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The Ramsey-Keynes dispute

from Lars Syll

Neoclassical economics nowadays usually assumes that agents that have to make choices under conditions of uncertainty behave according to Bayesian rules, axiomatized by Ramsey (1931) and Savage (1954) – that is, they maximize expected utility with respect to some subjective probability measure that is continually updated according to Bayes theorem. If not, they are supposed to be irrational, and ultimately – via some “Dutch book” or “money pump”argument – susceptible to being ruined by some clever “bookie”.

calvin-math-atheist3-2Bayesianism reduces questions of rationality to questions of internal consistency (coherence) of beliefs, but – even granted this questionable reductionism – do rational agents really have to be Bayesian? As I have been arguing elsewhere (e. g. here, here and here) there is no strong warrant for believing so.

In many of the situations that are relevant to economics one could argue that there is simply not enough of adequate and relevant information to ground beliefs of a probabilistic kind, and that in those situations it is not really possible, in any relevant way, to represent an individual’s beliefs in a single probability measure.

Say you have come to learn (based on own experience and tons of data) that the probability of you becoming unemployed in Sweden is 10 %. Having moved to another country (where you have no own experience and no data) you have no information on unemployment and a fortiori nothing to help you construct any probability estimate on. A Bayesian would, however, argue that you would have to assign probabilities to the mutually exclusive alternative outcomes and that these have to add up to 1, if you are rational. That is, in this case – and based on symmetry – a rational individual would have to assign probability 10% to becoming unemployed and 90% of becoming employed.

That feels intuitively wrong though, and I guess most people would agree. Bayesianism cannot distinguish between symmetry-based probabilities from information and symmetry-based probabilities from an absence of information. In these kinds of situations most of us would rather say that it is simply irrational to be a Bayesian and better instead to admit that we “simply do not know” or that we feel ambiguous and undecided. Arbitrary an ungrounded probability claims are more irrational than being undecided in face of genuine uncertainty, so if there is not sufficient information to ground a probability distribution it is better to acknowledge that simpliciter, rather than pretending to possess a certitude that we simply do not possess.

I think this critique of Bayesianism is in accordance with the views of John Maynard Keynes’ A Treatise on Probability (1921) and General Theory (1937). According to Keynes we live in a world permeated by unmeasurable uncertainty – not quantifiable stochastic risk – which often forces us to make decisions based on anything but rational expectations. Sometimes we “simply do not know.” Keynes would not have accepted the view of Bayesian economists, according to whom expectations “tend to be distributed, for the same information set, about the prediction of the theory.” Keynes, rather, thinks that we base our expectations on the confidence or “weight” we put on different events and alternatives. To Keynes expectations are a question of weighing probabilities by “degrees of belief”, beliefs that have preciously little to do with the kind of stochastic probabilistic calculations made by the rational agents modeled by Bayesian economists.

Stressing the importance of Keynes’ view on uncertainty John Kay writes in Financial Times:

Keynes believed that the financial and business environment was characterised by “radical uncertainty”. The only reasonable response to the question “what will interest rates be in 20 years’ time?” is “we simply do not know” …

For Keynes, probability was about believability, not frequency. He denied that our thinking could be described by a probability distribution over all possible future events, a statistical distribution that could be teased out by shrewd questioning – or discovered by presenting a menu of trading opportunities. In the 1920s he became engaged in an intellectual battle on this issue, in which the leading protagonists on one side were Keynes and the Chicago economist Frank Knight, opposed by a Cambridge philosopher, Frank Ramsey, and later by Jimmie Savage, another Chicagoan.

Keynes and Knight lost that debate, and Ramsey and Savage won, and the probabilistic approach has maintained academic primacy ever since. A principal reason was Ramsey’s demonstration that anyone who did not follow his precepts – anyone who did not act on the basis of a subjective assessment of probabilities of future events – would be “Dutch booked” … A Dutch book is a set of choices such that a seemingly attractive selection from it is certain to lose money for the person who makes the selection.

