On probability distributions and uncertainty

18 July, 2016 at 17:31 | Posted in Economics | Leave a comment

treatprobAlmost a hundred years after John Maynard Keynes wrote his seminal A Treatise on Probability (1921), it is still very difficult to find economics textbooks that seriously try to incorporate his far-reaching and incisive analysis of induction and evidential weight.

The standard view in mainstream economics – and the axiomatic probability theory underlying it – is to a large extent based on the rather simplistic idea that ‘more is better.’ But as Keynes argues – ‘more of the same’ is not what is important when making inductive inferences. It’s rather a question of ‘more but different.’

Variation, not replication, is at the core of induction. Finding that p(x|y) = p(x|y & w) doesn’t make w ‘irrelevant.’ Knowing that the probability is unchanged when w is present gives p(x|y & w) another evidential weight (‘weight of argument’). Running 10 replicative experiments do not make you as ‘sure’ of your inductions as when running 10 000 varied experiments – even if the probability values happen to be the same.

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.’ 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 often have preciously little to do with the kind of stochastic probabilistic calculations made by the rational agents as modeled by mainstream social economics.

How strange that writers of economics textbooks 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 mainstream economics carpet.

It’s high time that economics textbooks give Keynes his due.

There are at least two ways to formally distinguish Keynes’s idea that the future is unknowable in principle from the neoclassical idea that the future is stochastic-stable and that agents know, or act as if they know, this distribution with absolute certainty. First, as Keynes, Shackle, Vickers, and others have stressed, it is logically impossible for agents to assign numerical probabilities to the potentially infinite number of imaginable future states. Even Savage acknowledged that, taken literally, the assumption that agents are able to consider all possible future economic states “is utterly ridiculous” (1954, p. 16). Worse yet, many possible future events are not even imaginable in the present moment: such events obviously cannot be assigned a probability …

j_crotty_nov2011_cropped_smaller1Alternatively, we could — for the sake of argument — think of firms and portfolio selectors as somehow forcing themselves to assign expected future returns to all the assets under evaluation even though they are conscious of the fact that their knowledge of the future is inherently incomplete and unreliable. The key point is that such subjective probability distributions would not be knowledge, and –most important — any rational agent would know they were not knowledge … Hicks insisted that in the nonergodic real world, people “do not know what is going to happen and know that they do not know what is going to happen. As in history!” …

Therefore, even given the unrealistic assumption of the existence of these distributions, there is a crucial piece of information about agent decision making that would be missing from any subjectivist theory — the extent to which the agents believe in the meaningfulness of their forecasts or, in Keynes’s words, the “weight of belief” or “the degree of rational belief” the agents assign to these probabilities. When knowledge of the future is subjective and imperfect, as it always is, the expectations of rational agents can never be fully and adequately represented solely by probability distributions because such distributions fail to incorporate the agents’ own understanding of the degree of incompleteness of their knowledge. These functions neglect the agents’ “confidence” in the meaningfulness of the forecasts — “how highly we rate the likelihood of our best forecast turning out to be quite wrong” (Keynes 1936, p. 148).

Keynes stressed the centrality of agents’ consciousness of their ignorance: the state of confidence plays a crucial role in his theory of the investment decision. “The state of confidence [in the ability to make meaningful forecasts] is relevant because it is one of the major factors determining [investment]” (1936, p. 149). The central role of confidence in the investment decision-making process has disappeared from mainstream Keynesian models and cannot exist by assumption in New Classical and neoclassical models.

James Crotty

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