ALTERNATIVE KEYNESIAN AND POST KEYNESIAN PERSPECTIVES ON UNCERTAINTY AND EXPECTATIONS

Journal of Post Keynesian Economics, Summer 2001, vol. 23, no. 4, pp. 545-566

J. Barkley Rosser, Jr. Professor of Economics and Kirby L. Kramer, Jr. Professor of Business Administration MSC 0204 James Madison University Harrisonburg, VA 22807 USA Tel: 540-568-3212 Fax: 540-568-3010 E-mail: rosserjb@jmu.edu Website: http://cob.jmu.edu/rosserjb

August 2000

The author wishes to acknowledge useful remarks from Paul Davidson and Richard P.F. Holt. An abridged version of this paper is forthcoming as a chapter entitled “Uncertainty and Expectations” in The New Guide to Post Keynesian Economics, edited by Richard P.F. Holt and Steven Pressman, London: Routledge, 2001.

JEL Codes: E0, B2

Abstract: Keynesian and Post Keynesian perspectives on uncertainty and expectations are examined by initially reviewing the views of Keynes himself on these matters. Sources of uncertainty are seen by later Keynesians and Post Keynesians are seen as arising from potential surprise and history versus equilibrium, from nonergodicity, or from group dynamics. These imply the use of bounded rationality and conventions in forming expectations and a firm rejection of the hypothesis of rational expectations. Policy implications are then discussed.

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I. INTRODUCTION

It is a curious fact that A Guide to Post-Keynesian Economics (Eichner, 1979) has no chapter

on Uncertainty and Expectation, despite the fact that this topic was central to the concerns of

John Maynard Keynes. Two phenomena may be responsible for this lacuna.

First, the concept of uncertainty as developed by Keynes was largely hijacked by James

Tobin (1959) and turned into a concept of quantifiable risk. Although risk and uncertainty are

not identical concepts, Tobin made it seem acceptable to treat them as if they were, and one

finds many books that will use the term uncertainty, which is non-quantifiable in the view of

Keynes and now the Post Keynesians as well, and will discuss it in terms of objectively

measurable and quantifiable risk. This approach was picked up by the emerging financial

economists who would incorporate it into a model assuming rational expectations and efficient

markets, despite Tobins own skepticism regarding these matters (Weisman, 1984). This

violated the accepted division between measurable risk and unmeasurable uncertainty that had

been introduced by Frank Knight (1921) in the same year that Keyness own Treatise on

Probability was published.

Second, there was the baleful influence of the rational expectations revolution which up to

1979 Post Keynesians had not felt the need to respond to seriously as it seemed such a patently

ridiculous idea to them. Indeed, when most of the 1979 Guide was written in the mid-1970s, the

idea was not yet viewed as important by most economists in general. Although some Post

Keynesian economists worried about uncertainty and expectation in the original Keynesian sense

prior to 1979 (Shackle, 1955, 1972; Kregel, 1976; Loasby, 1976; Davidson, 1978; Vickers,

1978; Hicks, 1979), there was no concerted effort to critique the rational expectations

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assumption on the grounds of Keynesian uncertainty. The concept of rational expectations had

been introduced into microeconomics by John Muth (1961), but then was applied to

macroeconomics by Robert Lucas (1972). Lucas used this approach to argue against the idea

that governments can systematically affect the behavior of people in the economy because

people will take into account the actions of the government and act in ways to nullify anything

the government tries to do, based on their ability to forecast accurately on average what the

economy will do in the future.

During the late 1970s and early 1980s this New Classical view with its pro-laissez-faire

implications began sweep much of the economics profession and established itself as the

dominant approach in macroeconomics, especially in the US. Since then systematic critiques by

Post Keynesians of rational expectations have been voluminous, and the effort has generated

much discussion of the basic concepts of uncertainty and expectation themselves. It has become

clear that in order to combat the policy argument that nothing can (or should) be done, that

seemed to come out of the rational expectations/New Classical view, the core assumptions

regarding how people form expectations would need to be understood. This then opened the

door for the reconsideration of the old Keynes view of uncertainty as fundamental and

unquantifiable. In this way, the Keynes view of uncertainty undermines the foundation of the

rational expectations assumption and the policy arguments that flow from it.