I used to tell students who queried the premise of “rational” behaviour in financial markets – where rational means are based on Bayesian subjective probabilities – that people had to behave in this way because if they did not, people would devise schemes that made money at their expense. I now believe that observation is correct but does not have the implication I sought. People do not behave in line with this theory, with the result that others in financial markets do devise schemes that make money at their expense.

Although this on the whole gives a succinct and correct picture of Keynes’s view on probability, I think it’s necessary to somewhat qualify in what way and to what extent Keynes “lost” the debate with the Bayesians Frank Ramsey and Jim Savage.

In economics it’s an indubitable fact that few mainstream neoclassical economists work within the Keynesian paradigm. All more or less subscribe to some variant of Bayesianism. And some even say that Keynes acknowledged he was wrong when presented with Ramsey’s theory. This is a view that has unfortunately also been promulgated by Robert Skidelsky in his otherwise masterly biography of Keynes. But I think it’s fundamentally wrong. Let me elaborate on this point (the argumentation is more fully presented in my book John Maynard Keynes (SNS, 2007)).

It’s a debated issue in newer research on Keynes if he, as some researchers maintain, fundamentally changed his view on probability after the critique levelled against his A Treatise on Probability by Frank Ramsey. It has been exceedingly difficult to present evidence for this being the case.

Ramsey’s critique was mainly that the kind of probability relations that Keynes was speaking of in Treatise actually didn’t exist and that Ramsey’s own procedure  (betting) made it much easier to find out the “degrees of belief” people were having. I question this both from a descriptive and a normative point of view.

What Keynes is saying in his response to Ramsey is only that Ramsey “is right” in that people’s “degrees of belief” basically emanates in human nature rather than in formal logic.

Patrick Maher, former professor of philosophy at the University of Illinois, even suggests that Ramsey’s critique of Keynes’s probability theory in some regards is invalid:

Keynes’s book was sharply criticized by Ramsey. In a passage that continues to be quoted approvingly, Ramsey wrote:

“But let us now return to a more fundamental criticism of Mr. Keynes’ views, which is the obvious one that there really do not seem to be any such things as the probability relations he describes. He supposes that, at any rate in certain cases, they can be perceived; but speaking for myself I feel confident that this is not true. I do not perceive them, and if I am to be persuaded that they exist it must be by argument; moreover, I shrewdly suspect that others do not perceive them either, because they are able to come to so very little agreement as to which of them relates any two given propositions.” (Ramsey 1926, 161)

I agree with Keynes that inductive probabilities exist and we sometimes know their values. The passage I have just quoted from Ramsey suggests the following argument against the existence of inductive probabilities. (Here P is a premise and C is the conclusion.)

P: People are able to come to very little agreement about inductive proba- bilities.
C: Inductive probabilities do not exist.

P is vague (what counts as “very little agreement”?) but its truth is still questionable. Ramsey himself acknowledged that “about some particular cases there is agreement” (28) … In any case, whether complicated or not, there is more agreement about inductive probabilities than P suggests.

Ramsey continued:

“If … we take the simplest possible pairs of propositions such as “This is red” and “That is blue” or “This is red” and “That is red,” whose logical relations should surely be easiest to see, no one, I think, pretends to be sure what is the probability relation which connects them.” (162)

I agree that nobody would pretend to be sure of a numeric value for these probabilities, but there are inequalities that most people on reflection would agree with. For example, the probability of “This is red” given “That is red” is greater than the probability of “This is red” given “That is blue.” This illustrates the point that inductive probabilities often lack numeric values. It doesn’t show disagreement; it rather shows agreement, since nobody pretends to know numeric values here and practically everyone will agree on the inequalities.

