so that differential calculus (finding partial derivatives in partial equilibrium analysis) could be used. In fact, Marshall writes in Industry and Trade that it was the use of calculus that helped him develop his theory in a way he could not develop without calculus. Differential calculus led to theories with particular ontological presuppositions, such as the idea of ceteris paribus (which presupposes isolation, rather than a relational world).

    Later on, the tweentieth century mathematics, the use of fixed point theorems led to the development of a different type of equilibrium analysis, that is, different than that undertaken from Cournot to Marshall using calculus. The different types of mathematics used (arithmetic, calculus, fixed point theorems) led to various types of theories, shaped by the mathematics used.

    Even the substitution axiom emerged due to the way in which Cournot and Von Thunen used calculus, as becomes clear in Marshall’s analysis too (which is also driven by geometry, namely the geometry of supply and demand curves). The ergodic assumption is also a result of the use of mathematics. Mathematics is not just a language used to express axioms. Mathematics actually leads us towards certain axioms and theories. Moreover, science is not just, or maybe not even essentially, deduction from axioms. It is essentially a critical exercise of revision of axioms and theories.

    Furthermore, mathematics, be it arithmetic, geometry, calculus, or more specific theorems like fixed point theorems, always presuppose constants at some level, that is, closed systems. The social world is, however, an open system, where methods that presuppose exact regularities are not particularly useful.

    Of course, partial regularities may arise. But the appropriate tools to deal with them are often some basic arithmetic (such as Ricardo’s differences) or descriptive statistics. Mainstream
    economists will not be satisfied with that, because the purpose of the way in which mathematics is used in mainstream economics is not the description of reality. In mainstream economics, the more complex the maths is, the better (regardless of reality), since arithmetic and basic statistics do not make economics look as a “hard” science. But the really “hard” part of economics is the formulation of theories that capture reality, rather than theories that take us away from reality. Many authors went much further than mainstream economists using simple arithmetic, or using not maths at all. But their theories are not less rigorous, or less complex, than mainstream models. They simply were not constrained by an innappropriate method.

    • September 2, 2013 at 10:56 pm

      This reminds me of the point made by Boylan and O’ Gorman that when the use of actual infinity is deployed in General Equilibrium theory it shows how these theories cannot structurally be made to represent reality as lived in finite time:

      http://aran.library.nuigalway.ie/xmlui/bitstream/handle/10379/326/paper_0138.pdf?sequence=1

    • BFWR
      September 3, 2013 at 12:01 am

      The deeper problem has been the inaccurate economic epistemological assumptions which have lead us toward the all too human problem of dogmatism. The solution is to recognize that the economy/productive process ITSELF under current cost accounting conventions is not only not stable, but radically unstable. Combine that with the engineer’s perspective of fixing the problem observed/concluded from the empirical cost accounting data and their economic relationships instead of holding onto orthodox beliefs to the contrary and the maths will be fine and up to the task. Math is a wonderful and necessary tool, but a poor and too often fallacious supporter of belief.

  7. BFWR
    September 3, 2013 at 3:19 am

    Economics is so fraught with and attached to basic unexamined orthodoxy, and hence utterly condemned to banal “solutions” and regurgitative “thinking”, that it is like that psychotic sect of Christian fundamentalists that handle poisonous snakes to “prove” their faith. The three most blaring problems are easy to see:

    1) Banks have too much power because they have a monopoly on credit creation and the purposes for which credit is granted.
    2) Individuals don’t have enough money to make the system function.
    3) The value of the inexorable force and potential human blessing of Technological innovation is sabotaged and usurped by #1 and hence denied to #2.

    All of the erudite avoidance or dancing around the solution to these three problems….is just a generally deadly snake bite waiting to happen.

  8. Norman L. Roth
    September 3, 2013 at 2:36 pm

    Sept. 03, 2013, The last word ? On ‘Mathematical Modelling in Economics’

    In order to benefit from what follows, readers should refer to:
    ‘IT’S the MATH AGAIN’, specifically:[1] Norman L. Roth, Aug. 24, 2013, #18
    [2] Norman L. Roth, Sept.02, 2013, #27

    PLUS : Everything by Paul Davidson above: & Nuno Ornelas Martins’ beautifully clear exposition of how the analytic techniques chosen, even by mathematically adept economists, have often shaped the economic theories & paradigms they were trying to develop & teach. A theme that was emphasized in TELOS& TECHNOS, as How the failed but still dominant paradigms of academic economics actually “teach away” from economic reality.

    Post -Autistic Critique MANIA, between paradigms PANIC, and systemic model-CRASH disorder: With credits to the late Charles Kindleberger.