II. KEYNES ON UNCERTAINTY AND EXPECTATION

The reason that how people form expectations is important is that people actually act on the

basis of what they think is going to happen in the future. Rational expectations provides an

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answer to this problem that is very neat and has enormous appeal to many theorists because of its

simultaneous simplicity while granting great insight to economic agents: on average, people

expect what will really happen. This makes them both insightful, but it also makes it easy for

the theorist who can simply impose a theory of reality and say that people understand it and

expect what it forecasts. The assumption that they expect what the theorist says will happen then

reinforces the forecast that it really will happen. People do what the theorist says they will

because they know that the theorist is right and in so doing make the theorist right. Following

Lucas and the other New Classicals that rationally expected outcome will be a full employment

nirvana, unless the government messes things up by confusing peoples expectations through its

arbitrary policy actions. Lucas openly argued that his view overthrew the arguments of Keynes

which he deemed to be outdated and irrelevant.

Thus, it is understandable that Post Keynesians might respond to such an argument by going

back to Keynes himself in search of a critique of such a simple-minded view of expectations

formation. Post Keynesians thus rediscovered the old Keynes idea that the flighty bird of real

capital investment is not driven by long-run rational expectations, which are impossible, but

rather by essentially subjective and ultimately irrational animal spirits, a spontaneous urge to

action in the face of uncertainty.

Keynes presented his most extensive thoughts about uncertainty in his 1921 Treatise on

Probability (1973, Vol. VIII). He had some later remarks on the topic in the 1936 The General

Theory of Employment, Interest and Money (1973. Vol. VII) and in his 1937 article, The

General Theory of Employment, (1973, Vol. XIV). The most important link with expectation

formation comes in the famous Chapter 12 of The General Theory, The State of Long-Term

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Expectation (1973, Vol. VII). Here the ubiquity of unquantified uncertainty is seen as causing

people to look to the current facts and to the average state of opinion, the state of confidence,

to form their expectations. They will base their expectations on what they put weight on, a

point we shall return to later.

But while the state of long-term expectations may remain steady for long periods, it is also

subject to sudden and violent shifts, sometimes caused by speculation in markets (sometimes

irrational) as well as shifts of psychology. In Chapter 12 Keynes puts forth his theory of

animal spirits. He argues that these spirits lie behind capital investment, a spontaneous urge

to action rather than inaction, and not as the outcome of a weighted average of quantitative

benefits multiplied by quantitative probabilities (1973, Vol. VII, p. 161). Chapter 13 of The

General Theory also argues that uncertainty about the future of interest rates underlies liquidity

preference and thus constitutes part of the demand for money as well.

There has been much controversy about Keyness views on uncertainty. One reason for

this is that Keynes presented several different arguments regarding uncertainty, including a

possible shift in his view over time toward more emphasis on its absolutely unquantifiable

nature. However, the place to start is the 1921 Treatise on Probability, which undoubtedly

served as the foundation of his later views and is where he presents the fullest discussion of the

matter. In that volume he declares (1973, Vol. VIII, p. 33):

There appear to be four alternatives. Either in some cases there is no probability at all; or

probabilities do not all belong to a single set of magnitudes measurable in terms of a common

unit; or these measures always exist, but in many cases are, and must remain, unknown; or

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probabilities do belong to such a set and their measures are capable of being determined by us,

although we are not always able so to determine them in practice.

It is widely argued that he had the first case in mind for economic matters when he

contemplated long-term outcomes of decisions. Thus in his 1937 article he declares regarding

uncertain knowledge (1973, Vol. XIV, p. 113):

...not only 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; nor is the prospect of

a Victory bond being drawn. Or, again, the expectation of life is only slightly uncertain. Even

the weather is only moderately uncertain. 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, or the position of private wealth

owners in the social system in 1970. About these matters there is no scientific basis on which to

form any calculable probability whatever. We simply do not know.

The second case is associated with the problem of non-comparability or incomplete ordering

that he discusses at the end of Chapter 3 (The Measurement of Probabilities) of the Treatise on

Probability. He argues that some series of possible events may be ordinally ranked with respect

to each other in terms of greater or lesser probability, but without any cardinality to these

probabilities. But then there may be another series of events that can also be so ranked amongst

themselves but that no possible event from this series can be compared with any possible event

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from the first series. Or, there may be some event that is in both series and can be compared

with every event in each series, but that no others can be.1 A possible argument for such non-

comparabilities of series or non-cardinalities within series might be (using classical frequentist

statistics that Keynes rejected), that each possible event has a different shaped probability

distribution. Thus one event might have a Gaussian normal distribution with a lower mean than

the other. But the other might be skewed and have a lower median and mode than the former.

