Paul Samuelson — a case of badly invested intelligence

9 Jul, 2019 at 11:47 | Posted in Economics | 19 Comments

Paul Samuelson claimed that the ‘ergodic hypothesis’ is essential for advancing economics from the realm of history to the realm of science.

But is it really tenable to assume that ergodicity is essential to economics?

The answer can only be — as I have argued






here — NO WAY!

Obviously yours truly is far from the only researcher being critical of Paul Samuelson. This is what Ole Peters writes in a highly interesting article on Samuelson’s stance on the ‘ergodic hypothesis’:

Samuelson said that we should accept the ergodic hypothesis because if a system is not ergodic you cannot treat it scientifically. First of all, that’s incorrect, although I think I understand how he ended up with this impression: ergodicity means that a system is very insensitive to initial conditions or perturbations and details of the dynamics, and that makes it easy to make universal statements about such systems …

Another problem with Samuelson’s statement is the logic: we should accept this hypothesis because then we can make universal statements. But before we make any hypothesis—even one that makes our lives easier—we should check whether we know it to be wrong. In this case, there’s nothing to hypothesize. Financial and economic systems are non-ergodic. And if that means we can’t say anything meaningful, then perhaps we shouldn’t try to make meaningful claims. Well, perhaps we can speak for entertainment, but we cannot claim that it’s meaningful.

And this is Nassim Taleb’s verdict on Samuelson’s view on how to do economics:

mathscience The tragedy is that Paul Samuelson, a quick mind, is said to be one of the most intelligent scholars of his generation. This was clearly a case of very badly invested intelli­gence. Characteristically, Samuelson intimidated those who questioned his techniques with the statement “Those who can, do science, others do methodology.” If you knew math, you could “do science.” … Alas, it turns out that it was Samuelson and most of his followers who did not know much math, or did not know how to use what math they knew, how to apply it to reality. They only knew enough math to be blinded by it.

Samuelson was a formalist committed to mathematical economics. Where did this methodological stance take him? Nowhere I would argue. It is one thing to come up with ‘minimally realist’ models of ‘possibly true’ worlds.’ And something completely different to give us relevant truths about real-world systems. Just giving us a set of possible truths doesn’t suffice. We are looking for how-actually explanations and not how-possibly explanations. The model world is not the real world. Model worlds may well be ergodic. Real-world economies are not. So how then, could one possibly learn anything economically relevant and interesting using an ergodic model that obviously badly misrepresent the world in which we live? Providing us with knowledge of possibilities is not enough. Genuine understanding and explanation demand knowledge of causes, not knowledge of possibilities. Although mathematics may teach us — without empirical knowledge — why a mother cannot evenly divide her twenty-three apples among three children without cutting any of the apples, we have to remember that most relevant economic problems and issues are of a much more complex and different nature. In real-world economies, purely mathematical explanations do not take us anywhere.

Samuelson’s elaborations on revealed preference theory show this in an illuminating way. The very raison d’être for developing revealed preference theory in the 1930s and 1940s was to be able to ascertain people’s preferences by observation of their actual behaviour on markets and not having to make unobservable psychological assumptions or rely on any utility concepts. This turned out to be impossible. Samuelson et consortes had to assume unchanging preferences, which, of course, was in blatant contradiction to the attempt of building a consumer and demand theory without non-observational concepts. Preferences are only revealed from market behaviour when specific theoretical constraining assumptions are made. Without making those assumptions there are no valid inferences​ to make from observing people’s choices on a market.

But still, ​a lot of mainstream economists consider the approach offered by revealed preference theory ​great progress. As people like Robinson, Georgescu-Roegen, and Kornai have shown, this is, however, nothing but an illusion. Revealed preference theory does not live up to what it claims to offer. As part of the economist’s​ tool-kit, ​it is of extremely limited use.

If we want to be able to explain the behaviour and choices people make, we have to know​ something about people’s beliefs, preferences, uncertainties​, and understandings. Revealed preference​ theory does not provide us with any support whatsoever in accomplishing that.

