I recall writing a paper many years ago which ended with the statement 'Keynes was not a Keynesian though perhaps he was a post Keynesian'. The friend I showed it to suggested several minor improvements but his main objection- viz. that it was not in fact 'common knowledge', within the profession, that Hicks scissored Keynes and it is that unholy act of tribadism which IS-LM curves represent- militated against the publication of my paper in any respectable Academic Journal.
Today, I came across a paper which was published by the philosopher Donald Gillies which does indeed end in the same manner as mine.
Let us peruse it together, with bated breath, to discover whether Hicks really did the dirty deed with poor old Keynes.
I begin in medias res.
Keynes argues that the amount of investment is the key factor in determining the performance of the economy as a whole.
Though the performance of the economy as a whole was the key factor in determining the amount of Investment.
As we shall see he regards it as the ‘causa causans’ of ‘the level of output and employment as a whole’ (1937, 121).
Only if ceteris paribus obtained. But if the economy's performance suffered for any other reason- political, military, climate-related, religious, sociological etc. etc.- Investment couldn't do shit.
A decision to invest consequently depends on what Keynes calls the state of long-term expectation (the title of the famous chapter 12 of the General Theory).
But long term expectations depend on current investment decisions. This is circular.
Now the notions of expectation and of probability are interdefinable.
Not necessarily. Expectations may be wholly deterministic not stochastic at all. Alternatively, they may depend on Oracles, not statistical calculations. Indeed, the latter method may systematically outperform the former
If we take expectation as the starting point, we can define probabilities in terms of expectations, and vice versa.
No. A probability is a Tarskian primitive. It is undefined. We may say there are probability based expectations and oracle based expectations and expectations based on religious or other beliefs.
If then Keynes is using the notion of expectation in its standard sense, he is implicitly operating with a concept of probability, and it is natural to ask what should be the interpretation of the probabilities involved. This then brings us to the fundamental question with which this paper is concerned, namely: ‘what is the most appropriate interpretation of probability in Keynes’s General Theory?’ The Post-Keynesians have devoted a great deal of attention to this problem, but, before we can consider their arguments in detail, it will be necessary to give a brief explanation of the various interpretations of probability.
Keynes was simply saying that if people think things are gonna get worse before they get better then the slump will endure. If people think good times are around the corner then their prophesy will be self-fulfilling. Probability doesn't matter. Keynes was a confused man but he had made money and gained a reputation as an expert on Finance.
Different versions of the logical interpretation of probability have been developed by different authors, but here, naturally, we will be concerned with Keynes’s version as expounded in his 1921 Treatise on Probability. In the case of deductive logic a conclusion is entailed by the premises, and is certain given those premises. Thus, if our premises are that all ravens are black, and George is a raven, it follows with certainty that George is black.
No. George may have been painted white. You need an additional premise- viz. that no raven has been painted a different color.
But now let us consider an inductive, rather than deductive, case. Suppose our premises are the evidence (e say) that several thousand ravens have been observed, and that they were all black. Suppose further that we are considering the hypothesis (h say) that all ravens are black, or the prediction (d say) that the next observed raven will be black. Hume argued, and this is in agreement with modern logic, that neither h nor d follow logically from e.
Unless you add more premises. But all this is silly. What we want is a structural causal model that a particular type of bird would have such and such properties. That SCM might enable us to alter those properties for some useful purpose.
Yet even though e does not entail either h or d, could we not say that e partially entails h and d, since e surely gives some support for these conclusions? This line of thought suggests that there might be a logical theory of partial entailment which generalises the ordinary theory of full entailment which is found in deductive logic.
You could have Gentzen type 'sequent calculi' which appeared around this time.