Ramsey continued:

“Or, perhaps, they may claim to see the relation but they will not be able to say anything about it with certainty, to state if it ismore or less than 1/3, or so on. They may, of course, say that it is incomparable with any numerical relation, but a relation about which so little can be truly said will be of little scientific use and it will be hard to convince a sceptic of its existence.” (162)

Although the probabilities that Ramsey is discussing lack numeric values, they are not “incomparable with any numerical relation.” Since there are more than three different colors, the a priori probability of “This is red” must be less than 1/3 and so its probability given “This is blue” must likewise be less than 1/3. In any case, the “scientific use” of something is not relevant to whether it exists. And the question is not whether it is “hard to convince a sceptic of its existence” but whether the sceptic has any good argument to support his position …

Ramsey concluded the paragraph I have been quoting as follows:

“Besides this view is really rather paradoxical; for any believer in induction must admit that between “This is red” as conclusion and “This is round” together with a billion propositions of the form “a is round and red” as evidence, there is a finite probability relation; and it is hard to suppose that as we accumulate instances there is suddenly a point, say after 233 instances, at which the probability relation becomes finite and so comparable with some numerical relations.” (162)

Ramsey is here attacking the view that the probability of “This is red” given “This is round” cannot be compared with any number, but Keynes didn’t say that and it isn’t my view either. The probability of “This is red” given only “This is round” is the same as the a priori probability of “This is red” and hence less than 1/3. Given the additional billion propositions that Ramsey mentions, the probability of “This is red” is high (greater than 1/2, for example) but it still lacks a precise numeric value. Thus the probability is always both comparable with some numbers and lacking a precise numeric value; there is no paradox here.

I have been evaluating Ramsey’s apparent argument from P to C. So far I have been arguing that P is false and responding to Ramsey’s objections to unmeasurable probabilities. Now I want to note that the argument is also invalid. Even if P were true, it could be that inductive probabilities exist in the (few) cases that people generally agree about. It could also be that the disagreement is due to some people misapplying the concept of inductive probability in cases where inductive probabilities do exist. Hence it is possible for P to be true and C false …

I conclude that Ramsey gave no good reason to doubt that inductive probabilities exist.

Ramsey’s critique made Keynes more strongly emphasize the individuals’ own views as the basis for probability calculations, and less stress that their beliefs were rational. But Keynes’s theory doesn’t stand or fall with his view on the basis for our “degrees of belief” as logical. The core of his theory – when and how we are able to measure and compare different probabilities – he doesn’t change. Unlike Ramsey he wasn’t at all sure that probabilities always were one-dimensional, measurable, quantifiable or even comparable entities.

  1. paul davidson
    December 1, 2014 at 10:08 pm

    the whole thing is resolved if we emphasize that Keynes recognzed uncertainty in the form of a nonergodic stochastic process– Keynes did not know the stochastic theory — which was developed by the Moscow School of Probability in 1935 and this theory did not arrive in the West until after World War 2 and Keynes was dead..

    but as I have written innumerable times Keynes’s criticism of “Mr. Tinbergen’s Method” in the EJ where Keynes states economic data is not homogeneous over time, means that the system is nonergodic –for nonhomogeneous data is a sufficient condition for a nonergodic stochastic process.
    Read my textbook POST KEYNESIAN MACROECONOMIC THEORY for a thorough “scientific” discusssion of the matter!

    Paul Davidson
    Paul Davidson

  2. December 2, 2014 at 10:05 am

    I’ve always found it interesting that Ramsay’s ‘subjectivism’ actually emphasized belief in some Grand Calculus of Everything far more than Keynes’ ‘objectivism’. Ramsay tries to play the skeptic but he comes off as the True Believer while Keynes comes off as agnostic.

  3. Newtownian
    December 3, 2014 at 8:38 am

    You do know how to ruin a fella’s day Lars. Going nuts trying to understand the insight and wisdom of Judea Pearl and all I was looking for was some light reading. And there you go with Bayes. Bearing this in mind some comments noting apologies if all this is already familiar.

    Still, nice cartoon.