The third case is not explicated by Keynes, but might reflect the position of Knight (1921)

according to Lawson (1988), who categorizes views on probability according to whether they are

quantifiable or non-quantifiable and whether they are subjective or objective. Thus Keynes is

non-quantifiable-subjective; Knight is non-quantifiable-objective; Savage (1954) is quantifiable-

subjective, and rational expectationists such as Muth (1961) are quantifiable-objective.

The fourth case represents epistemological problems of how to know what we know whose

causes may be many and have been debated at length by Post Keynesian economists. A few

simple examples would be where cases from which one might calculate the probabilities are very

hard to observe or generate data that is hard to measure or estimate or that there are too few

cases to meaningfully estimate such probabilities.

Furthermore it must be made clear that Keynes recognized the possibility of quantifying

fairly exact probabilities for certain kinds of cases, as in the roulette wheel example given above.

He also talks about the classic examples of flipping coins and rolling a die. He accepts that for

some situations insurance companies may be able to make such quantifiable calculations, but

that there are others for which their estimates are essentially arbitrary guesses.

An important aspect of Keyness view of probability is that he viewed it as fundamentally

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subjective, something that can be constructed from internal logic rather than from mathematical

calculations of distributions from external observations. Possible events are to be viewed in

comparison with each other by their probability relation, possibly unmeasurable. He raises the

problem of induction even for the cases where a priori knowledge and logic might well yield an

apparently definitive quantitative answer. Thus, we can say a priori that a fair die will have a

one sixth probability of landing on each side. But how do we know it is a fair die, especially if

as we roll it we see one side coming up regularly more than the others?

Keyness subjectivism is more radical and more uncompromising than that of most other

subjectivist probabilists and followers of Bayes, although Poirier (1988) argues that some

Bayesians are fully subjective in the Keynesian sense. Such subjectivists as von Neumann and

Morgenstern (1944) and Savage (1954) see a frequentist underpinning to the subjective

probabilities assigned by agents. In the usual Bayesian formulation there is ultimately a

convergence of the subjective and the objective probability as the number of observations

increases,2 a kind of foreshadowing of the rational expectations view and one that certainly

assumes an ultimate validity to the concept of objective probability. Keynes rejects this

ultimate objectivity of probability, despite accepting that logical deductions can result in

reasonable quantified probabilities some of the time. This subjectivism carries over into

Keyness views on expectations formation and economic decision making. There is simply no

way that Keynes would have accepted Muths (1961, p. 316) view that expectations are rational

in the sense that expectations of firms (or more generally the subjective probability of

outcomes) tend to be distributed, for the same information set, about the prediction of the theory

(or the objective probability distribution of outcomes).

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As noted above, Keynes suggested that agents form their expectations based on how much

weight they put on different possibilities. He discusses this concept of weight in Chapter 6 of

the Treatise on Probability, an issue whose philosophical aspects have been discussed by Runde

(1990) and ODonnell (1990). It is identified with the amount of relevant evidence that an

agent has gathered regarding the probability of a possible outcome. It is not the same as the

probability of that outcome. In that regard it is tempting to identify this concept with that of

statistical significance in classical frequentist statistics. But it is also clear that Keynes rejects

the definite quantitative comparing of such weights. However he does emphasize that the

determination of degrees of belief is a rational and logical process. But later, writing of Frank

Ramsey in the Essays in Biography in 1931 (1973, Vol. X, pp. 336-339), he moved from a view

that probability is an objective relation between propositions (subjectively known through logic)

to a view that probability is mostly about degrees of belief. And those beliefs, which can

change suddenly, are most strongly influenced by current reality, whose “salience” (Akerlof,

1991) impresses and thus contributes greatly to weight, at least for a time..

III. POST KEYNESIAN PERSPECTIVES ON UNCERTAINTY AND EXPECTATION

A. POTENTIAL SURPRISE AND HISTORY VERSUS EQUILIBRIUM

The main figure who developed the implications of non-quantifiable uncertainty was G.L.S.

Shackle (1955, 1972).3 He, along with Loasby (1976), took an uncompromising stance regarding

the absolute ontological nature of Keynesian uncertainty and strongly emphasized its role in

investment and the unpredictability and peculiar variability of investment. This uncertainty was

seen as tied to the creativity and free will of the investor, his or her ability to create ex nihilo a

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new reality that constantly churns and upsets previous realities as potential surprises emerge.