    How many different ways can we rake-over the same ashes ? Done so well & so often by “on-site” insiders like Norbert Wiener, Vasily Leontieff, master debunkers Philip Mirowski & Stanley Wong, the great ones like Ludwig Von Mises, Friedrich August Hayek, Keynes & Marshall themselves, and so many others. Diminishing returns set in long ago for the incessant blame and punishment bagatelles directed at : “inappropriate methods” & choice of ” messenger”, flawed interpretation of Statistical methods,’Market fundamentalism’, a “creatively accounting” conspiratorial, banking system [BFWR]; a “One-percent” 24/7 conspiring elite, whose skill at solving the “co-ordination problem” puts “the devil and all his works” to shame. As Shakespeare might have commented: The [superceding] paradigm’s “the thing”.The old “play’s” not. . Never was.

    Norman L. Roth, Toronto, Canada.
    Please GOOGLE: [1] Technos, Norman Roth [2] Origins of Markets, Norman Roth,
    [3] Telos & Technos, Roth

    • BFWR
      September 3, 2013 at 3:32 pm

      There is “a “creatively accounting” conspiratorial, banking system” as the shaping of the FASB rules to allow mark to fantasy instead of mark to market in real estate, and the reason for this is obvious to avoid disaster for the banks and their dissolution and reorganization. Nothing must delay or subvert their control. However, I’ve never posted about this mostly because anyone with a scrap of objectivity can see it. The fact is there doesn’t need to be any conspiracy when the entire system is rigged to necessitate the continual over borrowing of money in order to avoid implosion. The problem is actually a lack of appropriate accounting creativity resulting from an adherence to neo-classical orthodoxy which blinds and prevents economists from confronting obviously significant factors like technological innovation. Orthodoxy blinds and economists are godawfully blind as a result.

  9. September 3, 2013 at 5:37 pm

    (My answer to the thread is a little bit lengthy, but worth reading. I promise.)

    It’s again a very interesting discussion here for me. As it reflect the two actual main-drifts in economics: One is to refuse mathematics as non relevant for economics (as a seemingly pure social science). And the second is, to finally get the (seemingly not yet found) correct mathematical theory. Well the first drift of course stems from the fact, that most neo-classical mathematical models are contradicted by reality, which is often mistaken as a proof of mathematics not working in economics. The second claim but is more sophisticated: How to find the correctly formulated main theory of (macro-)economics?

    I myself came from physics to economy and from my education I have a large knowledge on modeling real systems (originally modeling in high-energetic low-density plasmas, which here is but of no big importance). In theoretical physics one has to have also a very general overview on mathematical tools and theory as well (which means you have not to know everything, but you have to know in any case where to look for…). What I want to say is, that although this is a forum of critical economists, one can see the same problematic in understanding maths and how to model real systems, as one can find with neo-classical economists. By now I had a lot of scientific contacts with even prominent economists and in most cases the same problem occurred: They, regardless of being critical or not, are not able to see the elephant in the room! Mostly the general mathematical, and physical, knowledge is regrettable low.

    To demonstrate some points, I will cite and comment the postings here:

    Lars Syll, citing Tony Lawson: “…Especially influential, in due course, was the classical reductionist programme, the idea that all mathematical disciplines should be reduced to or based on the model of physics, in particular on the strictly deterministic approach of mechanics, with its emphasis on methods of infinitesimal calculus …Mathematics, especially through the work of David Hilbert, became increasingly viewed as a discipline properly concerned with providing a pool of frameworks for possible realities.” Well of course. Mathematics is nothing more or less than (formalized) pure logic. It is the science of pure logic. The thing indeed is: Everything, every thought, can be formulated mathematically in principal. Although sometimes it may be a very complicated tasks and sometimes even practically unsolvable.

    paul davidson: “…unfortunately it is not mathematics per se that is the problem — it is the axioms underlying classical and neo classical mathematical economics — namely (1) neutrality of money axiom, (2) gross substitution axiom, and (3) the ergodic axiom in stochastic models [ or the ordering axiom in deterministic models]…Do not blame the messenger for the message!” This is exactly the problem: Mathematics can (just by construction) never fail! It is always the scientist who fails. Indeed, namely the “(1) neutrality of money axiom”, is the most prominent economical failures of today’s macro-economy. The “ergodic axiom” but is a more difficult thing. Right, drop “stochastic models”, which are of only small analytical merit. But the stochastic “ergodic axiom” in analytical models means the theory of invariants (or often said to be symmetries). Indeed it is one of the main findings in theoretical physics, that every real systems depends crucially on some invariants (see: Noether theorems). It must be mentioned, that such invariants are not always easy to find. But they exist.

    lyonwiss: “..Neoclassical economics has the strength that it has a logic that one can follow, which is more than can be said for other economics. There is a shame that the logic is founded on false axioms and that the conclusions contradict reality…..Mathematics and science have been faked or practiced poorly in economics. …Without a single, truly scientific economic paradigm, economics continues to be fractured into many different sets of contradicting opinions….”. Yes that’s the thing: Mathematics and science is practiced (and mentioned too) very poorly in economics.

