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Keynes on the use of mathematics in economics

from Lars Syll

But I am unfamiliar with the methods involved and it may be that my impression that nothing emerges at the end which has not been introduced expressly or tacitly at the beginning is quite wrong … It seems to me essential in an article of this sort to put in the fullest and most explicit manner at the beginning the assumptions which are made and the methods by which the price indexes are derived; and then to state at the end what substantially novel conclusions has been arrived at …


I cannot persuade myself that this sort of treatment of economic theory has anything significant to contribute. I suspect it of being nothing better than a contraption proceeding from premises which are not stated with precision to conclusions which have no clear application … [This creates] a mass of symbolism which covers up all kinds of unstated special assumptions.

Letter from Keynes to Frisch 28 November 1935




  1. bruceedmonds
    July 7, 2014 at 9:54 am

    Any tool can be used wrongly – mathematics is no exception. Well used, formal tools, such as mathematics, can be used to make assumptions explicit, and indeed reveal hidden assumptions. However the spirit of the Keynes quotes hits somewhere close to the mark – neo-classical economics took analytic mathematics as the crucial mark of science, and has largely ignored the bit about evidence trumping theory. Thus the wish for analytically tractable maths has biased economics away from more appropriate tools (such as agent-based simulation), but the biggest error is the drift away from explaining what we observe rather than what fits neat formalisms.

  2. July 7, 2014 at 12:31 pm

    Totally agree with Keynes’ remark on mathematics in economics. Economists are lousy mathematicians. Contrary to Krugman’s comment about mathematical beauty in economics, I find the mathematics in economics generally very ugly. Often, symbols are used wastefully, equations appears much more complicated than they need to be, formulas are repetitious, etc. all signs of mathematical incompetence.

    Pick up nearly any paper on mathematical modelling in economics, you will find assumptions galore, spread randomly all over the paper (if stated at all), typically without economic justification, seemingly made in an ad-hoc fashion in order to draw some conclusions. The conclusions themselves, as far as economic content is concerned, are either weak or unclear. What great theorem of real substance has economics ever deduced?

    Nothing much has changed since Keynes’ remark (GT, 1936, p.298):

    Too large a proportion of recent ‘mathematical’ economics are merely 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.

    Mathematics is undoubtedly important in economics, but it has not been proven to be important due to pretentious incompetence.

  3. Esteban Perez Caldentey
    July 7, 2014 at 2:40 pm

    • One can find statements by Neo-Classical economists arguing how Keynes despised mathematical economics. A classical example is Samuelson (1946, Econometrica):

    “From Marshall’s early influence, no doubt, stems Keynes’s antipathy toward the use of mathematical symbols, an antipathy which already appears, surprisingly considering its technical subject, in the early pages of the Treatise on Probability” (p. 197).

    • One can also find a similar point of view in non Neo-Classical economists. I think Athol Fitzgibbons, Keynes’s Vision (1990) (pp.138-143) where he argues that “Keynes’s opposition to mathematical economics was part of well defined philosophy which is particularly crucial to understanding the General Theory” (p.139). Skidelsky is another example.

    • But it seems to me that if one reads Keynes carefully [especially the sources quoted by those who are convinced of his antipathy towards mathematics such as his exchange with Harrod for example on method following the Harrod’s speech on the Scope and Method of Economics, August, 1938, pp. 295-300, his comments on Tinbergen’s regressions and empirical work (‘hocus’) Vol. XIV pp.306-319; his comments on Edgeworth’s Psychics, Vol. X, p.262 (2010, Palgrave McMillan edition) and the GT], one will find that Keynes protested more against what he called pseudo mathematics than against mathematics proper.

