chanical use of formulas permits one to calculate a value for an arithmetic

mean, standard deviation, and so on, of any data set collected over time. The

question is what meaning the values calculated in this way should carry. If

economists do not possess, never have possessed, and conceptually never will

possess an ensemble of macroeconomic worlds, then it can be logically

argued that objective probability structures do not even ¬‚eetingly exist, and a

distribution function of probabilities cannot be de¬ned. The application of

the mathematical theory of stochastic processes to macroeconomic phenom-

ena would be therefore highly questionable, if not invalid in principle. Hicks

(1979, p. 129) reached a similar judgement and wrote:

I am bold enough to conclude, from these considerations, that the usefulness of

˜statistical™ or ˜stochastic™ methods in economics is a good deal less than is now

conventionally supposed. We have no business to turn to them automatically; we

should always ask ourselves, before we apply them, whether they are appropriate

to the problem at hand. Very often they are not.

Clearly, the objective probability environment associated with the rational

expectations hypothesis involves a very different conception. In the context

of forming macroeconomic expectations, it holds that time averages calcu-

lated from past data will converge with the time average of any future

realization. Knowledge about the future involves projecting averages based

on the past and/or current realizations to forthcoming events. The future is

merely the statistical re¬‚ection of the past and economic actions are in some

sense timeless. There can be no ignorance of upcoming events for those who

believe the past provides reliable statistical information (price signals) re-

garding the future, and this knowledge can be obtained if only one is willing

to spend the resources to examine past market data.

For the rational expectations hypothesis to provide a theory of expect-

ational formation without persistent errors, not only must the subjective and

objective distribution functions be equal at any given point of time, but

these functions must be derived from what are called ergodic stochastic

processes. By de¬nition, an ergodic stochastic process simply means that

averages calculated from past observations cannot be persistently different

from the time average of future outcomes. In the ergodic circumstances of

objective probability distributions, probability is knowledge, not uncer-

tainty! Non-stationarity is a suf¬cient, but not a necessary, condition for

non-ergodicity. Some economists have suggested that the economy is a

non-stationary process moving through historical time and societal actions

can permanently alter economic prospects. Indeed, Keynes™s (1939b, p. 308)

famous criticism of Tinbergen™s econometric methodology was that eco-

nomic time series are not stationary for ˜the economic environment is not

466 Modern macroeconomics

homogeneous over a period of time (perhaps because non-statistical factors

are relevant)™.

However, at least some economic processes may be such that expectations

based on past distribution functions differ persistently from the time average

that will be generated as the future unfolds and becomes historical fact. In

these circumstances, sensible economic agents will disregard available mar-

ket information regarding relative frequencies, for the future is not statistically

calculable from past data and hence is truly uncertain. Or as Hicks (1977,

p. vii) succinctly put it, ˜One must assume that the people in one™s models do

not know what is going to happen, and know that they do not know just what

is going to happen™. In conditions of true uncertainty, people often realize

they just don™t have a clue!

Whenever economists talk about ˜structural breaks™ or ˜changes in regime™,

they are implicitly admitting that the economy is, at least at that stage, not

operating under the assumptions that allow the objective probability to hold.

For example, Robert Solow has argued that there is an interaction of histori-

cal“societal circumstances and economic events. In describing ˜the sort of

discipline economics ought to be™, Solow (1985, p. 328) has written: ˜Unfor-

tunately, economics is a social science™ and therefore ˜the end product of

economic analysis is ¦ contingent on society™s circumstances “ on historical

context ¦ For better or worse, however, economics has gone down a differ-

ent path™.

The possibility of true uncertainty indicates that while objective probabilities

and the rational expectations hypothesis may be a reasonable approximation in

some areas where actions are routine, it cannot be seen as a general theory of

choice. Moreover, if the entire economy were encompassed by the objective

probability environment, there would be no role for money; that is, money

would be neutral! In all Arrow“Debreu type systems where perfect knowledge

about the future is provided by a complete set of spot and forward markets, all

payments are made at the initial instant at market-clearing prices. No money is

needed, since in essence goods trade for goods.

