# Non-ergodicity, Keynesian uncertainty and probabilistic risk

## Knight's and Keynes's distinction between risk and uncertainty

As noted above, Keynes drew a sharp distinction between the analysis of decision making in traditional theory and the conditions faced by decision makers in the 'real world'. But Keynes was not alone in noting the failure of traditional theory.

One of the first economists to call attention to the difficulty of analysing uncertainty was Frank Knight. Knight considered uncertainty to exist when an agent faced what he called a 'unique situation'. Since the agent cannot fall back on past experience to provide a guide, there will be no frequency distribution to provide the basis for the formulation of a probable estimate of the possible outcome (Knight, 1921, p. 233). Any formulation of a numerical probability could be based only on 'pure judgement'. Knight was interested in such cases because he considered them to describe the conditions which entrepreneurs actually face when they take business decisions. It was essential to analyse them in order to be able to understand the evolution of the actual economy.

An example of such a situation would be the formulation of a plan of action based on the proposition 'investing in technology *y* is profitable'. In the absence of any prior quantitative knowledge or experience of the operation of technology *y*, the businessman's evaluation of the returns to be earned from adopting the technology can be based only on personal intuition.

Knight contrasted such cases with what he called 'risk', a situation in which there was 'measurable uncertainty' (see Knight, 1921, pp. 224-5). Here it was possible to formulate 'a priori probabilities' (determined mathematically) or 'statistical probabilities' (determined by empirical observation of frequency of occurrence). By drawing this sharp distinction between risk and uncertainty, Knight sought to highlight the important characteristics of uncertainty that he believed standard theory had neglected. Thus, Knight's concerns are very similar to what we have identified as Keynes's attempt to outline a more 'general' approach to decision making in the face of uncertainty as applying to cases in which the future is not perfectly known so that probabilities can be defined over the set of all possible results.^{1}

Keynes makes a distinction between events that are uncertain and events that are only probable in his famous article in the 1937 *Quarterly Journal of Economics:*

By 'uncertain' knowledge, let me explain, I do not mean merely to distinguish what is known for certain from what is only probable.

The game of roulette is not subject, in this sense, to uncertainty ....

The sense in which I am using the term is that in which the prospect of a European war is uncertain, or the price of copper and the rate of interest twenty years hence, or the obsolescence of a new invention .... About these matters, there is no scientific basis on which to form any calculable probability whatever. We simply do not know.

(Keynes, 1973e [1937], pp. 113-14)

Keynes even denies the possibility of describing the game of roulette as being uncertain even though it is the most common example of uncertainty cited by traditional theory. The crucial point for Keynes, as for Knight, is the inadequacy of statistical quantification in the form of a probability for the analysis of uncertainty since 'human decisions affecting the future, whether personal or political or economic, cannot depend on strict mathematical expectation, since the basis for making such calculations does not exist' (GT, pp. 162-3).

According to Keynes, orthodox economists have neglected this 'embarrassing fact' by supposing that simple extrapolation of past events was a suitable guide for the future, that *natura non facit saltum,* as Alfred Marshall wrote on the title page of his *Principles* (Marshall, 1890). Thus, Keynes accuses 'the classical economic theory of being itself one of these pretty, polite techniques which tries to deal with the present by abstracting from the fact that we know very little about the future' *(GT,* p. 115).