    – “Bayesianism reduces questions of rationality to questions of internal consistency (coherence) of beliefs,”

    My reading of Pearl (and his friends – noting I’m not probability wiz) who seems to have started the modern Bayes revisitation, suggests things may have moved on a bit. He appears that to be more concerned about understanding and systematizing causality e.g. how we deal with chicken and egg situations. So the Bayes net stuff is more an emergent result rather than a central issue as your article suggests.

    My own experience with Bayes nets is that they will do all sorts of different things, some precise, some dodgy depending on how you frame the problem. Some models are deterministic, some are not credible, some are in between. The point is Bayesian Belief nets are a general tool for capturing reasoning which may be good or bad. So they are more like spreadsheets than a philosophy.

    So to suggest there is something called Bayesianism is a very big worry. It sounds a lot like scientism.

    – A different issue is that to make Bayes nets work you need good variables and cause and effect models and links. That’s fine say in engineering where the links are often deliberately and experientially deterministic and there are buckets of relatively objective data. Notoriously though the social sciences have more vague variables making the task much harder. Environmental science faces similar challenges because of system complexity and there has been much angst. Medicine where these probabilities are used to combine prior knowledge and posterior test data are an intermediate case.

    Its the old computer maxim GIGO.

    So from my reading of your posts which are great by the way I wonder if the problem here is not Bayes but that economics is still not a true science and as a result is still thrashing about in a protoscience phase or as Phillip Pilkington might describe its scholastic period. Although some economic ideas may eventually prove useful and be sustained, this possibility suggests economics application of Bayes concepts is clobbered by there still being no economic atomic theory to use in developing – ideas – just a bunch of indicators of variable credibility. As a result whether Ramsey or Keynes are closer to the truth may be as much a non issue as two witchhunters arguing over whether succubi or incubi are of more concern.

    – Though there is nothing wrong with it that Dutch book reference has too much maths for non maths wizs. Can I recommend instead KORB, K. B. & NICHOLSON, A. E. 2011. Bayesian artificial intelligence, 2nd ed CRC press. The Wiki explantation isnt bad either. The only real problem is identifying a bunch of bookies offering sufficiently different odds that you can make a profit. K and N also have a nice list of mistakes that would be Bayesians are guilty of. It might be interesting to compare this to what economists are doing with Bayes Nets.

    – Scientific ‘proof’, or at least falsification that real economic agents arent rational is SLEMBECK, T. & TYRAN, J.-R. 2004. Do institutions promote rationality? An experimental study of the three-door anomaly? Journal of Economic Behavior & Organization, 54 337-350. This shows how bad people are at doing cause>effect probability calculations and experimentally falsifies the idea that investors know what is good for them. The latter three door problem by the way says dont trust your intuition in matters of money and betting.

    – “For Keynes, probability was about believability, not frequency. He denied that our thinking could be described by a probability distribution over all possible future events”

    One thing that seems to have annoyed Pearl is the vagueness of concepts thrown about including by frequentists in the name of probability and precision in particular the nature of causality. In case that is of interest see PEARL, J. 2009. Causal inference in statistics: An overview. 96-146.

    But how correct was Keynes. To me its a question to be addressed not by looking at debates and opinions but rather by looking at the causality logic – maybe using a graduate economics student.

  4. Newtownian
    December 3, 2014 at 9:19 am

    “Science according to Keynes should help us penetrate to “the true process of causation lying behind current events” and disclose “the causal forces behind the apparent facts.” Models can never be more than a starting point in that endeavour. He further argued that it was inadmissible to project history on the future. Consequently we cannot presuppose that what has worked before, will continue to do so in the future. That statistical models can get hold of correlations between different “variables” is not enough. If they cannot get at the causal structure that generated the data, they are not really “identified.”

    How strange that writers of statistics textbook as a rule do not even touch upon these aspects of scientific methodology that seems to be so fundamental and important for anyone trying to understand how we learn and orient ourselves in an uncertain world. An educated guess on why this is a fact would be that Keynes concepts are not possible to squeeze into a single calculable numerical “probability.” In the quest for quantities one puts a blind eye to qualities and looks the other way – but Keynes ideas keep creeping out from under the statistics carpet.”