    “….There can be no other way forward for economics except to stop pretending and to start following the arduous road of science, which is a difficult process of building theoretical consensus based on hard facts.”. This is also true: The “difficult process of building theoretical consensus” is but a nearly hopeless task, as the gross of economists can not even see a correct solution if presented to them. They are absolutely blinded by old fashioned methods and models of macro-economy. They even fail to see such simple but important differences between ad hoc modeling, like e.g. Cobb-Douglas-Production-Functions, AK-models and so on, and predictive systems of initial value problems of differential calculus. Mostly they don’t see even the difference between stringent analytical theory and statistical methods (as regressional methods on data). It’s really to become desperate. The elephant in the room has always best chances to disappear.

    Lars P Syll: “And please notice that Lawson is certainly not — at least to my reading of his oeuvre — critical of mathematics per se, but rather of the rather monomaniac insistence that to be scientific economics has to be mathematically formalized — and more specifically — that it embraces an axiomatic-deductivist methodology.”. Well, this (“rather monomaniac insistence that to be scientific economics has to be mathematically formalized ”) has at least two answers: In any modeling of real systems, you have to have something back of the head: There are always some fundamental rules and behavior in systems, but they are always shrouded by less fundamental secondary side-effects, at least by some statistical fluctuations. Some times the signal-to-noise ratio can be that high, that it prohibits to see the elephant clearly.

    As classical example take Newtons theory of forces like gravity: His giant achievement was to see the fundamentals behind such things like falling objects (like e.g. apple, but also feathers or planets) which follow from a simple analytical differential equation: a= ddot x . Yes, it is really that simple! It explains (by using a lot of more sophisticated maths, sorry) falling apples as well as flying feathers (due to forces by air drag) as also circling planets and moons. Such achievements, which in this case let really explode techniques and wealth in the world since 1700, are impossible to make with out a large amount of intuition. Intuition that has to be accompanied by analytical considerations plus (statistical) measurements plus experiments which isolate special effects (like e.g. let fall a feather in a vacuum chamber! Sometimes side-effects can be stronger than the searched for main effect.).

    paul davidson: “…If you are going to have any economic theory that is logical, then you must start with some axioms and then follow the logic to reach conclusions Therefore the axiomatic –deductive approach is essential for any logical theoretical science whether it be economics or seismology, etc. Without axioms and deductions you are JUST ENCOURAGING PEOPLE to tell stories….The question should be what axioms are relevant for an economic theory that is relevant to the entrepreneurial capitalist system that we operate under!” And then lyonwiss: “…Formalization of economics does not have to be in terms of mathematics, e.g. could be formalized in propositional logic, although some mathematical formalization would be natural due to a substantial quantitative content in economics….Economics needs to overcome the restricting set of neoclassical axioms and to formalize a new set of axioms. As a result of this new set of axioms, economics will need a greatly expanded set of mathematical tools. The resulting new economic paradigm will have a much better chance of explaining observations.”

    This both is also correct: “The question should be what axioms are relevant for an economic theory…The resulting new economic paradigm will have a much better chance of explaining observations”! Indeed it is crucial to find the underlying axioms, or better say invariant(s). The solution besides is more obvious than thought. We’ll see later.

    And correctly BFWR states: “…Money is basically accountancy. Those empirical accounting facts DO expose undeniable mathematical and economic consequences which cannot be abstracted out by theory. Those consequences are the fact that the monetary and economic systems are inextricably intertwined by the conventions of cost accounting.”. Indeed it is that easy, just do correct accounting (which in the actual case basically could be done in a simple homework for students in theoretical physics). Just account correctly, and you will get the first very well guess for correct growth theory in just some hours work.

    The next cites are but also of some relevance. Podargus: “…Both economics and psychology claim to be sciences. That is a spurious claim as they both are dealing with human thought and behaviour where science is not applicable.”. This is a the old bad argument used by classical economists. Science is always applicable, maybe but sometimes not very useful: “ …dealing with human thought and behaviour” is easily done if the number of individuals is very large. If you refer but to individuals, it make no big sense indeed. To tell it in the picture of Newtonian gravity: Of course only few people know about the theory of gravity, but (nearly) everyone will behave very much according to it. So no one will jump out of a window, as he may very well guess what will happen. But some do anyway.

    paul davidson: “…The purpose of theory is to EXPLAIN observable phenomena — Seismology is a science even though it can not predict the date and time the next earthquake will hit California. But it can explain the geological conditions that causes an earthquake. …Economics can NOT predict the NEXT financial crisis but it can explain the conditions that (psychologically?) cause the financial panic to occur.” Yes and No. In a closed national economy (with no external money, like foreign money or just printing money) the crisis will always come after about 60 years. It just follows from simple dependencies between the different evolution of capital and GDP and the back influence by interests. Of course it is sometimes covered by effects of foreign money. It has to do very few with psychology, which can just do something more or less for the always effective statistical fluctuation.