This is the starting point of Keynes’s approach to probability. He writes (1921, 52): ‘Inasmuch as it is always assumed that we can sometimes judge directly that a conclusion follows from a premiss, it is no great extension of this assumption to suppose that we can sometimes recognise that a conclusion partially follows from, or stands in a relation of probability to a premiss.’ 5 So a probability is the degree of a partial entailment. Keynes further makes the assumption that if e partially entails h to degree p, then, given e, it is rational to believe h to degree p. For Keynes probability is degree of rational belief not simply degree of belief.
But it is not rational to waste brain power on useless shite. SCM's are useful. What Keynes was doing was useless.
As he says (1921, 4): ‘ ... in the sense important to logic, probability is not subjective. It is not, that is to say, subject to human caprice. A proposition is not probable because we think it so. When once the facts are given which determine our knowledge, what is probable or improbable in these circumstances has been fixed objectively, and is independent of our opinion. The Theory of Probability is logical, therefore, because it is concerned with the degree of belief which it is rational to entertain in given conditions, and not merely with the actual beliefs of particular individuals, which may or may not be rational.’
Keynes was wrong. Logic, like everything else, must be useful. It must pay for itself. The correct SCM is useful because you could use it to get a better type of raven or a better macro-economic outcome.
Here Keynes speaks of probabilities as being fixed objectively, but he is not using objective to refer to things in the material world. He means objective in the Platonic sense, referring to something in a supposed Platonic world of abstract ideas.
So there is a probability of probability of probability and so on just as there is a shit of shit of shit. To say something has a Platonic sense, means it is nonsense.
The next question which might be asked regarding Keynes’s approach is the following: ‘how do we obtain knowledge about this logical relation of probability?’ Keynes’s answer is that we get to know at least some probability relations by direct acquaintance or immediate logical intuition.
Which is also how we can be sure the Virgin Mary was a Virgin or that Lord Ganesa has the head of an elephant.
As Keynes says (1921, 13): ‘We pass from a knowledge of the proposition a to a knowledge about the proposition b by perceiving a logical relation between them. With this logical relation we have direct acquaintance.’
Also there may be a sexual relation to George the raven. Keynes was notorious in that regard.
A problem which arises on this account is how we can ever assign numerical values to probabilities. Keynes indeed thinks that this is possible only in some cases, and writes on this point (1921, 41): ‘In order that numerical measurement may be possible, we must be given a number of equally probable alternatives.’
This is obviously false. What we need is a SCM which predicts what percentage of a thing will be true to type and what percentage might want to fuck George the raven.
So in order to get numerical probabilities we have to be able to judge that a number of cases are equally probable
We know of no such things. If we did, there would be a method of distinguishing random from pseudo random sequences. We'd know what is or isn't a 'law-less' choice sequence. Everybody now knows that Keynes was wrong. Why won't Gillies not simply tell us this? Why write a paper about a cretin who was already behind the times?
and to enable us to make this judgement we need an a priori principle.
Or else we could just be as stupid as shit.
This a priori principle is called by Keynes the Principle of Indifference, and he gives the following statement of it (1921, 42): ‘The Principle of Indifference asserts that if there is no known reason for predicating of our subject one rather than another of several alternatives, then relatively to such knowledge the assertions of each of these alternatives have an equal probability.’
This is like the 'maximal uncertainty principle', or maximal entropy or 'principle of indifference'.
Unfortunately the Principle of Indifference leads to a number of paradoxes. Keynes gives a full account of these in chapter IV of his Treatise, and makes an attempt to solve them. Yet is has to be said that his solution is far from satisfactory. This concludes my brief account of Keynes’s version of the logical theory of probability. Let us now turn to the subjective interpretation. The subjective theory of probability was discovered independently and at about the same time by Frank Ramsey in England, and Bruno de Finetti in Italy.
Both were smart. One may mention William Ernest Johnson in this context. The notion of 'exchangeability' underlies both. If observations are judged to be exchangeable, then they must be a random sample from some model and there must exist a prior probability distribution over the parameter of the model. But this is an existence theorem: it is non informative. Additional assumptions are needed to get to a model or a prior probability distribution. The point about subjectivity is that it is subjective all the way down. We don't really know if we have access to anything truly random.