So why did Samuelson basically fail in his theoretical endeavours?

One reason is that he did not — like most of mainstream economists that have followed in his footsteps — seriously reflect on the fact that limiting model assumptions in economic science always have to be closely examined since if we are going to be able to show that the mechanisms or causes that we isolate and handle in our models are stable in the sense that they do not change when we ‘export’ them to our ‘target systems,’ we have to be able to show that they do not only hold under ceteris paribus conditions and a fortiori only are of limited value to our understanding, explanations or predictions of real economic systems.

Another reason is that he confused epistemology and ontology. The validity of the inferential models we as scientists use ultimately depends on the assumptions we make about the entities to which we apply them. Applying a relevant modelling strategy presupposes far-reaching ontological presuppositions. If we are prepared to assume that societies and economies are like urns filled with coloured balls in fixed proportions, then fine. But — really — who could earnestly believe in such an utterly ridiculous analogy? We are not mainly interested in what could be true, but what is true. In a real world full of ‘unknown unknowns’ and genuine non-ergodic uncertainty, urns are of little avail.

The ‘ergodicity hypothesis’ provides a totally wrong-headed picture of the processes that operate in real-world economies. Ergodicity is not relevant for studying actual economic processes. It doesn’t actually explain anything of what goes on in real-world economies. How it could be claimed by Paul Samuelson to be essential for advancing economics to the realm of science is beyond comprehension.


  1. Lars,

    The link to Peters’ paper doesn’t seem to work.

    Do you have the title of the paper?

  2. Fixed 🙂

  3. It was really Samuelson that started the whole thing of conflating mathematics with science. He seems to have fancied himself of something of an Einsten who could apply universal laws to the workings of an economy – something for which it is totally inappropriate. Apparently this gimmickry was an ‘advancement’ on history. The truth is that whatever history was known has certainly been forgotten, and the legacy of Samuelson has been picked up by equally and even more fanatical anti-social morons – Sargent, Fama… the list goes on. The social and political consequences of their excesses on a discipline that does not ask basic ontological or epistemological questions is becoming very evident.

  4. it is remarkable to me that Samuelson was smart enough in the right way that he could articulate that he had assumed ergodicity, but still stupid enough or blind enough in another way that he would refuse to acknowledge a recognition that the actual market economy could not be an ergodic system (and that the actual economy is not ergodic has vastly important consequences for how we can think about the economy as a system.
    That latter — the not-seeing that the economy cannot possibly be ergodic — is the part worth exploring. Samuelson had to abstract away from the aspects of the actual economy that make it certain that it cannot be ergodic, What was he not seeing and how did he justify deliberately not-seeing it?

  5. Contrary to Prof. Syll:
    1). Álvarez & Ehnts:
    “It is not correct to say that Samuelson in his “quest to provide a hard scientific basis for the economics discipline modern economists” requires the acceptance of the ergodic theorem.”
    – Álvarez & Ehnts, JPKE 2016 – Samuelson and Davidson on ergodicity: A reformulation
    2). Yoshinori Shiozawa:
    “Samuelson nowhere claimed that “ergodic hypothesis” is “a sine qua non of economics as science” as Davidson argues. Samuelson only pointed that ergodicity is necessary if the classical dichotomy works independent of initial distribution of money. Ergodic axiom is not an axiom of neoclassical economics but rather a scarecrow invented by Davidson. It is not exact to say that the ergodic axiom is
    one of three axioms that Keynes rejected. It may be implied from his idea but Keynes had no clear idea of the axiom. In addition, Davidson’s concept of ergodicity does not exactly correspond to physics concept of ergodicity. Alvarez and Ehnts (2014) reasonably propose to use terms stochastic and non-stochastic randomness instead of ergodicity which has an ambiguous meaning in economics.”
    – Shiozawa 2016 – Comment

    – Shiozawa 2016 – Microfoundations of Evolutionary Economics, page 34, fn 16

    • I think these comments are missing the forest for the trees. When Samuelson makes comments like “Those who can, do science, others do methodology” he clearly is not terribly interested in the wider consequences of his methodology and supposed laws. Likewise, Keynes may not have mentioned the word ergodicity but I think we can make a fairly good deduction on where he would stand on the issue, and for that matter on Samuelson’s methodological approach:

      “But these more recent writers like their predecessors were still dealing with a system in which the amount of the factors employed was given and the other relevant facts were known more or less for certain (Keynes, 1937).”

