Post-Keynesians, historical time and crucial decision making

However strongly they voiced their concern for the importance of uncertainty, both Knight and Keynes seem to have failed to convince economists that the vast majority of the theorems in modern economics dealing with uncertainty in fact analyse what both authors defined as risk. To highlight the difference between the traditional analysis of uncertainty by methods that are undifferentiated from those applied to the analysis of risk, many Post Keynesian economists have adopted the terms 'true' or 'fundamental' uncertainty to identify this original, but now often overlooked, definition of uncertainty originally formulated by Knight and Keynes. In doing so they hope to distinguish their extensions of the Knight-Keynes analysis from the traditional neoclassical approach in which agents are either presumed to know the future results of their actions, so that they are simply choosing the optimal set of future results, or are viewed as exploring possible decisions to discover those that are deemed to be suboptimal. The idea is simply to distinguish between two diametrically opposed traditions in analysing the impact of the future on the present.

Many Post Keynesians have attempted to elaborate the explanations of uncertainty given by Knight and Keynes in order to better distinguish the concept from the traditional analysis of risk.

They have thus attempted to develop Keynes's alternative analysis in ways that do not rely on the existence and/or the knowledge of the probability distributions of future events. In addition to emphasizing that they are interested in 'fundamental' uncertainty', they have sought to characterize the existence of such conditions in the conceptions of

'historical time' and crucial 'decision making'. Thus, 'Post-Keynesian theory ... is concerned primarily with the depiction of an economic system expanding over time in the context of history' (Eichner and Kregel, 1975, p. 1294; emphasis in the original) so that time is 'a real- world device which prevents everything from happening at once' (Davidson, 1981, p. 158).

Since the basic economic decisions concerning production and investment are processes that take time and are essentially irreversible, they are said to take place in 'historical' or 'calendar' time. As a result, actions cannot be reversed; decisions that lead to actions that cannot be reversed or repeated to produce more desirable outcomes are called 'crucial' decisions.

In the neoclassical approach, on the other hand, either time is considered as a logical and thus reversible process or agents are simply discovering an already known future; their actions cannot determine the future. As a result, when these issues are treated from the neoclassical perspective, it is in terms of probabilistic risk since true uncertainty as defined by Knight is not considered.^{2}

Shackle was the first to note that historical time implied what he called 'crucial' decisions. An agent faces a crucial decision when he ' cannot exclude from his mind the possibility that the very act of performing the experiment may destroy forever the circumstances in which it is performed' (Shackle, 1955, p. 6). '[C]rucialness is the real and important source of uniqueness in any occasion of choosing' (Shackle, 1955, p. 63). Thus, as Davidson has pointed out, 'when agents make crucial decisions they necessarily destroy any stochastic processes that may have existed at the point of time of the decision' (Davidson, 1982-83, p. 192). In other words, crucial decisions describe situations in which the act of taking a decision destroys the existing distribution functions.

The identification of cruciality as an important element in economic decisions under uncertainty produces a clear line of demarcation between Post Keynesian authors and modern neoclassical theory. The latter assumes that there is sufficient information available in the present concerning the probability functions of future events, so that whatever decision is actually taken it is not considered crucial. As Shackle emphasizes, the existence of the distribution functions implies that the future 'is already existent and merely waiting to appear. If this is so, if the world is determinist, then it seems idle to speak of choice. Choice ... is originative; it is the start of a new train of influences' (Shackle, 1972, pp. 122-3).^{3}

Among Post Keynesians Davidson has argued that these two characteristic features of uncertainty in the 'real world'—historical time and crucial decisions—imply that the stochastic process that generates real world events is 'non-ergodic'. He has used this observation as the basis for a modern reinterpretation of Keynes's distinction between probable and uncertain events. However, such a reinterpretation of the real world in terms of stochastic processes that are more usually associated with the frequency-based theory of probability appears to contradict Keynes's statement that it is impossible to calculate probabilities for some events.^{4 }Indeed, Davidson himself has pointed out that, in conditions of true uncertainty, 'objective probability structures do not even fleetingly exist, and a distribution function of probabilities cannot be defined' (Davidson, 1991, p. 132). Further, in order to apply the traditional frequency approach it is desirable to be able to repeat experiments in identical conditions so that the moments of the random functions can be calculated on the basis of a large number of realizations. This would be difficult, if not impossible, in the environment to which Keynes referred. All this seems to exclude any application of the mathematical theory of stochastic processes, which requires the existence, at least conceptually, of a universe of realizations.