    Lars – Further to my previous comment I had a look at your other offerings such as the quote above. I hope I dont offend but I suggest you might want to have a look at Pearl’s stuff. My reading is he wants to do exactly what Keynes wanted to do. That is understand causality.

    Regarding the inadmissability of using models – hard science never uses models as the be all and end all so this is a non argument. But it does use them for prediction and projection. The results often seem crazy but that is covered by falsification. So I cant accept this inaddmissability. Perhaps the problem here is the rationalization of bad decisions using selective models and scientism. But that is not a problem with Bayes.

    Regarding statistics not touching on causality that is exactly a concern of Pearl and he explicit identifies it through references such as RUBIN, D. B. 1974. Estimating causal effects of treatments in randomized and nonrandomized studies. Journal of educational Psychology, 66, 688.

    Also note the following:

    – Keynes was writing before the modern ideas of hypothesis testing and paradigm development were seen as central to science, and he wasnt a scientist so his views need to be treated with some reserve, as insightful as he was.
    – The Bayesian people I know – scientists or working with scientists – are acutely aware of the elicitation problem which I suggest is your real concern – the garbage in garbage out issue and as interested in causation as anyone.
    – The Bayes nets I’ve been working with tally with other model predictions generally seen as credible. All the Bayes nets seem to do is express variables in a slightly different way than you would do when say using a spreadsheet – but this has many advantages e.g. intuitive explanation and allowing you to reason backwards in scenario modelling rather than having to produce scenarios. i.e. use for decision support not decision per se.
    – We’ve trialed replacing a range of ISO 31000 risk management tools with Bayes nets and they give the same results.

    So based on experience Bayes seems to work as a tool for quantifying cause and effect – at least where you have credible models, data and understanding of like causality pathways.

  5. davetaylor1
    December 4, 2014 at 11:05 am

    It seems difficult to know exactly when Bayes developed his theorem, since it was published posthumously in 1763. However, it is likely to have been before 1739 (i.e not influenced by Hume’s discussion about drawing balls out of bags [i,e, closed sets], since by 1742 he was already sufficiently advanced to be elected to the Royal society. The interest in probability originated in Pascal’s Wager (published posthumously in 1663, which is about “horses for courses”. In my view, the difference between what Keynes (Bayesian) and Ramsey (frequentist) were saying and what Keynes was after is very clearly illustrated at http://en.wikipedia.org/wiki/Bayes'_theorem, except that the explanation of the Bayesian belief doesn’t explain the causal reasons for the initial belief, i.e. the symmetry of a coin (or better, a die), which here can be seen, but a blind man could infer as probable, given the data from experimental tossings.

    Unlike Hume’s choice between red and white balls (one or the other, true or not true, two independent but similar random variables), the chance of throwing a particular outcome with a die or betting on a horse is of one vs. the rest, i.e. an item or a group, which are logically quite different things. This difference is expressible visually as their being at right angles, the independence of ‘up’ and ‘across’ arising with symmetry in the angular as against linear subdivision of a straight line. A little way down the Wiki article, Sir Harrold Jeffreys, whose “Theory of Probability, which first appeared in 1939, played an important role in the revival of the Bayesian view of probability”, made the telling remark that Bayes’s theorem “is to the theory of probability what Pythagoras’s theorem is to geometry”.

  6. December 4, 2014 at 9:20 pm

    Could economists get their economics right before philosophizing about uncertainty?Comment on ‘The Ramsey-Keynes dispute’

    Keynes had his fingers in many pies, mostly in those where “nothing is clear and everything is possible.” (Keynes, 1973, p. 292)

    Let us become more specific. Keynes realized that something was wrong with classical economics. In this he was ahead of his fellow economists. But he went not far enough. As a matter of fact he accepted the premise that economics is about choice according to the famous definition:

    “Economics is the science which studies human behavior as a relationship between ends and scarce means which have alternative uses.” (Robbins, 1935, p. 16)

    Indeed, this directive sent economists, and Keynes among them, into scientific nirvana: “Economics studies human behavior.”