This led him to reject the concept of equilibrium and to declare that reality is kaleidic

(Shackle, 1974), constantly changing and swirling like the colors of a kaleidoscope. Coddington

(1982)4 cited Shackle and Loasby approvingly as exponents of the logical implications of

Keynesian uncertainty, even as he rejected the idea as nihilistic.

Eventually Shackle (1969) argued that potential surprise lay at the basis of the creative

decision making of firms. This inspired others to attempt formalize this concept. Vickers

(1978) postulates surprise functions and attractiveness functions that represent their

attention-commanding power that draws decision makers to focus upon different potential

surprises as the basis for behavior. This approach has drawn criticism for potentially opening

the door to imputing subjective probabilities and thus violating the spirit of true Keynesian

uncertainty (Williams and Findlay, 1986), a criticism rejected by Vickers (1986) who argues that

the irreversibility of time renders this critique irrelevant. This Shackle-Vickers approach to

microeconomic decision making by firms has been further developed by Katzner (1990).

Running through the arguments of Shackle, Loasby, and Vickers is an emphasis on the

unidirectional nature of time and the significance of this for the unknowability of the future and

the ontological nature of uncertainty. This theme has been emphatically emphasized by others as

well, most clearly Bausor (1982-83, 1984). He draws into the argument two strands that

emphasize the irrevocability of decisions. One is the entropy-related argument of Georgescu-

Roegen (1971) which argues that tendency for the degree of disorder (entropy) to increase over

time in the universe according the Second Law of Thermodynamics is the fundamental reason

for the unidirectional nature of time . The other is the eloquent distinction between historical

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time and equilibrium drawn by Joan Robinson (1974) who argues that actual, non-repeatable,

historical time has little relation to the abstract time appearing in most theoretical economic

equilibrium models. In Bausors work these themes reinforce the kaleidic vision of Shackle.

Gowdy (1985-86) throws this discussion into a more explicitly ecological-evolutionary

framework.

B. NONERGODICITY AND UNCERTAINTY

Probably the most influential of all Post Keynesian arguments regarding the ontological

foundations of Keynesian uncertainty has been the identification of nonergodicity as endemic in

the dynamics of economic systems due to Paul Davidson (1982-83, 1991, 1994, 1996), drawing

on earlier arguments of Shackle (1955) and Hicks (1979).5 An ergodic process is one for which

time and space averages are equal; what happens at points in time for different initial states

coincides with what happens over time for a given initial state. This suggests that economic

processes over time follow averages that can be discovered by rational agents, thus implying the

possibility of rational expectations. Recognizing that Keynes was unaware of this concept, per

se, Davidson nevertheless interprets his arguments for uncertainty as implying nonergodicity of

economic time series. For Davidson this becomes a battle axe with which to directly attack the

rational expectations hypothesis.

One problem that arises, indeed arises more broadly for the emphasis upon uncertainty, is

how can there be any predictability regarding policy outcomes if there is such profound

uncertainty, essentially the argument of nihilism made by Coddington (1982). Davidson

responds to this by citing Shackles (1955) argument regarding cruciality. Potential surprise

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and nonergodicity arise only with crucial decisions such as major capital investments, or for an

individual the choice of a career. Routine decisions may well be governed by ergodicity and be

somewhat predictable, including much of consumption behavior. But the essential creativity of

animal spirits-driven capital investment process is inherently surprising and nonergodic, thereby

providing an onotological foundation for uncertainty. Davidson sees uncertainty as the source of

the long-run non-neutrality of money, following up on Chapter 13 of Keynes General Theory,

an argument further developed by Runde (1994).

The issue of stationarity, if not of nonergodicity per se, has attracted much attention among

more conventional time-series macroeconometricians.6 Thus many studies have found unit roots

in macroeconomic variables that imply level nonstationarity (Christiano and Eichenbaum, 1990),

although unit roots can be consistent with trend stationarity which would seem to violate the

spirit of Keynesian uncertainty. A unit root exists when a change in a variable persists and the

variable does not return to its previous value.

Also, there has been an effort by many to model surprising events using leptokurtosis, or

fat-tailed distributions. It is now a stylized fact that at least most time-series of asset prices

exhibit such leptokurtosis, with some even arguing that it is asymptotically infinite (Loretan and

Phillips, 1994).7 However such models generally still assume some kind of stationarity of the

mean which would lead Davidson at least to argue that they are not truly Post Keynesian in

approach because they contain an element of ergodicity, although in the case of asymptotically

infinite moments there is a violation of ergodicity, strictly speaking.. With regard to the

criterion of Davidsonian nonergodicity such cases must be viewed as somewhat ambiguous.