    And now, let as come to the large Elephant, the solution of the (main) macro-economical problem:

    Well, what should first of all an macro-economical theory explain? Of course the evolution of GDP and also Capital in time and there interdependencies. At the best self-consistently, or at least, leaded by just very few micro(!)-economical parameters, such as the prominent interest rates.

    Now, what can one do for a first guess of a possible solution?

    a) You said it: recommend every(!!) capital (asset) which is in the economy. Indeed there is no ad hoc reason to not respect any money or financial product in the economy.
    b) Just take serious, what is obvious: There is an interdependency in the evolution on capital (K) and GDP (Y). The most prominent link between them are the interest rates p (what else?).
    c) If we want to get a self explanatory model between Y(K,p) and K(Y,p), which mathematical gadget do we have to choose (at least!) for modeling?
    d) The last thing then to fix the model needs a little economical intuition, which is really the only thing here which needs a little sophistication. The a,b,c is nothing that should be any principal problem.

    So, what follows from (a)? Well it is to take into account the whole of all assets in an economy, not just more or less small parts of it like loans, or M1 or so on. The difficulty there is just the case, that most statistical institutes don’t give you this number. You have to add up this sum from different information on the banking accounts. But in Germany it is easy, as the Bundesbank indeed advertises this number. What follows from (b)? It means that the functional behavior of Y and K must be coupled. What follows from (c)? The gadget has to be at least(!) a system of two coupled differential equations of Y an K. This is just a minimum requirement! Any less is useless and irrelevant. What means (d)? Well, we will have to take a seemingly unimpressive, but crucial, fact into account: There is an intimate difference between commercial banks business (CBB) and banks own business (BoB, often so called Investmentbanking): In BoB, the interests of the sold financial products are mostly earned at once, while in CBB the interests for the loans into the real economy are earned definitly sometimes later, as when credits are repaid. For modeling techniques this means, that those functions have to be retarded in time. Retardation is often a prominent fact in real systems and must be considered. The only thing you have to know now is, what is the relation in the country between CBB and BoB. Luckily the Bundesbank advertises the sum of CBB too, and the relation is easily to find out.

    What happens now, if we use the mathematical representation of the ideas (a) to (d) seriously? The outcome (simple basic model) can be found here in the paper http://www.paecon.net/PAEReview/issue57/PeetzGenreith57.pdf . It is nothing more than the above implications packed into the most simple non-trivial possible model (if you don’t understand it, just ask me for more details).

    Well, what do we see there in Chart 2 on page 44? We see the astonishing agreement between theory and real data. Especially for the GDP. The buckle in capital is indeed related to the DotCom bubble which gave reason for huge amount of foreign money (the basic model doesn’t account for foreign money. Like feathers and apples…). The same model you can do for whatever country, you will find always the same fundamental behavior, very close to real data. But I have here to explain more exactly what you see there: This are the real data from year 1950 to 2010 for Germany in comparison with the modeled data. But the model data are fully predictional! You have to know just the values of Y and K of the year 1950 as starting point! The rest the model does, is just prediction from the knowledge of 1950 data! This is what an initial value problem of differential calculus means.

    But the astonishing thing for me is, that economists regularly don’t see the esprit of it, as the reason is that they usually don’t know what such an initial value differential equation really means (the often think it is just another regression method or something else, which but is nonsense). What you see is indeed the Elephant in the room that no one can or want to see (if you still don’t see it, well I can’t help. Possibly no one then will ever help.).

    So well, lets come to the last, but most sophisticated thing of macro-economic-modeling to do, which is to find out: Which invariant(s) are underlying this system? The thing is: If you can find these invariants, you then can calculate the differential equations of motion of the system by Noether’s theorem uniquely. You just have to solve the related Euler-Lagrange equations and you’ll get the fully self-consistent non-linear set of equations (as every interdependency of competitive forces leads to non-linear equations). By relinearizing them you then will come back to the basis model shown here in the mentioned article again.

    And by this, Noether’s theorem guarantee the uniquiness of the solutions! There is no need to search for principal others, there aren’t any! Except of the fact, that the same principal equations may be formulated in some equivalent mathematical representations (classical example is here: Quantum theory, which came with the Schrödinger-, Heisenberg- and Dirac- formulations, which all look very different, but are indeed fully equivalent. This stems from the principal uniqueness of mathematics: As it is nothing but pure logic, regardless of what mathematical pathway you use, you will always come to the same conclusions.).

    To make it short, the main invariant is, that the well known quantity equation MV=HP holds at least locally. Nothing more, the rest is self consistent. What has to be mentioned here but is, that the trivial classical use of the quantity equation MV=HP as a “rule of thumb” must be more generalized, and also better defined in suitable dimensions. Which means e.g. that the equation must be split up at least to (Mreal + Minvest) * (Vreal+Vinvest) = (Hreal+Hinvest) * (Preal+Pinvest) to get non-trivial solutions. From this we’ll get a full unique theory instead of just a model.

