by Philip Pilkington
In a recent post I dealt with Keynes’ opinions on the application of statistics and theories based on probability (e.g. econometrics). There I noted that Keynes thought that much applied work failed because it improperly deployed the use of Analogy and Induction.
The natural question, which some then asked, was “what on earth are Analogy and Induction?” In this post I will deal with Keynes’ views on these two processes of reasoning — again, this is not hero-worship, Keynes was fallible and I disagree with him on many points, but I think that were contemporary economists to have a better understanding of these issues much of the disciplines irrelevance would begin to fade away.
According to Keynes all science is basically a process of Analogy and Induction. In his A Treatise on Probability Keynes draws on an argument laid out by Hume in the latter’s Treatise on Human Nature. It might be worth quoting from Hume at length here in order to move the argument along:
In reality, all arguments from experience are founded on the similarity which we discover among natural objects, and by which we are induced to expect effects similar to those which we have found to follow from such objects… Nothing so like as eggs; yet no one, on account of this appearing similarity, expects the same taste and relish in all of them. It is only after a long course of uniform experiments in any kind, and we attain a firm reliance and security with regard to a particular event. Now where is that process of reasoning which, from one instance, draws a conclusion so different from that which it infers from a hundred instances that are nowise different from that single one?
What Hume refers to as the similarity between objects — in this case, eggs — Keynes refers to as “Analogy”. We look at an egg, eat it, taste it and then look at another expecting the same taste simply because we equate the two by the way they look, feel and so on. This is a fundamental part of our reasoning that often goes unnoticed and it is what Keynes calls Analogy. It is the comparison of objects that we think to be alike.
Induction refers to the latter part of Hume’s argument; namely, increasing the number of instances of observation. In fact, Keynes refers to this increase in the number of experiments as Pure Induction. And he refers to any argument that combines Pure Induction and Analogy to be an “inductive argument”.
An inductive argument is thus one like that undertaken by Hume with his eggs. He draws an Analogy between what he thinks to be like objects and the undertakes experiments — by eating them — to see if they yield the same “taste and relish”. The argument comes to a close after Hume has eaten sufficient eggs to convince himself that he does indeed get said “taste and relish”.
Keynes, however, is not satisfied with Hume’s presentation. He thinks it too simple. So, he introduces some more distinctions that help us understand further the nature and form of inductive arguments. The most important of these is what he calls Negative Analogy. What is a Negative Analogy? Well, say we said to Hume “Mr. Hume, your egg experiment is very good but perhaps you should vary it somewhat. Why not take them…” — and this is Keynes’ example — “…to the country and the city and try them there to see if they still taste the same? Then why not try them first in June and then in July?”
If Hume engaged in such an experiment he would, of course, find that the same eggs tasted the same in the country and the city, but that whereas they were delicious in June had gone rotten in July.
Keynes says that when we increase the instance of Negative Analogy we increase certainty because we eliminate the possibility that other factors might be affecting our experimental results. The more instances of variations that we can show that do not affect the underlying relationship we are trying to establish the firmer is the Negative Analogy in question.
This framework then allows us to evaluate the Probability that our argument might be true. Keynes considers this in light of a hypothetical case where we try to find Analogy based on two variables — perhaps imagine that Hume not only wanted to see if the objects called “eggs” tasted the same but also whether they would taste bad after leaving them for a month. In his Treatise on Probability Keynes writes:
In an inductive argument, therefore, we start with a number of instances similar in some respects AB, dissimilar in others C. We pick out one or more respects A in which the instances are similar, and argue that some of the other respects B in which they are also similar are likely to be associated with the characteristics A in other unexamined cases. The more comprehensive the essential characteristics A, the greater the variety amongst the non-essential characteristics C, and the less comprehensive the characteristics B which we seek to associate with A, the stronger the likelihood or probability of the generalisation we seek to establish. (pp219-220)
So, let’s apply that to our egg example. We want to establish that eggs taste the same and that they all go bad when left for a month. We can test this, and thus affirm the Positive Analogy through experiment. But we must further strengthen the argument through Negative Analogy — so we must, for example, eat the eggs in different places or use different means to eat them or undertake different postures while eating them to ensure that these aspects are not affecting the experiment. As Keynes writes:
These are the three ultimate logical elements on which the probability of an empirical argument depends — the Positive Analogies and the Negative Analogies and the scope of generalisation. (p220)
Keynes then further breaks down two different types of generalisation. On the one hand, we have Universal Inductions in which the relationship will always and invariably hold true. And on the other we have Inductive Correlations where the relationship holds good some of the time — possibly with a given probability (1 in 50 swans are black and so on).
What should be stressed, however, is that Keynes does not, like those before him, seek out absolutely true inductions; rather inductions provide us with a probability of an induction being true or not. Keynes again:
An inductive argument affirms, not that a certain matter of fact is so, but that relative to certain evidence there is a probability in its favour. The validity of the induction, relative to the original evidence, is not upset, therefore, if, as a fact, the truth turns out to be otherwise. (p221)
“Aha!” the econometrician will say, “We know all this already. This is precisely what we try to do in econometrics. Keynes was one of us, after all!”
While it is true that econometrics aims at the same goal as Keynes’ probability theory of induction, this is not to say that what is being done is the same. Keynes’ problem with econometrics was that it was a poor means to undertake an inductive argument. One example of this is the assumption of the homogeneity of historical time in econometric studies. Keynes discusses this in his Professor Tinbergen’s Method:
Put broadly, the most important condition is that the environment in all relevant respects, other than the fluctuations in those factors of which we take particular account, should be uniform and homogeneous over a period of time. (p566)
Let’s say that we are undertaking an investigation of the relationship between interest rates and the rate of investment. And let’s say that we are taking a twenty year time period. We cannot, as econometricians typically do, study this by simply running regressions on twenty years of historical data. Instead we must examine it on a case-by-case basis — we must study each change in the rate of interest and see if each change had relatively constant effects on the rate of investment. As Keynes says:
The first step, therefore, is to break up the period under examination into a series of sub-periods, with a view to discovering whether the results of applying our method to the various sub-periods taken separately are reasonably uniform. If they are, then we have some ground for projecting our results into the future. (p567)
This may sound like nitpicking but I think we would get wildly different results from both methods. It is likely that the twenty year regression would produce a result that hinted that there might be some relatively continuous effect of changes in the interest rates on the rate of investment. Whereas if we broke the period up into sub-periods corresponding to each time the interest rate moved, we would likely find that it had highly indeterminate effects on the rate of investment.
After all, if an economist cannot see the wildly different effects that raising interest rates had in, say, 1928 in the US versus the effects they had in 1980 then I would suggest that a new career is in order. The simple fact is that context matters in such cases and Keynes understood that well. To assume homogeneity of historical time when dealing with economic relationships displays a poor and hobbled capacity for inductive argument.
This is merely one example, but there are many more. Keynes’ more general point is that induction is an extremely difficult procedure and to think that we can automate it in some way is completely fallacious. Instead he advocates a more intuitive approach based on the weighing up of arguments. Not necessarily numerically, as Keynes recognises that many arguments cannot be given numerical weights; even those that might have as their material numerical or quantitative data.
What I have outlined above is merely the skeleton of the framework he provides to engage in such weighting. But it at least gives the reader a flavour of how Keynes thought that arguments should be made and why this is so far from what much of the economics profession does today.