    For example take the GT p.297: “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 in disallowed”

    And then on p. 298: “Too large a proportion of recent ‘mathematical economics’ are mere concoctions…”

    In the draft to the GT the passage I think was more direct because it clearly highlighted the difference between pseudo math and math proper (my highlights below) Vol. XIV (CW) p. 512: “ ‘mathematical economics,’ especially such as increasingly disfigure the pages of contemporary journals, are mere concoctions, which serve no purpose except to give non-mathematicians, a spurious aesthetic satisfaction, aping that of mathematics proper ” .

    Another quote to illustrate that point: is one his exchanges with Harrod following Harrod’s Scope (1938) Keynes explains (Vol. XIV, p. 299): “I think we are a little bit at cross purposes…I think it most important, for example, to investigate statistically the order of magnitude of the multiplier…to convert a model into a quatitative formula is to destroy its usefulness as an instrument of thought.’

    • The fact that one finds many equations in the GT as well as the use of empirical methods in the estimation of the multiplier for example the differences in magnitude between the US and Great Britain also point in the direction that Keynes’s disliking and criticism was aimed at pseudo mathematics. O’Donnell (1989) is of this opinion.

    • In the GT he makes a related criticism which is that NC theory often presents its arguments in terms of what he called Ignoratio Elenchi (refers back to the sophists. Using an argument to purport an argument that does not follow from it. i.e., applying real analysis to analyze the workings of monetary economies.

    • I don’t think also that he expressed particular rejection say to Ramsey’s Mathematical Theory of Saving neither in their exchange of letters on it (CW, Vol. XII, pp. 784-789) or in his biographical piece on Ramsey in Essays in biography. Also he makes use of math in his lectures and transition from the Treatise to the GT.

    • From my point of view I think a useful starting point is how he addressed the problem of the precise expression of concepts in economics. Vol. XIX pp.35-39.

  4. davetaylor1
    July 9, 2014 at 7:18 am

    Esteban, your comments rang all sorts of bells, having encountered Keynes through his “Treatise on Probability”, Ramsey’s rebuttal of it through Passmore’s “100 Years of Philosophy”, met up with Athol Fitzgibbons to discuss his 2000 book, “The Nature of Macroeconomics” (with its Appendix on Keynes’ [supposed] recantation), worked with the precise definition of concepts in computing, and just read this interesting review of CW XIX: http://www.lrb.co.uk/v04/n10/peter-clarke/can-maynard-keynes-do-it ].

    I’ve seen in this blog that Samuelson found Keynes difficult, so never read him (c.f. Chesterton on Christianity), which is about on a par with formalist Ramsey’s inability to see through Keynesian eyes, in which reality came first and over-concise mathematics failed to draw attention to it. (C.f. Chesterton in “G F Watts” on words indexing experience: on verbal and artistic languages triangulating the meaning of e.g. “Hope”).

    I keep mentioning Chesterton because academic appreciation of his insights anticipating the findings of split-brain scientific research and the solution to Russell’s contemporary logical problem, unresolvable in the language of Principia Mathematica, has been on a par with that of Samuelson on Keynes. Chesterton’s solipsistic adversary in an early autobiographical essay “The Diabolist” may be taken either as, if not David Hume, one of his disciples at that beginning of the Logical Positivist period, among whom Keynes was brought up and endevouring to find himself. The problem of Keynes’s “Treatise” was that of Hume’s “Treatise”: finding an alternative to the dubious logic of Induction as portrayed by Hume in defence of the atheistic (diabolical) scientific and social democracy which now passes for “method” in the social sciences, not least our financier’s form of political economics.

    What I discovered only comparatively recently, by actually reading classics I had had on my shelves for years, was Sir Francis Bacon inventing a real scientific method (and encyclopaedias as a way of recording, transmitting and sharing its findings), precisely by rejecting the naive view of Induction Hume had still taken for granted almost a hundred and fifty years later. This from Bacon’s “The Great Instauration”(the arguments for the several parts, paras10-12). [http://www.constitution.org/bacon/instauration.htm]

    “For the induction of which the logicians speak, which proceeds by simple enumeration, is a puerile thing, concludes at hazard, is always liable to be upset by a contradictory instance, takes into account only what is known and ordinary, and leads to no result.