    An academic preprint of the full story can be found under http://genreith.de/index.php?id=economics-of-growth-and-crisis to be read also online. It is written not in very good english, sorry, also something unconvenient and lengthy. This stems from the fact that I published a book on the issue in 2011 in German language and translated it very roughly one by ne to english. This makes the online text very bumpy. I am working on an English version with a much more intuitive and concise composition of the book (including a lot of new advances, some corrections and new graphics).

  10. Jeff Z.
    September 3, 2013 at 8:01 pm

    A few points.

    I am in general agreement with lyonwiss (@#3 and #6) and Paul Davidson (@#5 and #11) and Nuno Martins (@#14)

    Lyonwiss writes @#8 “Economics is far from ready to produce great deductive insights, simply because there is currently no set of useful axioms which are sufficiently consistent, realistic and powerful to build valid and insightful economic propositions.” Is it possible that the idea of a ‘surplus’ might fulfill this criterion? Surely, it is not fleshed out sufficiently here, but I am not willing to dismiss this entirely out of hand for the following reason. It seems to me that any society needs to generate a ‘surplus’ beyond what it consumes in order to grow. Not to imply that ‘growth’ is necessary for other societies the way is seems to be imperative for capitalist ones. From this, I can conclude that a society that does not generate this ‘surplus’ will not grow in sense of simply expanding production. Further, a society that generates such a surplus may grow faster, and generate the means for further rapid and increasing growth. This surplus also tends to generate additional technological and scientific awareness (if used that way), which allows for both further growth and generating an awareness of environmental costs and account for them (thanks BFWR @#9). Another question: Does the generation and regeneration of ever larger surpluses result in more hierarchical class structures and more elaborate social relationships? It seems that you can then ask questions about distribution of the surplus, what institutions arise to handle this, and whether path dependency arises or not. That said, there remains a lot of work to be done, such as satisfactorily defining a ‘surplus’ in all its gory detail, and ‘social class.”

    Martins made the point about modeling and how choice of technique can shape thinking. Anybody can observe and record a series of prices for a gallon of gas (or importantly these days in poorer nations – the price of grain). There exists in economics at least two possible explanations for the observed price. One arises out of marginal utility and is encapsulated by consumer choice theory – neoclassical economics if you will. This is supposedly handled by the calculus of optimization. The other arises out of a structural dynamic – captured by simultaneous equations modeled by techniques of linear algebra – some Marxists and Sraffa, and possibly Ricardo. Both methods have their limits. In their extreme forms, the structural equations limit the role of individual choice, and the consumer choice ideas imply costs to others are automatically covered by the price paid. However, thinkers that are more of an ‘individualist’ bent might be more attracted to neoclassical techniques, while the opposite might be true for more ‘structuralist’ thinkers.

    I read Genreith’s post (#18) and I recall sitting through my macro growth class and seeing that growth could be explained in some ways by capital, interest rates, and their impact on GDP. IS there only structure, or do we want to explain the idea that structure and individual choice mutually condition one aonother. If so – how? What is the path and process? We must ask whether GDP is an adequate measure of welfare on its own. If not, how do we change it?

    Every time I look in this direction, I am always confronted by the issues of adequate definition repeatedly raised by lyonwiss on this blog. The paths and processes may be real and important, and the numbers are the clues about how they work.

  11. September 4, 2013 at 1:49 pm

    Hi Jeff,

    there are a lot of great points in your post.

    Lets begin with the „surplus“. Citation Jeff Z.: „(Cite Lyonwiss:“Economics is far from ready to produce great deductive insights, simply because there is currently no set of useful axioms which are sufficiently consistent….”) Is it possible that the idea of a ‘surplus’ might fulfill this criterion? ….It seems to me that any society needs to generate a ‘surplus’ beyond what it consumes in order to grow…..seems to be imperative for capitalist ones. From this, I can conclude that a society that does not generate this ‘surplus’ will not grow in sense of simply expanding production.“

    Yes that’s right. There is an intimate correlation between interest rates p growth g and inflation i with approximate p=i=g. Not exact but in order of close together numbers with usually p>i>g; see also http://genreith.de/EEGenreith/EEGenreith-311.html. Here we should have a look at equation 31.7: The last square term is not very important in good times. So we have a look at the first leading term. It says that the growth in Trade is: Interest rates plus Change in money-velocity. The main part is indeed interest rates which ignite the GDP growth. And Interest rates close to zero of course imply also GDP growth of close to zero (stagnation).