The subjective probability environment and true uncertainty In the subjec-

tive probability environment, the concept of probability can be interpreted

either in terms of degrees of conviction (Savage, 1954, p. 30), or as relative

frequencies (von Neumann and Morgenstern, 1953). In either case, the under-

lying assumptions are less stringent than in the objective probability

environment; for example, the Savage framework does not rely on a theory of

stochastic processes. However, true Keynesian uncertainty will still exist

when the decision maker either does not have a clue as to any basis for

making such subjective calculations, or recognizes the inapplicability of to-

day™s calculations for future pay-offs.

The Post Keynesian school 467

This environment of ignorance regarding future outcomes provides the

basis of a more general theory of choice, which can be explained in the

language of expected utility theorists. In expected utility theory, ˜a prospect

is de¬ned as a list of consequences with an associated list of probabilities,

one for each consequence, such that these probabilities sum to unity. Conse-

quences 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 ¦ [and] An individual™s preferences are de¬ned

over the set of all conceivable prospects™ (Sugden, 1987, p. 2). Using these

de¬nitions, an environment of true uncertainty (that is, one which is non-

ergodic) occurs whenever an individual cannot specify and/or order a complete

set of prospects regarding the future, either because: (i) the decision maker

cannot conceive of a complete list of consequences that will occur in the

future; or (ii) the decision maker cannot assign probabilities to all conse-

quences because ˜the evidence is insuf¬cient to establish a probability™ so

that possible consequences ˜are not even orderable™ (Hicks, 1979, pp. 113,

115).

A related but somewhat different set of conditions that will lead to true

uncertainty can be derived from Savage™s observation (1954, pp. 11“13) that

his integration of personal probabilities into expected utility theory ˜makes

no formal reference to time. In particular, the concept of an event as here

formulated is timeless™. Savage develops an ordering axiom of expected

utility theory, which explicitly requires ˜that the individual should have a

preference ordering over the set of all conceivable prospects™ (Sugden, 1987,

p. 2) and that the ordering be timeless. Hence, even if a decision maker can

conceive of a complete set of prospects if the pay-off is instantaneous, as

long as he or she fears that tomorrow™s prospects can differ in some unknown

way, then the decision maker will be unable to order tomorrow™s pay-off

completely, Savage™s ordering axiom is violated, and Keynes™s uncertainty

concept prevails.

Interestingly enough, Savage recognized (although many of his followers

have not) that his analytical structure is not a general theory; it does not deal

with true uncertainty. Savage (1954, p. 15) admits that ˜a person may not know

the consequences of the acts open to him in each state of the world. He might

be ¦ ignorant™. However, Savage then states that such ignorance is merely the

manifestation of ˜an incomplete analysis of the possible states™. Ignorance

regarding the future can be de¬ned away by accepting the ˜obvious solution™ of

assuming that the speci¬cation of these timeless states of the world can be

expanded to cover all possible cases. Savage (1954, p. 16) admits that this ˜all

possible states™ speci¬cation presumption when ˜carried to its logical extreme

¦ is utterly ridiculous ¦ because the task implied in making such a decision is

not even remotely resembled by human possibility™.

468 Modern macroeconomics

By making this admission, Savage necessarily restricts his theory of choice

to ˜small world™ states (Savage, 1954, pp. 82“6) in which axioms of expected

utility theory apply, and hence he writes: ˜[T]his theory is practical [only] in

suitably limited domains ¦ At the same time, the behavior of people is often

at variance with the theory ¦ The main use I would make of [expected utility

postulates] ¦ is normative, to police my own decisions for consistency™

(Savage, 1954, p. 20). Any monetary theory that does not recognize the

possibility of non-ergodic uncertainty cannot provide a non-neutral role for

money and hence is logically incompatible with Post Keynesian monetary

theory. In a Keynesian ˜large world™ as opposed to Savage™s small one,

decision makers may be unable to meet the axioms of expected utility theory

and instead adopt ˜haven™t a clue™ behaviour one time and ˜damn the torpe-

does™ behaviour at another, even if this implies that they make arbitrary and

inconsistent choices when exposed to the same stimulus over time.

8.10 Keynesian Uncertainty, Money and Explicit Money Contracts