    “Now what the sciences stand in need of is a form of induction which shall analyze experience and take it to pieces, and by a due process of exclusion and rejection lead to an inevitable conclusion. … Nor is this all. For I also sink the foundations of the sciences deeper and firmer; and I begin the inquiry nearer the source than men have done heretofore, submitting to examination those things which the common logic takes on trust. … I hold that true logic ought to enter the several provinces of science armed with a higher authority than belongs to the principles of those sciences themselves, and ought to call those putative principles to account until they are fully established. … For the testimony and information of the sense has reference always to man, not to the universe; and it is a great error to assert that the sense is the measure of things. To meet these difficulties, I have sought on all sides diligently and faithfully to provide helps for the sense — substitutes to supply its failures, rectifications to correct its errors; and this I endeavor to accomplish not so much by instruments as by experiments”.

  5. Hepion
    July 14, 2014 at 2:55 am

    “Lots of what they are doing… is not economics” -Joseph Stiglitz

    That’s right. Economics is a study of economy, political propaganda is quite an another thing. But there are lots of political propaganda masquerading as economics.

    It is time to call spade a spade.

  6. July 18, 2014 at 10:21 pm

    Although a sceptic of Keynes it can be seen that in the British education system, particularly at university at places such as LSE, the use of maths in economics represents the majority of what you do and how you are taught and that in order to succeed in the area you must be good at maths before being good at economics. It seems the economics of today is seen by some to be based on maths, rightly or wrongly.

    • July 19, 2014 at 12:34 pm

      In the latter part of the 1980s, I was part of the diaspora of “rocket scientists” who became “quants” in investment banking and funds management. I made far more money than I would have in academia.

      But after several years, I left, being disillusioned by my superiors who were using my efforts to make far more money selling deception to other pretentious managers managing other people’s money.

      Nothing was learned by regulators from a string of disasters around that time: Orange Country, Gibson Greeting Cards, Metallgesellschaft, etc, then later LTCM. To avoid LTCM-type of revelation, derivatives were formally deregulated by Summers, Greenspan et al. The quadrillion OTC derivatives market today, with “anything goes” mark-to-model-myth accounting is probably hiding trillions of losses.

      The mathematics in financial economics was, and still is, way, way ahead of micro or macroeconomics, which have, even now, no real notion of risk, assuming nothing (particularly its “laws”) could ever go wrong. It is laughable that standard advanced textbook such as Walsh’s “Monetary Theory and Policy” has less than four pages mentioning credit default risk.

      The truly stupid assumption of academics like Krugman and the central bankers is that “the amount of debt doesn’t matter”, because there are always also assets balancing the debts and that “sophisticated investors” such as investment banks would have full and completed knowledge, making rational and calculated decisions. My personal experience is that the situation is nothing like that.

      Mathematics has been used too often as an instrument of deception. It has been effective fraud because, like the emperor’s new clothes, everyone was always smart enough to see how beautiful and ingenious the deals or the arguments were. We will know about this deception when the OTC derivatives market explodes as a weapon of financial mass destruction in a startled world.

      The City of London is the global epicenter of financial fraud: money laundering, rigging markets, extorting governments etc. using a dazzling array of mathematics, economic models, AI algorithms, HFT etc. Sophisticated mathematics has been an essential instrument of accounting control fraud. It pays very well.

      • July 21, 2014 at 10:36 pm

        I’m not sure if you’re disagreeing or agreeing with what I have said or whether you are just voicing your experience, all the while still an insightful look into investment banking.

      • July 22, 2014 at 4:39 am

        Yes, mathematical skills in economics and finance pay very well, for reasons I explained. LSE and other UK universities are responding to demand by students who want high paying jobs. This is one of main reasons for the mathematization we see and it is not a good reason.

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