    How does this work on micro-scale? Well if a entrepreneur gets a 1000 $ loan with say 10% interst rates, he then has to produce and sell for at least additional 1000 $loan + 100$interest+X$profit. The X$-profit he will think should also at best be around 100$, as otherwise he would prefer not to produce anything but would give is money himself as a loan to a bank. As it is known banks interest rates for loans (100$) are higher than interest rates for deposits, it will be enough for him to earn say 80$ extra. So he have to sell for 1180$ additional products. At the end capital grows by 180 $ and GDP also by 180$ in this simple example, which would be quite o.k. Without interest rates, there would be much lower growth, as the entrepreneur would have no stress to produce much more than pari.

    But this is not the whole story! It is just the usual badly accounted story told with just micro-economic arguments. But in a national economy we have strong substitutional effects. First of all: the additional(!) 1180$ must be paid by consumers. But they don’t get that amount from nothing, but have to substitute it by choosing then not to buy other products. Now, from the 1000$ loan, there were say 800$ expended by the entrepreneur for additional wages, 200$ expended for basic materials etc. Now lets account this rule-of-thumb example: Growth of spending power or GDP is 800+200+80=1080$. Growth of Capital: exact this 1080+100interest =1180$. Marginal growth of price level: 1180/1080. In percentages is this: GDP 8%, Capital 10%, Inflation is 9,26%. So we see p>i>g. This marginal rates here assume starting from zero stocks K=Y=0, what happens further on when K>0 and Y>0 I will come to later.

    This story here is something different from what is told mostly in economics: It is said usually, that the original 1000$ loan is eliminated when it is paid back to the bank (balanced to zero) and thus disappears. But this is entirely not true: The money was spend for labor and goods. It didn’t disappear, it is just in other hands. After some time and a chain of trades it comes back to the banking system. Close to full, only diminished by a possible increase in cash money (M0), which is at the whole mostly neglectible (for the exact story we have to take the role of central banks in account to. They give credits to banks in exchange for the opposed debts. They were it, who created the money in the end).

    Cite „This surplus also tends to generate additional technological and scientific awareness (if used that way), which allows for both further growth and generating an awareness of environmental costs and account for them…“. Yes it does. Even the ancient Romans did so, as with the growing industries the Tiber got more and more dirty there were made first in history environmental laws.

    Cite: “Another question: Does the generation and regeneration of ever larger surpluses result in more hierarchical class structures and more elaborate social relationships? It seems that you can then ask questions about distribution of the surplus, what institutions arise to handle this, and whether path dependency arises or not. That said, there remains a lot of work to be done, such as satisfactorily defining a ‘surplus’ in all its glory detail, and ‘social class.”. Well the question of inequality and its driving powers is a very interesting analytical task. A task I did not focus much on until now. But the main thing is the ability of someone getting shares of the really high return investments. And the more money you have, the larger naturally is your share on such high returns investments.

    Cite: „Martins made the point about modeling and how choice of technique can shape thinking. …There exists in economics at least two possible explanations for the observed price. One arises out of marginal utility and is encapsulated by consumer choice theory… The other arises out of a structural dynamic … Both methods have their limits…“. Well, you may put the cart before or after the horse. It is just a question what works better or easier. In mathematics and modeling there are several possible paths. But which (must) lead all to the same macroeconomic outcome if applied correctly.

    We take to show just the example from above: What happens further on when we start at K>0 and Y>0? So lets account further the rule-of-thumb example:

    Growth of spending power or GDP now is Y+800+200+80=Y+1080$. Growth of Capital: K+1080+100interest =K+1180$. Marginal growth of price level: (K+1180)/(Y+1080). In percentages is this: GDP <8%, Capital <10%, Inflation is i>g with declining absolut numbers for upgrown economies. The decline is further enforced by the fact, that K in principal always will grow faster than Y, such that at the end is K>>Y. From which then follows crisis as interests and growth both go slowly to zero.

    Well, what is the credo of this simple example? From modeling you can go from top to bottom or from bottom to top as well. Top to bottom mostly is easier, but less intuitive. Going from bottom to top is the path, which are tried by so called agent-based models or accounting-models. But there the imperative for any model is the same as top down: If and only if the principal ansatz is correct (which means close enough to reality) , the outcome will be correct (close to reality). So: If you give your agents the real nature, you will get real outcomes. Otherwise you will fail, regardless how correct and sophisticated your following mathematical derivations may be. And to say it once more, the macro-outcomes will be the same, as logic, which means math, is unique. Besides: The classical example for such a successful application of an agent-based model is the so called Statistical physics or commonly known as Thermodynamics. Agents for example are there elementary particles, or Atoms or Molecules. If you give them the correct nature, the sum of the stochastic interplay of this micro-agents give you indeed exact the same macro-formulas as those which can be derived from macroscopic facts also.

    Cite „…do we want to explain the idea that structure and individual choice mutually condition one another. If so – how? What is the path and process?

    Yes both condition each other. It is as with gravity or also with thermodynamics: Everybody deals with forces and heat although not knowing how it works exactly. It is experience and behavior. In the sum of millions of agents (people) the individual behavior doesn’t matter very much. But at small numbers it gets more interesting: e.g. in economy the behavior at stock markets where a relatively small number of agents are working together with there special rules.