Their two versions of the theory are broadly similar, though there are important differences which are well described in Galavotti (1991). In what follows I will concentrate mainly on Ramsey since his work is directly connected with that of Keynes. Ramsey was a younger contemporary of Keynes at Cambridge.
Both were taught by Johnson who also tried but failed to teach Wittlesstein. Ramsey's great importance is related to our pessimism regarding getting access to true randomness. Within a large enough disordered system there must be some order.
His fundamental paper introducing the subjective approach to probability was read to the Moral Sciences Club at Cambridge, and Ramsey begins the paper by criticizing Keynes’s views on probability. According to Keynes there are logical relations of probability between pairs of propositions, and these can be in some sense perceived. Ramsey criticizes this as follows (1926, 161): ‘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.
Or relations of any other type save by seeing x as some y where the y might be statistical correlation or sexiness or crappiness or anything else. Probability, like Beauty is in the eyes of the beholder. It would be nice to know that randomness really exists and that when all information is available there is still the miracle of freedom.
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.’
I say x is sexy, you disagree but there is some y which you find is sexy. Sexiness is still a relation, its just that everybody has different sequent calculi with respect to it.
This is an interesting case of an argument which gains in strength from the nature of the person who proposes it. Had a less distinguished logician than Ramsey objected that he was unable to perceive any logical relations of probability, Keynes might have replied that this was merely a sign of logical incompetence, or logical blindness. Indeed Keynes does say (1921, 18): ‘Some men - indeed it is obviously the case - may have a greater power of logical intuition than others.’
But, if the thing is an intuition, it can't be purely algorithmic,; some people just start off with better conditional tautologies and thus better sequent calculi. If 'intuition' differs there are uncorrelated asymmetries. A bourgeois strategy- e.g. deferring to expert opinion- is rational.
Ramsey, however, was such a brilliant mathematical logician that Keynes could not have claimed with plausibility that Ramsey was lacking in the capacity for logical intuition or perception - and Keynes did not in fact do so. In the logical interpretation, the probability of h given e is identified with the rational degree of belief which someone, who had evidence e, would accord to h. This rational degree of belief is considered to be the same for all rational individuals. The subjective interpretation of probability abandons the assumption of rationality leading to consensus. According to the subjective theory different individuals (Ms A, Mr B and Master C say). although all perfectly reasonable and having the same evidence e, may yet have different degrees of belief in h. Probability is thus defined as the degree of belief of a particular individual, so that we should really not speak of the probability, but rather of Ms A’s probability, Mr B’s probability, or Master C’s probability.
So the thing is Bayesian. But 'Aumann agreement' is undesirable and not Muth Rational save if it solves a particular sort of coordination game. Indeed, Aumann himself gave one reason why this is the case.
Now the mathematical theory of probability takes probabilities to be numbers in the interval [0, 1].
It doesn't have to. We could have negative probabilities as Dirac pointed out. Ultimately, probability theory is merely a Schelling focal way of solving coordination problems. But it is rational to hedge on discoordination games.
One helpful way of regarding the intersubjective interpretation of probability is to see it as intermediate between the logical interpretation of the early Keynes,
which failed because it was not Gentzen type
and the subjective interpretation of his critic Ramsey. According to the early Keynes, there exists a single rational degree of belief in some conclusion c given evidence e.
For a given sequent calculus- sure, why not?