      When Keynes refers to “pretty and polite techniques” in his 1937 article on uncertainty, it is very much the kind of stuff Samuelson did which he had in mind:

      “All these pretty, polite techniques, made for a well-panelled Board Room and a nicely regulated market, are liable to collapse. At all times the vague panic fears and equally vague and unreasoned hopes are not really lulled, and lie but a little way below the surface (Keynes 1937)

      More here:

      “And even to this day, people still reject Keynes’s overall philosophical claims, or at least continue to follow those who made this mistake. For example Paul Samuelson automatically rejected this philosophical issue on the basis of the assumption of the ergodic axiom and did much work under this assumption, see for example, Samuelson’s “Optimality of Sluggish Predictors under Ergodic Probabilities” (1976) or “What Classical and Neoclassical Monetary Theory Really was” (1968). It is worth to note that his answer for using the ergodic assumption, thus rejecting Keynes’s philosophical emphasis, was on the grounds that if one rejected the ergodic principle, one rejected calling economics a science (1969: 12).

      Samuelson does have a point, how can a subject be in the realm of the subject of science if we can not make precise quantitative predictions similar to how we do hard science? There is no clear answer to this, but one argument that appeals to me is that there is a clear difference to what a hard science is and what a social science is. Different subjects often calls for different sets of tools and different questions to answer. Economics is in the category in trying to explain the ‘irrational’ subjective human.”

      • @ Nanikore
        I can’t see how you are able to “make a fairly good deduction”, or indeed any deduction, about Keynes undertanding of ergodicity from the quotes which you mention above.
        Likewise your lengthy quote from “radicalsubjectivist” has no force because he (like Davidson and Prof. Syll) fundamentally misunderstands the Samuelson articles which he references.
        These articles provide no evidence whatsoever that Samuelson believed that if “one rejected the ergodic principle, one rejected calling economics a science”.
        Please deal with the pertinent arguments in the references which I gave above.

        • Again, I think you are missing the forest for the trees. The issue is if an economy is not an ergodic system, is Samuelson helpful? I would argue, no it is not. You are entitled to agree or disagree – and please make the case that you find Foundations helpful and not a costly distraction for understanding capitalism, Keynes and dealing with our current problems. But at least there should be a discussion of what the real underlying philosophical foundations of Samuelson’s Foundations actually are and what the alternatives to neo-classical economics could be.

  6. I think this man done worse harm than even Milton Friedman! Reading his horrible, “Economics” in courses in grad studies,still leave horrible memories. and one had to be de-promoted for a long time after that!

    • I disagree with Friedman, but at least it was slightly interesting. I have also got terrible memories of wasted youth reading the dreary banality of Samuelson’s Foundations.

  7. I absolutely agree Jan. At least Friedman can be refuted with evidence. Very interesting Lars to see this reference to Samuelson in the Black Swan. Economists like Wren Lewis are whinging that there is a lot of scepticism among the general public towards experts. In the case of economists, however, this is fully justified. It is important that the undeification of Samuelson, Sargent et al takes place. This is only way we can start then studying capitalism properly, start coming up with answers to its problems and then be in a credible position to start taking on dangerous populists – Trump, Farage etc.

    During the Neo-liberal heyday (1980-2008) economists, like Goldman Sachs traders, were sacrosanct. This was the era when Summers, Greenspan and Rubin were on the cover of Time Magazine and called the “Masters of the Universe”. Economists, armed with battalions of obfuscating algebra, got their way. I remember a writer in the FT, clearly ahead of his time, wrote a very critical obituary of Samuelson – accusing him of dumbing down the subject and creating ‘mechanical vacuity”. Krugman publicly objected. I think the FT then edited it for their online editions. That was the degree of power and influence economists had during the so-called Great Moderation.