    Cite: „We must ask whether GDP is an adequate measure of welfare on its own. If not, how do we change it? Every time I look in this direction, I am always confronted by the issues of adequate definition repeatedly raised by lyonwiss on this blog.“

    Well, my opinion is that this new mode in economics stems from the fact that GDP numbers are not well enough (stagnating or even decreasing), so lets think of another advertising number which sounds better. So it is with hedonizing inflation and even GDP in the USA, UK and Commonwealth countries. To hedonize this numbers means to take into account not the money paid in reality for it, but a fictional price which multiplies the real number with a (growing) quality factor. This leads to seemingly lower inflation rates but to much higher growth and absolute GDP as well. Even a stagnating GDP seems to grow then. Especially the US-growth is much overestimated by this obscure system. E.g. not only computers, but nearly everything including rents for flats are multiplied every year with a ever growing „quality“-factor, which assumes of course ever growing quality with better techniques. E.g. TV-Screens in HD double the resolution of pictures as well as the hedonised price. And of course flats always get better in time, they should have a closer look Detroit City I think. Decrease of quality self-evidently is never taken into account. At a rule of thumb we can estimate that US-GDP thus is about 3 to 4% less than advertised, and since the 1990ties there is indeed a more or less stagnation.

    Now may be, measuring „luckiness“ may be a „better“ number for the people. But it has at least two big problems: First of all, for economic calculations it is useless (useless as hedonized numbers). Second: How will you measure such creamy numbers? Will the measure be stringent and reliable and also advertise declining „luckiness“? And if you do, what are the numbers for in practical issues? E.g. years ago I remember there was a international study here in luckiness of the average people. It showed that Germany, one of the richest countries in the world, got a very bad rank. Astonishingly on the first rank was Pakistan, one of the poorest countries, a quasi failed state full of corruption and mismanagement. So what shall we do? Follow the „best“ of all countries?

  12. sergio
    September 5, 2013 at 4:04 pm

    As far as I know, economics is the only social science which uses mathematical modeling.
    I cannot imagine if mathematical modeling is used, for example, in preschool pedagogy.
    Even in business they have hundreds of different business models, but they are not founded on purely mathematical models, but on logic, strategy and experience of others. In economics we have tyranny of only ONE model “utility maximization – profit maximization”. It would be complete disaster if firm in reality did as neoclassical models tells it to. Of course firms do not listen to neoclassicals, but whole countries are being forced to live as neoclassicals tell them. That is why we have disasters. Any country is free to do according to its own unique business model.

    • September 7, 2013 at 2:19 pm

      one can always search wikipedia for mathematical sociology, etc. or look at the journals such as j math sociology, j math psychology, social networks, math linguistics, math law, jurisdynamics scientrometrics sociometrics math anthro etc neoclassical economists aren’t the only ones overlooking some details

      • sergio
        September 7, 2013 at 3:49 pm

        Thanks ishi! I did not know about existence of those fields simply because they are not mainstream in sociology, psychology or linguistics and they advanced much further in understanding of society than neoclassical economics which still lives in 18th century.
        And I looked at some papers of those fields and I think neoclassical economist better look at methods used in those fields if they want to be called science, which goal is objective inquiry how society works, and not invention of laws which do not exist in reality, to defend itself as the only scientific in economics.
        The complaint about neoclassical economics is not only about its misuse of math, but their primitive vision of reality.

  13. sergio
    September 7, 2013 at 3:55 pm

    Even this paper is more scientific and realistic than whole neoclassical theory of firm.
    “A mathematical model to determine strategic options for a firm using time based financial accounting and physics equations” by Carias, Rui Manuel Roteiro

  14. September 9, 2013 at 7:11 pm

    Lawson makes a lot of sense, but it seems to me that he should be criticising not ‘mathematical modelling’ as such, but what he calls ‘deductivism’, including ‘deductivist mathematical modelling’. It seems to me ( http://djmarsay.wordpress.com/bibliography/debates/which-type-of-mathematics-in-finance/ ) that Turing’s work can be viewed as a ‘mathematisation’ of the work of his mentor, Keynes, that it is not subject to Lawson’s critique, and that it even illustrates the type of emergence that Lawson – rightly – emphasizes. Is Turing’s work not a mathematical model, albeit not of the same type that economists have tended to favour?

