### Discussion Paper

Uncertainty: A Diagrammatic Treatment

(Published in Special Issue
Radical Uncertainty and Its Implications for Economics)

## Abstract

In spite of superficial similarities, the way in which uncertainty is understood as a feature of the crisis by mainstream economics is very different from Keynesian fundamental uncertainty. The difference stems from the mainstream habit of thinking in terms of a full-information benchmark, where uncertainty arises from ignorance. By treating uncertain knowledge as the norm, Keynesian uncertainty theory allows analysis of differing degrees of uncertainty and the cognitive role of institutions and conventions. The paper offers a simple diagrammatic representation of these differences, and uses this framework to depict different understandings of the crisis, its aftermath and the appropriate policy response.

## Comments and Questions

It is always a pleasure to read Sheila Dow on Post Keynesian economics. Her forthrightness on uncertainty harks back to the classics on the subject. On that ground, I missed reference to Shackle’s work. Charges of nihilism made against him were ably addressed by John D Hey and others but ...[more]

... even in Prof GLS’s abundant work, diagrams proper on uncertainty will be found. I would substitute the word “pictorial” in Prof Dow’s title.

I wondered whether the category beliefs might not have some role to play, along with ambiguity, in the distinction between the mainstream and Keynes. They intervene in expectations about expectations. With Keynes, there was confidence, and beliefs held in that confidence. There are degrees of belief.

I enjoyed the solid attack on given information sets. Is there scope for dialogue with Hayek, von Mises and others here? People construct their own information sets from their surroundings.

I am not sure that the crisis had much to do with problems of information. Fraud or “strategic default” (if an academic handle is required) were on display. In Minsky terms, the runup could be described in the following terms: Risk aversion in the “hedge” phase gave way to risk love as the “great moderation” gathered momentum. There is no formal border to be crossed, moving “speculative” trade to “Ponzi” finance. Complex derivative products are one thing. On the high of an upswing and under competitive pressures, a Rubicon is crossed and illegitimate mixes and matches become routine business.

I am grateful to Romar Correa for his comment on my paper. He is right to point out that Keynes was not alone in criticising mainstream views on uncertainty. I could indeed have explored also the epistemology of von Mises and Hayek. I focused on Keynes because his theory of ...[more]

... uncertainty was, in my view, the most fully developed and also the richest in exploring both degrees of uncertainty and the (behavioural and institutional) stratagems for addressing it.

The mention of Shackle is particularly apposite, given his efforts to formalise uncertainty diagrammatically in terms of ‘potential surprise’. The charges against him of nihilism arose from an interpretation along the lines of my Figure 2, while in fact his system encompassed degrees of potential surprise. But he set aside altogether the notion of probability and with it Keynes’s degrees of belief. So, while up to a point his system might be represented by something like my Figure 4, the categories and their interpretation would be rather different from the Keynesian ones I have presented.

An error inadvertently crept into the causal sequence I suggested in my comment. I proposed data/information - confidence - beliefs. The correct path associated with Keynes is data/information - beliefs - confidence.

I agree with Sheila Dow’s argument that Keynes’s theory of decision-making is more subtle than the much simpler Knightian risk/uncertainty duality. Keynes’s notions of logical probability and weight of argument allow considering, at least, four types of situations in decision-making. Here follows my tentative taxonomy:

1) Situations wherein there are ...[more]

... numerical probabilities and the calculus of probability is possible. Additive laws are applicable; full rationality and calculable risk reign.

2) Situations in which there are no numerical probabilities but logical probabilities are possible. There exists an ordering (in terms of more or less), although it might be a partial one, of logical probabilities. This situation also includes Brady’s interval-based probabilities, as well as numerical approximate probabilities, and other cases. Situation 2) is the main domain of Keynes’s extended notion of logical probability in TP. It is the realm of reasonableness, of non-demonstrative logic, of logical probable judgements and limited knowledge (“we have some reasons to believe”). In addition to logical probability, Keynes also considers another attribute of judgement in conditions of limited knowledge, i.e. the weight of argument (that is confidence; weight of argument thus provides at best, exactly as probability itself, partial orderings) and joint judgements of probability and weight.

3) Situations wherein logical probabilities are not comparable. Rational dilemmas (Buridan’s ass dilemma) belong to this situation. Qualitative logical probabilities do exist, but partial ordering or comparison of probabilities is not possible (see TP, CW VIII p. 32 on the umbrella dilemma). For example, there is a conflict between partial reasons, between evidences. Practical rules of decision prevail (for example, caprice in the umbrella dilemma of the TP; various practical rules for decision, imitation and conventions in the GT and the QJE 1937 article).

4) Finally, the miscellaneous ensemble of the different situations grouped under the heading “we do not know”: ignorance; intrinsic incommensurability of logical probabilities; very low weight of argument. These situations do not derive from the fact that we do not know the logical or numerical probabilities (it is the so-called problem of unknown probabilities), but depend on lack of reasons (even some partial reasons) and evidence. Practical rules of decision are here used as well.

Keynes’s true uncertainty clearly covers situation 4) but also, despite fundamental neglect in the literature, situation 3). Chapter 12 in the GT and the 1937 QJE describe both situations. In conditions of true uncertainty, a notion of reasonableness based on rationalization prevails; but rationalization, here, is not the kind of reasonableness that characterises situation 2). Chapter 12 in the GT, however, requires more careful reading, since contrary to what one would perhaps expect, it provides more direct continuity with situation 2) of TP and Keynes’s early writings on speculation and stock exchange. In fact, professional speculators and skilled agents follow decision rules described by situation 2).

I am grateful to Anna Carabelli for her contribution to my paper. She sets out a typology which refines my characterisation of Keynesian uncertainty, demonstrating the richness of his conceptualisation. She fleshes out what I have termed ‘ambiguity’ (as opposed to the mainstream ambiguity) and degrees of fundamental uncertainty. She ...[more]

... notes the role of practical decision rules in each case.

My diagrammatic representation was certainly a simplification of this theory and I have been thinking about how to incorporate Anna Carabelli’s typology so that it is less of a simplification. However it is complicated by thinking, as I have tried to do, in terms of dynamic shifts in uncertainty, as in the crisis and the run-up to the crisis. Thus, while she argues that professional speculators use decision rules consistent with situation (2), they often operate as if within situation (2), when in fact the situation is (3), or even (4). But this can change. New evidence of ignorance can reveal that situations which were thought to yield comparable probabilities in fact do not. A crisis can change the actual scope for comparable probabilities and the reasonableness of decision rules, but more importantly it changes the understanding of the scope for comparable probabilities and thus the reasonableness of the rules. It can change judgements as to whether or not, and to what degree, there is a lack of reason or evidence. It was the combination of these factors which I was trying to capture in the transition from Figure 7 to Figure 8.

see attached file

Please find attached a pdf file with my responses to the referee

Sheila Dow