Debunking the use of mathematics in economics

28 May, 2015 at 20:02 | Posted in Economics | 3 Comments

What guarantee is there … that economic concepts can be mapped unambiguously and subjectively – to be terribly and unnecessarily mathematical about it – into mathematical concepts? The belief in the power and necessity of formalizing economic theory mathematically has thus obliterated the distinction between cognitively perceiving and understanding concepts from different domains and mapping them into each other. math-520x245Whether the age-old problem of the equality between supply and demand should be mathematically formalized as a system of inequalities or equalities is not something that should be decided by mathematical knowledge or convenience. Surely it would be considered absurd, bordering on the insane, if a surgical procedure was implemented because a tool for its implementation was devised by a medical doctor who knew and believed in topological fixed-point theorems? Yet, weighty propositions about policy are decided on the basis of formalizations based on ignorance and belief in the veracity of one kind of one-dimensional mathematics.

K. Vela Velupillai

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  1. Hold the handle, not the blade
    Comment on ‘Debunking the use of mathematics in economics’
    .
    What Velupillai criticizes is the application of topology in equilibrium theory. The persistent abuse of mathematics is a rather obvious fact that has been observed by many — notably heterodox economists.
    .
    “It is difficult to contemplate the evolution of the economic science over the last hundred years without reaching the conclusion that its mathematization was a rather hurried job.” (Georgescu-Roegen, 1979, p. 271)
    .
    That economists misapply mathematics is what Velupillai said on numerous occasions. He said also:
    “Somewhere between the Political Arithmetician, alias the National Income Accountant, and the Financial Analyst, alias the Accountant, lies the task of the quantitative economist’s analytical role, and none of the theoretical or applied tasks of these two pragmatic and paradigmatic figures requires anything more than arithmetic, statistics and the rules of compound interest.” (Velupillai, 2005, p. 866)
    .
    The fact of the matter is that economists even messed up the simple mathematics of accounting (2012).
    .
    What economists have attempted again and again is to take a mathematical tool and then to reformulate the economic problem so that it fitted the tool. Calculus, for example, required the introduction of a production function and decreasing returns. This led to some funny cognitive dissonances.
    .
    “’So, Brian, what are you working on these days?’ Arthur had given him the the two-word answer just to get started: ‘Increasing returns.’ And the economics department chairman, …, had stared at him with a kind of deadpan look. ‘But — we know increasing returns don’t exist.’ ‘Besides,’ jumped in Rothenberg with a grin, ‘if they did, we’d have to outlaw them!’ And then they’d laughed.” (Waldrop, 1993, p. 18)
    .
    This is how reality vanished from economics. The same funny logical headstands happened with topology.
    .
    “Surely it would be considered absurd, bordering on the insane, if a surgical procedure was implemented because a tool for its implementation was devised by a medical doctor who knew and believed in topological fixed-point theorems?” (See intro and also Nadal, 2004, p. 36)
    .
    From the fact that Orthodoxy always holds the knife at the blade with terrible results, however, does not follow that knives have to be abandoned but only that Orthodoxy has to be abandoned.
    .
    By the way, the appropriate mathematical tool for the solution of the ‘age-old problem of the equality between supply and demand’ is not a set of equations but a simulation (2015, Sec. 4).
    .
    Egmont Kakarot-Handtke
    .
    References
    Georgescu-Roegen, N. (1979). Energy and Economic Myths, chapter Measure,
    Quality, and Optimum Scale, pages 271–296. New York, NY, Toronto, etc.:
    Pergamon.
    Kakarot-Handtke, E. (2012). The Common Error of Common Sense: An Essential
    Rectification of the Accounting Approach. SSRN Working Paper Series, 2124415:
    1–23. URL http://ssrn.com/abstract=2124415.
    Kakarot-Handtke, E. (2015). Essentials of Constructive Heterodoxy: The Market.
    SSRN Working Paper Series, 2547098: 1–10. URL http://papers.ssrn.com/sol3/
    papers.cfm?abstract_id=2547098.
    Nadal, A. (2004). Behind the Building Blocks. Commodities and Individuals in
    General Equilibrium Theory. In F. Ackerman, and A. Nadal (Eds.), The Flawed
    Foundations of General Equilibrium, pages 33–47. London, New York, NY:
    Routledge.
    Velupillai, K. (2005). The Unreasonable Ineffectiveness of Mathematics in Economics. Cambridge Journal of Economics, 29: 849–872.
    Waldrop, M. M. (1993). Complexity. London: Viking.

  2. Reblogged this on DAMIJAN blog.

  3. “Especially in the last few decades, the dominant
    direction among our economists at home and in the Anglo-Saxon
    Countries limited their view more than before, more than
    Marshall and Adam Smith, who actually was more of institutionalists.

    They thus, as I see it, strayed further and further from the true
    reality. In their basic high-theoretical works they write
    for each other as one from any other civics isolated
    sect, which must do their research increasingly less realistic and
    relevant.
    Meanwhile, they have expanded their research apparatus in econometrics,
    ie, mathematical, direction which should mean a further
    restriction of the field of view.

    Gustav Cassel, who was indeed a highly trained mathematicians before
    he became an economist, used to say that when he met wordy
    mathematical expositions,that he usually read only the text that
    accompanied them to see if the author could have something relevant to say,
    and if it could be true. Otherwise,he lay the scripture aside. Formulas
    can at best only be illustrations, he told.

    Cassel had a rare ability to so to speak, to think concretely and
    abstract at the same time. And the practical knowledge he picked up
    by a diligent reading of statistics and newspapers, and from conversations, became immediately and without having formulated inserted directly into his theoretical generalizing.

    In what he himself wrote, he was referring to the greatest simplicity and
    comprehensibility. Cassel aspired to, as he used to say,
    write so that “a farmer with common sense would understand him.”
    Behind this setting low in him the belief that “nature is fundamentally simple,”
    as healso used to say. He had his intellectual maturation during
    influence of the neo-darwinism before and around the turn of the century.

    I have on the contrary been taught that human relationships are extremely
    complicated, and this is the deeper meaning of my
    institutionalism. But just because of that, I have to strive for the greatest possible
    simplification and comprehensibility, and I therefore follow Cassel well , although for the opposite reason.”
    Gunnar Myrdal Hur styrs landet?page 16-18


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