And finally there has recently arisen a new emphasis on regime switching (Flood and

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Garber, 1994). Perhaps more than any of these this may come close to the Davidsonian vision,

as it implies that there are periods of routine behavior during which ergodicity and

predictability may hold. But then crucial decisions are made that move the system to another

position or regime in an unpredictable manner. Despite these similarities there are major

differences between the Flood and Garber approach and that of Davidson. First, Flood and

Garber emphasize government policies rather than private capital investment as the source of

regime switches. Furthermore, they argue that market agents attempt to forecast such regime

switches in futures markets, although not always successfully. Indeed, they, along with Sargent

(1993, pp. 26-27), see such an approach as consistent with rational expectations in that agents

may be able to fully incorporate the probabilities of such regime switches into their forecasts as

part of the initial data set. Certainly they and other advocates of this approach do not hold to a

view of uncertainty as deeply ontological and unavoidable as do most Post Keynesians as they

argue that it can be eliminated by governments maintaining widely known and time-consistent

policies.

C. GROUP DYNAMICS

While discussing dynamics in his crucial chapter on The State of Long-Term Expectation

(Keynes, 1973, Vol. VII), Keynes gives numerous examples where interactions between agents

and their expectations about each others expectations play crucial roles. This is implicit in the

argument that agents watch closely the average state of expectations in forming their own

expectations, if for no other reason than if they are wrong they can point to the fact that most

others were wrong in order to avoid blame for their mistakes. The most famous example of this

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interaction between agents is his example of the beauty contest (Keynes, 1973, Vol. VII, p.

156):8

Or to change the metaphor slightly, professional investment may be likened to those

newspaper competitions in which the competitors have to pick out the six prettiest faces from a

hundred photographs, the prize being awarded to the competitor whose choice most nearly

corresponds to the average preferences of the competitors as a whole; so that each competitor

has to pick, not the faces which he himself finds prettiest, but those which he thinks likeliest to

catch the fancy of the other competitors, all of whom are looking at the problem from the same

point of view. It is not a case of choosing those which, to the best of ones judgment are really

the prettiest, nor even those which average opinion genuinely thinks the prettiest. We have

reached the third degree where we devote our intelligences to anticipating what average opinion

expects our the average opinion to be. And there are some, I believe, who practise the fourth,

fifth and higher degrees.

Such observers as Carabelli (1988) , Davis (1993), and Arestis (1996) see this problem of

peoples uncertainty about each others expectations as being the fundamental source of general

uncertainty. Since we can never know for certain at what degree other people will be thinking

about how average opinion will be forming its expectation of itself, we cannot never know for

certain what other peoples expectations of average opinion will actually be.

This dependence of people for each other on the formation of their expectations opens up the

possibility of sudden mass changes of these expectations, mob psychology. As noted by

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Rotheim (1988) an early inkling in Keyness work of this was an assertion of organicism in his

1926 obituary of Edgeworth when he declared (Keynes, 1973, Vol. X, p. 262):9

The atomic hypothesis which has worked so well spendidly in physics breaks down in

psychics. We are faced at every turn with the problems of organic unity, of discreteness, of

discontinuity---the whole is not equal to the sum of the parts, comparisons of quantity fail us,

small changes produce large effects, the assumptions of a uniform and homogeneous continuum

are not satisfied.

This vision of Keynes of the interaction of the expectations of different people leading to

sudden and unpredictable changes in group dynamics has inspired an enormous literature

regarding various phenomena. One has been the topic of speculative bubbles in asset markets

(Galbraith, 1954; Kindleberger, 1999; Shiller, 1989; Rosser, 1997). People bid up the price of

an asset because they expect that other people will also be doing so. This can become a self-

fulfilling prophecy, at least for awhile. It is even possible that such behavior may be rational

in some sense, although the sources cited above tend to emphasize the irrational fad element of

such behavior.10 Speculation also can lead to the proliferation of new assets (Carter, 1991-92),

although the proliferation of new options may actually induce greater uncertainty rather than

reduce it (Bowman and Faust, 1997).