  8. In the spirit of the post, when some evoke the term economist I plainly ask which school of they are referring too …. the looks I get …. chortle …

    • I think the problem is the opposite – there is a strong orthodoxy (neo-classical economics, a derivative of classical economics) which at its core is Ricardian. We need more pluralism and more questioning of how this school of thought and underlying Victorian philosophy became and remained so dominant.

      • The thrust of the observation is the lack of opposing views or the suggestion that for most sundry and in some cases practitioner – economics is a monolithic undertaking. Some of this can be simply reconciled by educational factors – see Philip Mirowski et al.

        Terms like path dependency and incentive come to mind, along with other heterodox observations.

        Curious that you say ‘Victorian philosophy’ when sometimes I get the sensation that were still living through the extenuation of the Council of Nicea.

  9. Nanikore quoted:
    “At all times the vague panic fears and equally vague and unreasoned hopes are not really lulled, and lie but a little way below the surface (Keynes 1937)”
    We know how to fix those fears: insure, hedge, print money to end runs.
    Fears and real-world uncertainty may still exist, but we can remove financial uncertainty by ending panic-stricken runs on banks with monetary expansion.
    Basic income gives those of us who don’t want to work for banks an option to self-realize and advance knowledge in a non-profit-motivated way.

    • I am not convinced RM. The history of the build up to the Financial crisis had arguably one of its causes monetary expansion and excess liquidity. Likewise for the problems that led ultimately to the crash in the Euro-periphery. In Japan again a familiar story of loose excess liquidity leading to real estate speculation and bubble.

      The problem is that there has been a mismatch of credit and investment. This will not be solved by printing money.

      I would argue that the only solution is that the Government has to get involved in credit allocation decisions. This goes against the ideas that led up to the 1951 Accord. But to some extent we are already seeing a weakening of this with post 2007 unconventional monetary policy. I would also argue we need to see European style prices and incomes policies.

      The problems in capitalism go much deeper than that which can be solved singularly with macro, particularly monetary, expansions and contractions.

      • “the Government has to get involved in credit allocation decisions.”
        By printing money, but distributing it more equally.
        “The problems in capitalism go much deeper than that which can be solved singularly with macro, particularly monetary, expansions and contractions.”
        Making money artificially scarce for some and not others is the chief problem with capitalism. Making money scarce for banks is politically infeasible; they will elect Reagans and Thatchers and Trumps and Johnsons to repeal any regulations. So, print money for all.

    • Disagree with the premise that “individuals” will – self actuate – from a socially productive perspective based solely on the concept of a basic income aka Free Money.

      Nothing from the historical record supports it, albeit it can keep things ticking over for a time, although it never reconciles the core political flaws that have roots in perspectives like biopolotics.

      Further more banks got the stick post GD only to have the aforementioned rescinded, after a protracted period of effort by the same sorts that initiated the event in the first place. Hence lending with a risk premium was never the issue in the first place, lest one wants to discuss events which parallel certain social views and not intrinsic to banking in of its self e.g. wages and productivity diverging, regulatory forbearance, fiduciary duty, various views on what constitutes democracy, share holder value, rights of citizens comported to legal constructs for investment, I digress.

      So were clear I don’t have much time for the fake warehouse receipts view.

      • Consider Aristotle in Metaphysics Book 1:
        “the sciences which do not aim at giving pleasure or at the necessities of life were discovered, and first in the places where men first began to have leisure. This is why the mathematical arts were founded in Egypt; for there the priestly caste was allowed to be at leisure.”
        Socrates proposed he be maintained in the Prytaneum, which amounts to getting a basic income, in the Apology.
        Athens had a sort of basic income because they distributed proceeds from the mines at Laurion evenly amongst citizens, until Themistocles ended the practice to fund warships.
        The “core political flaws” that basic income addresses is the fundamental theory of value. Basic income says we have value independent of income arbitrarily allocated by capitalists.

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