However, a less extreme interpretation of Keynes's position is possible. For example, if probabilities are assumed to exist for all events, but agents do not possess sufficient information to construct satisfactory probability estimates for some future events they may conclude that the objective distribution functions are, to use Keynes's terms, 'subject to sudden changes' (Keynes, 1973e [1937], p. 119) over time, such that the economic environment cannot be assumed to be in a state of statistical control. Alternatively, agents may recognize that exogenous changes may produce radical reconsideration of the subjective distribution functions that they have formed. Either of these results would preclude the convergence of the psychological functions to the objective functions (even stochastically). And this would be true even if these latter functions are homogeneous over short periods of calendar time.

Such an interpretation would allow Keynes's analysis of uncertainty to be recast in terms of non-ergodic stochastic processes. Indeed, such an interpretation would explicitly integrate the possibility that the probability structures (both the objective and the psychological functions), even if they exist at every point in time, would be subject to sudden and violent fluctuations. It thus follows that the expectations produced on the basis of the calculation of probabilities may be completely independent of the actual future events.

Neither is the reformulation of Keynes's analysis in terms of non-ergodic stochastic processes incompatible with the rejection of the traditional theory of choice under uncertainty based on either objective or subjective probability distributions. The reformulation allows Post Keynesian criticism of objective probability analysis to be expressed in the fact that the traditional approach is valid only in an ergodic world. The criticism of subjective probability analysis appears less straightforward if probability is interpreted either in terms of 'degrees of conviction' (Savage, 1954, p. 30) or in terms of 'relative frequencies' (von Neumann and Morgenstern, 1953) because the hypotheses required are less strict. In particular, the model proposed by Savage does not even rely on a theory of stochastic processes.

This environment of potential ignorance about future results allows a more general theory of decision making on the basis of expected utility analysis. In the theory of expected utility, according to Sugden,

a prospect is defined as a list of consequences with an associated list of probabilities, one for each consequence, such that these probabilities sum to unity. Consequences are to be understood to be mutually exclusive possibilities: thus a prospect comprises an exhaustive list of the possible consequences of a particular course of action ... An individual's preferences are defined over the set of all conceivable prospects.

(Sugden, 1987, p. 2)

However, a close examination of this characterization of the theory of expected utility clearly shows that it is incompatible with Keynes's conception of uncertainty and with the reformulation in terms of non- ergodic processes.

Savage (1954, p. 10) defines an event as 'having every state of the world as an element' and insists on an order axiom implying that 'in deciding on an act, account must be taken of all possible states of the world, and the consequence implicit in each act for each possible state of the world' (Savage, 1954. p. 13). Further Savage notes that his approach 'makes no formal references to time' (Savage, 1954, p. 13). Thus, the decision maker seeking to maximize his utility is presumed to have a preference ordering that is both non-temporal and complete over the set of all possible realizations. It is clear that in a situation of real uncertainty these two conditions are rarely satisfied. In these conditions, it is understandable that Savage himself recognizes that his approach cannot be considered as a general theory because it does not cover 'true' uncertainty. The theory of expected utility appears to be more a code of coherent conduct for the individual than a system for the formation of expectations of future events. In other terms, it no longer deals with forecasting the behaviour of the majority of economic agents or of businessmen, but provides a specification of the behaviour that economic agents should adopt in order to be rational as defined by its initial axioms.

In this approach the antithesis of analytical structures (certainty/ uncertainty, logical time/historical time, ergodic/non-ergodic process) is superimposed on a divergence of objectives. In fact, the axiomatic construction has as its explicit objective the derivation of the optimal state or behaviour from its postulates, while Keynesian theory adopts, as we have emphasized, the opposite path, looking above all to characterize the decision making environment and economic decision making on empirical observations taken from the real world.

This Post Keynesian presentation of the characteristic features of the real world in terms of historical time and crucial decisions thus leads to the reinterpretation of Keynesian uncertainty as a non-ergodic stochastic processes which is clearly incompatible with the decisionmaking environment assumed in other, alternative approaches within the neoclassical tradition based on probabilistic risk, in terms of either objective or subjective probability. This result has even broader theoretical interest. The identification of the conditions of non-ergodicity and the rejection of the traditional probability-based analysis not only highlights the deficiencies of the way uncertainty is defined and analysed in neoclassical theory, it also calls into question the traditional analysis of economic rationality in a truly uncertain environment.