Classifying Decision-making Environments
Time is a device that prevents everything from happening at once. In every
real-world choice, the prospective pay-off associated with any action is necessarily
separated by some period of calendar time from the moment of
choice. The production of commodities requires considerable time; the consumption
of capital goods and consumer durables needs even more. Because
of this fundamental fact of elapsing time, all economic decisions can be
conceived of as occurring under one of the following mutually exclusive
environments:
1. The objective probability environment
Decision makers believe that the past is a statistically reliable guide to the
future. This is the rational expectations hypothesis, where knowledge regarding
future consequences of today’s decisions involves a confluence of subjective
and objective probabilities.
2. The subjective probability environment
In the individual’s mind, subjective (or what Savage, 1954, calls personal)
probabilities regarding future prospects at the moment of choice govern
future outcomes. These subjective probabilities need not coincide with objective
distributions, even if well-defined objective distributions happen to exist.
3. The true uncertainty environment
Regardless of whether objective relative frequencies can be shown to have
existed in the past and/or subjective probabilities exist today, the economic
agent believes that during the time between the moment of choice and the payoff,
unforeseeable changes will occur. The decision maker believes that no
information regarding future prospects exists today and therefore the future is
not calculable. This is uncertainty (or ignorance about future consequences) in
the sense of Keynes (1937, p. 113). Keynes wrote that by uncertainty he did
‘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 … there is no scientific basis on
which to form any calculable probability whatever. We simply do not know’.
Moreover, Keynes (1937, p. 122) added ‘the hypothesis of a calculable future
leads to a wrong interpretation of the principles of behaviour’. The longer the
lapse between choice and consequence, the more likely individuals are to
suspect that they must decide in an environment of true uncertainty.
The objective probability environment and true uncertainty Keynes (1936,
pp. 148–50, 161) claimed that some future consequences could have no prob
ability ratios assigned to them. Of course, as a computational matter, mechanical
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 fleetingly exist, and a
distribution function of probabilities cannot be defined. The application of
the mathematical theory of stochastic processes to macroeconomic phenomena
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 calculated
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 reflection 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) regarding
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 expectational
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 definition, 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 uncertainty!
Non-stationarity is a sufficient, 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 economic
time series are not stationary for ‘the economic environment is not
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 market
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 historical–
societal circumstances and economic events. In describing ‘the sort of
discipline economics ought to be’, Solow (1985, p. 328) has written: ‘Unfortunately,
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 different
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 subjective
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 underlying
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 today’s
calculations for future pay-offs.
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 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 … [and] An individual’s preferences are defined
over the set of all conceivable prospects’ (Sugden, 1987, p. 2). Using these
definitions, an environment of true uncertainty (that is, one which is nonergodic)
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 consequences
because ‘the evidence is insufficient 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 defined away by accepting the ‘obvious solution’ of
assuming that the specification 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’ specification 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’.
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 torpedoes’
behaviour at another, even if this implies that they make arbitrary and
inconsistent choices when exposed to the same stimulus over time.
Time is a device that prevents everything from happening at once. In every
real-world choice, the prospective pay-off associated with any action is necessarily
separated by some period of calendar time from the moment of
choice. The production of commodities requires considerable time; the consumption
of capital goods and consumer durables needs even more. Because
of this fundamental fact of elapsing time, all economic decisions can be
conceived of as occurring under one of the following mutually exclusive
environments:
1. The objective probability environment
Decision makers believe that the past is a statistically reliable guide to the
future. This is the rational expectations hypothesis, where knowledge regarding
future consequences of today’s decisions involves a confluence of subjective
and objective probabilities.
2. The subjective probability environment
In the individual’s mind, subjective (or what Savage, 1954, calls personal)
probabilities regarding future prospects at the moment of choice govern
future outcomes. These subjective probabilities need not coincide with objective
distributions, even if well-defined objective distributions happen to exist.
3. The true uncertainty environment
Regardless of whether objective relative frequencies can be shown to have
existed in the past and/or subjective probabilities exist today, the economic
agent believes that during the time between the moment of choice and the payoff,
unforeseeable changes will occur. The decision maker believes that no
information regarding future prospects exists today and therefore the future is
not calculable. This is uncertainty (or ignorance about future consequences) in
the sense of Keynes (1937, p. 113). Keynes wrote that by uncertainty he did
‘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 … there is no scientific basis on
which to form any calculable probability whatever. We simply do not know’.
Moreover, Keynes (1937, p. 122) added ‘the hypothesis of a calculable future
leads to a wrong interpretation of the principles of behaviour’. The longer the
lapse between choice and consequence, the more likely individuals are to
suspect that they must decide in an environment of true uncertainty.
The objective probability environment and true uncertainty Keynes (1936,
pp. 148–50, 161) claimed that some future consequences could have no prob
ability ratios assigned to them. Of course, as a computational matter, mechanical
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 fleetingly exist, and a
distribution function of probabilities cannot be defined. The application of
the mathematical theory of stochastic processes to macroeconomic phenomena
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 calculated
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 reflection 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) regarding
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 expectational
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 definition, 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 uncertainty!
Non-stationarity is a sufficient, 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 economic
time series are not stationary for ‘the economic environment is not
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 market
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 historical–
societal circumstances and economic events. In describing ‘the sort of
discipline economics ought to be’, Solow (1985, p. 328) has written: ‘Unfortunately,
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 different
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 subjective
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 underlying
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 today’s
calculations for future pay-offs.
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 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 … [and] An individual’s preferences are defined
over the set of all conceivable prospects’ (Sugden, 1987, p. 2). Using these
definitions, an environment of true uncertainty (that is, one which is nonergodic)
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 consequences
because ‘the evidence is insufficient 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 defined away by accepting the ‘obvious solution’ of
assuming that the specification 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’ specification 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’.
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 torpedoes’
behaviour at another, even if this implies that they make arbitrary and
inconsistent choices when exposed to the same stimulus over time.
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