    The outcome — inevitable and fatal like Greek tragedy — has been neatly summarized by Newtownian: “… whether Ramsey or Keynes are closer to the truth may be as much a non issue as two witchhunters arguing over whether succubi or incubi are of more concern.” This metaphor is paradigmatic for the vacuousness of economic debates.

    While distracted by non-issues, Keynes messed up the basics of economics with this syllogism: Income = value of output = consumption + investment. Saving = income – consumption. Therefore saving = investment. (Keynes, 1973, p. 63)

    That is rather elementary mathematics. It cannot be said that formalization or the axiomatic-deductive method ruined Keynesianism. It is pure conceptual sloppiness (2014). Keynesians and the rest of the profession simply cannot tell the fundamental difference between income and profit (2011).

    This, though, is exactly what is expected from an economist. Time, therefore, to relinquish the filibuster about human behavior, choice, rationality and the three-door anomaly to psychologists, sociologists, anthropologists, philosophers, theologians and other adherents of the so-called social sciences.

    What can be learned from Keynes is:
    “Nothing is more difficult than to turn an entire discipline around, asking in effect to jettison its own history over the last 200 years.” (Blaug, 1990, p. 205)

    Economics is not a science of behavior (Hudík, 2011). This, then, could be the new directive: Economics is the science which studies how the monetary economy works.

    It will be a glorious day in the history of economic thought when the representative economist can summarize in a simple formula how the profit mechanism functions.

    Egmont Kakarot-Handtke

    References
    Blaug, M. (1990). Economic Theories, True or False? Aldershot, Brookfield, VT:
    Edward Elgar.
    Hudík, M. (2011). Why Economics is Not a Science of Behaviour. Journal of
    Economic Methodology, 18(2): 147–162.
    Kakarot-Handtke, E. (2011). Why Post Keynesianism is Not Yet a Science. SSRN
    Working Paper Series, 1966438: 1–15. URL http://ssrn.com/abstract=1966438.
    Kakarot-Handtke, E. (2014). The Three Fatal Mistakes of Yesterday Economics:
    Profit, I=S, Employment. SSRN Working Paper Series, 2489792: 1–13. URL
    http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2489792.
    Keynes, J. M. (1973). The General Theory of Employment Interest and Money.
    The Collected Writings of John Maynard Keynes Vol. VII. London, Basingstoke:
    Macmillan. (1936).
    Robbins, L. (1935). An Essay on the Nature and Significance of Economic Science.
    London, Bombay, etc.: Macmillan, 2nd edition.

  7. davetaylor1
    December 5, 2014 at 5:58 am

    “While distracted by non-issues, Keynes messed up the basics of economics with this syllogism: Income = value of output = consumption + investment. Saving = income – consumption. Therefore saving = investment. (Keynes, 1973, p. 63)”.

    We’ve had this argument before, Egmont, and evidently you are an economist in the “autistic” or in any case sensory-minded micro-foundations tradition, for you haven’t listened either to me (coming at this as an insider, inter alia, to causal logic, language, and probability theory) or to the whole of Keynes’ or Newtownian’s arguments. Keynes was not yet an economist when he thought out for himself the probability theory he brought to economics, and I’m looking not as an economist but as a fellow intuitive thinker at what Keynes (1973, c. p.63) was actually saying and leading up to.

    As I said before, then, you are quoting Keynes out of context. He is summarising what other economists inevitably say, given their terminology and inability to differentiate it stably, and concludes by proposing stable terminology which ENABLES HIM TO DISAGREE with savings being what one doesn’t consume and equal to investment, i.e. ‘propensity to consume’ and ‘liquidity preference’.

    The same critique applies to discussing probability theory here. If economies involves uncertainty, how CAN economists get their economics right if their understanding of probability logic is mistaken? Have a look at the last two paras in Newtownian’s first comment above.

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