  15. sergio
    September 14, 2013 at 6:08 pm

    My concern on the use of mathematics in economics is following. Economics is very attractive to mathematicians and former physicists. But economics is the field of their intellectual exercise and nothing more. They do not want to solve or understand real world problems or at least they naively believe that they can solve real world problems by simple mathematical solution, which can be found by manipulating variables.
    The problem however that the main school which welcomes naive intellectual exercisers (IE) is neoclassical economics, including its branch financial economics. Not institutional economics or others. So, the bad thing is that most of those naive IEs have no idea what evil ideology they serve to. Indeed, neoclassical economics is founded not only on wrong or false but on very evil ideology. It promotes selfishness and greed. It is anti-social and anti-state ideology. And those naive IEs simply serve neoclassical evil ideology to promote it by covering it under pseudo-scientific methods. Of course very few of them ask themselves such questions as Are we really utility maximizing selfish individuals? Is government necessarily bad? Is free market indeed as perfect as my bosses from Chicago tell me? Is cooperation and not competition the driving force of market? Is real world works exactly the same way as my bosses tell me? Very few ask these questions. And most of them spend all their lives in intellectual exercise as brainwashed zombies without recognizing that they contribute to promotion of neoclassical ideology and not to understanding of economies.
    The solution is not that other schools must use more mathematics too in order to attract IEs.
    The problem is in dominating ideology. Unless the selfishness and greed dominates economics we never understand anything else and never solve real world problems.
    However we can model cooperative behavior, we can model good government, we can model non-price non-monetary solutions, we can model social behavior. We can model anything. For good, to understand how economies really work. And those talented individuals can contribute to it. Unfortunately, gifted but naive IEs spend their talents to promote neoclassical ideology and not to understand reality. What a waste!
    Neoclassical economists say that moral values do not matter for science and their method and vision of economy is objective and irrelevant to moral values. That is big lie. If that was true their models would include dozens more types of behaviors of individual, where social behavior was the main. Moral values of researcher do matters in Economics, as in any social science!
    So the problem is NOT in mathematical modeling but in dominating ideology.

    I am talking about truly naive gifted individuals, not about those who know what they do for what they get, who after series of complex mathematical manipulations “discover” that deregulation of markets is scientific solution.

    • September 16, 2013 at 6:04 pm

      Economists and financiers have employed mathematicians to either support their views or to make money in the short-run, which only requires the type of mathematics that you deplore. But Keynes started as a mathematician, and drew on the insights of Whitehead and Russell to critique economics as he found it (which was much like that you deplore).

      My view is that we would all benefit from such mathematics being used now, and I fear that we will repeat the crises of the past if we do not. Hence my blog.

  16. sergio
    September 16, 2013 at 4:13 pm

    Interesting article on the topic “Models in Economics Are Not Nomological Machines:
    A Pragmatic Approach to Economists’ Modeling Practices” by Cyril Hédoin

    • September 16, 2013 at 6:00 pm

      The Cartwright assumption is that economic modelling has only one purpose and her hypothesis is nomology or discovery of laws. This is clearly an absurd assumption, which does not need a long philosophical dissertation to dismiss.

  17. sergio
    September 16, 2013 at 4:29 pm

    Another interesting paper about “objective scientists- neoclassical economists”
    “Ideology and the theory of financial economics” by George M. Frankfurtera, Elton G. McGoun

  18. sergio
    September 17, 2013 at 4:32 pm

    In the book “Economic Development” by Todaro and Smith there is a small section about false-paradigm. It seems that the whole neoclassical economics is just false-paradigm. It is designed, invented and promoted through education with the only goal – to foolish. However even “foolish” does not seem so altruistic, and I wonder what may be the real motive behind false-paradigm of neoclassical economics.

  19. March 6, 2014 at 3:52 pm

    Let me add a remark on the application of mathematics to human constructs. The Hausdorff dimension of the human brain is approximately 2.72. That sounds like a complex multi-fractal to me. There exists mathematics that can handle such complexity; that is the Singulaity Spectrum. Economists simply must learn it and shun Newtonian mechanics.

  20. March 7, 2014 at 6:45 pm

    I my humble opinion, the discussion about the applicability of mathematics to economics arises from the the attempt to apply the axioms of perfect competition to modern markets. In perfect competition all the assumptions of homogeneity, complete information and the tendency toward an equilibrium, etc.,are true. Of course, there are a few incongruities; as Steve Keen has demonstrated, the demand curve of a single firm is not linear. In perfect competition, if a firm (consumer) increases its endowment by one unit, that will have an infirm impact on the equilibrium price. However, this will not prevent the achievement of an equilibrium. Walras has observed a pure exchange market at the Bourse of Paris. If one can observe the budget distribution and the endowments of each consumer, the system matrix is a positive Metzler matrix, and the equilibrium is a stable fixed-point.
    Problem arises when one attempts to apply these assumptions to a modern market, which should be analyzed as a stochastic and non ergodic process.
    The mathematics of perfect competition are not applicable to modern markets. If economists are blamable is for not have turned the page as physicists have done after Maxwell.

  21. santini
    March 12, 2014 at 3:27 am

    Mathematical modellers in economics are similar to mathematical modellers in climate – if only they were as proficient at modelling as they are at explaining why their models didn’t fit events in the real world.
    Does mathematics bring anything useful to the understanding of economics ? Not at present. Will it eventually be useful ? Maybe.

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