If this were really so, we would expect nearly all human beings to have this single rational degree of belief in c given e, since, after all, most human beings are rational. Yet in very many cases different individuals come to quite different conclusions even though they have the same background knowledge and expertise in the relevant area, and even though they are all quite rational. A single rational degree of belief on which all rational human beings should agree seems to be a myth. So much for the logical interpretation of probability, but the subjective view of probability does not seem to be entirely satisfactory either. Degree of belief is not an entirely personal or individual matter. We very often find an individual human being belonging to a group which shares a common outlook, has some degree of common interest, and is able to reach a consensus as regards its beliefs. Obvious examples of such groups would be religious sects, political parties, or schools of thought regarding various scientific questions. For such groups the concept of intersubjective probability seems to be the appropriate one. These groups may be small or large, but usually they fall short of embracing the whole of humanity. 10 The intersubjective probability of such a group is thus intermediate between a degree of rational belief (the early Keynes) and a degree of subjective belief (Ramsey). The three views we have considered so far have in common that they regard probability as a measure of human belief, whether it is degree of rational belief, degree of individual belief, or the degree of a consensus belief of a group. Such theories are called epistemological theories of probability, and they can be contrasted with objective theories of probability. Here objective does not, as in Keynes, mean objective in the Platonic sense, but rather in the sense of belonging to the objective material or physical world. The probability of a radioactive atom disintegrating in a year is an example of an objective probability in this sense. It is an objective feature of the physical world, and does not depend on human beliefs. Such objective probabilities are to be found in the natural sciences in situations where we have a set of repeatable conditions. This concludes my brief survey of some main interpretations of probability.
Surely, something more up to date could be offered? Probability and Randomness, like God, may be useful things to believe in but they are most accessible when they aren't at all.
Let us now see how these views might be applied to Keynes’s economics
In his Treatise of 1921 Keynes advocated the logical interpretation of probability as degree of rational belief.
This is reasonable if there is a 'black box' mechanism generating objective probability.
Should we therefore adopt the natural supposition that he is implicitly using this logical interpretation of probability in the General Theory? Or are there reasons for thinking that Keynes changed his views on probability between 1921 and 1936?
What would be the point? He wasn't doing any very rigorous type of Econ or praxeology. Moreover, he'd made and lost money in financial markets. Does it matter if you subjectively feel qualms but objectively follow the herd? You sacrifice bragging rights to having called a turn in the market in order to get your piece of the action while the going is good. Anyway, a general disaster is nobody in particular's tragedy. Marg-e-amboh, Jashne darad- as the old Persian proverb goes.
I think Keynes's views- those of a man who straddled the world of finance, Government and Academia- were something he was himself trying to elucidate and to put on a logical basis for academic purposes. He failed because the thing was impossible to do with the tools that were available. Even now, all we can say is there may be 'univocal foundations' for 'the practice' and 'the theory' of people like Keynes- who may straddle the three worlds previously mentioned- but we there may be many different 'univocal foundations' which currently are 'observationally equivalent' but which may cease to be so at a future point. In other words, we have not really gone any further down the road than Keynes in any substantive manner. Keynes's generation did not predict that two World Wars would turn their world topsy turvey. They didn't get that 'the economic consequences of Mr. Churchill' was that the Royal Navy would lose hegemony and the Empire would be lost. Colored people would benefit from the maniacal ambitions of Herr Hitler- a thoroughgoing racist. The odd thing was that the British upper middle class gained by being displaced from control of the Empire. As the 'proletariat' rose up, they themselves gained greater freedom. Homosexuality was legalized. Divorce became no grave matter. The stain of illegitimacy- for example endured by the children of widowers who married their late wife's sister- was removed. Keynes would have approved of the post-Keynesian world. He would have discovered that the people who lived in the dormitory suburbs of great Cities, or the decaying tenements of inner cities, had a rich, creative life. Keynes enabled 'Butskillism'- i.e. a commitment to full employment and a 'welfare state'. Butskillism gave us the Beatles. Keynesian analysis was class based. But class was ceasing to matter. Economists could pay their way in a Society with very rapid technological progress. True, they'd be working for Sciencey nerds like Gates or Bezos, but they'd be helping to economize on the use of scarce resources. Keynes did not live long enough to enter a paradise which his ilk could little envisage. But, at least posthumously, Keynesianism- if not the man himself- played a part in bringing about what turned out to be a happier state of affairs.
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