Another approach along this line has been that of the sunspot equlibrium theories

(Azariadis, 1981; Cass and Shell, 1983). In this approach agents respond to some extrinsically

uncertain event (sunspots, the Oracle of Delphis predictions) to believe or not believe in some

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outcome that then becomes a self-fulfilling prophecy. Some of this literature departs from

Keynesian uncertainty by positing that the extrinsic event may obey some known probability

distribution, leading Davidson (1996) to dismiss such models as merely a variety of theories

where reality is unknown in the short-run due to some epistemological difficulty, thus

corresponding to Keyness fourth case of potentially learnable probabilities that are not easily

learned. Nevertheless this approach has the potential for modeling the arbitrariness of social

choice if the extrinsic process is left unknown.

Generally sunspot models exhibit multiple equilibria, depending on the state of expectations

which must be determined somehow. Another large and related literature has focused on the

problem of coordinating expectations in order to select among equilibria (Cooper and John,

1988; Guesnerie, 1993; Colander, 1996). Davidson (1996) again dismisses these approaches as

merely raising epistemological problems of finding a self-adjusting immutable equilibrium, but

the very openness of the system to the essentially arbitrary choices of the agents suggests that

this is not necessarily the case.

A natural extension of these models is the question of adjustment and learning processes with

regard to the selection of equilibria out of such a multiplicity of possible self-fulfilling

prophecies. It is now clear that such processes may not be convergent on any equilibria and may

generate all kinds of instabilities and even chaotic dynamics (Brock and Hommes, 1997;Sorger,

1998; Hommes and Sorger, 1998; Hommes and Rosser, 2000).11 Their propensity to lead to

self-fulfilling mistakes has led to Grandmont (1998, p. 742) to declare the existence of an

uncertainty principle: learning, when agents are somewhat uncertain about the dynamics of the

economic or social system, is bound to generate local instability of self-fulfilling expectations, if

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the influence of expectations on the dynamics is significant. This would seem to represent the

very essence of the kinds of problems that Keynes had in mind when he raised the problem of

the interaction of peoples expectations in his beauty contest tale.

D. CONVENTIONS AND BOUNDED RATIONALITY IN FORMING EXPECTATIONS

A close reading of Keynes suggests that people adopt conventions in the face of uncertainty,

with attempting to guess the expectations of others playing a crucial role, until current conditions

become such as to undermine the convention and the unpredictable extraordinary impinges upon

them and they must make crucial decisions that move things to a different zone. Such a view

has been recently gaining ground broadly against the extreme simple-mindedness of the rational

expectations hypothesis, driven by a variety of factors including many contained in the

arguments listed above. Even Thomas Sargent (1993), one of the originators of the rational

expectations hypothesis, has declared that dynamic complexity implies bounded rationality.12 An

additional component of this has been the increasing reporting of experimental economics

studies and studies from psychology showing that people focus upon their current environments

and are susceptible to the views of those around them, many of these involving so-called

anomalies and paradoxes of behavior in which people rather clearly do not follow the

predictions of standard neoclassical theory (Kahneman, Slovic, and Tversky, 1982; Thaler,

1994). These studies further emphasize the fact that people do not have some higher level

ability to form rational expectations by thinking and weighing all things and options, but instead

are attempting to learn from the behavior and attitudes of those nearest to them and from the

most dramatic or salient events or phenomena that capture their attention, as they are unable to

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understand everything. They are limited and bounded in what they can perceive and understand.

Some Post Keynesians are unhappy with the idea of bounded rationality, which is often

associated with models in which people optimize over the search for information in a world

where there is a definite ergodic equilibrium and objective probability distribution which is

merely costly to learn about. However, it is clear that Keynes himself felt that agents would

engage in rational choice subject to the information they had the expectations that they formed,

both of which are clearly bounded inevitably. Following the argument that uncertainty

undermines rational expectations, Heiner (1983, 1989) argues that uncertainty actually induces

predictable behavior as people adopt rules of thumb, or conventions, when a gap emerges

between their competence to judge a situation and the difficulty of doing so. Others arguing for

the emergence of conventions in the face of uncertainty include Carabelli (1988), Carvalho

(1988), and McKenna and Zannoni (1993), a view strongly supported in Chapter 12 of The

General Theory (Keynes, 1936, p. 152: In practice we have tacitly agreed, as a rule, to fall back

on what is, in truth, a convention.).

But even for the formation of these conventions within more or less routine situations agents

must assign weights to their observations based on epistemic reliability (Gardenfors and

Sahlin, 1982; Vercelli, 1991). This may lead them to operate with mixtures of conventional

probability estimates and conventions for uncertainty. In credit markets these can lead to models

that involve both conventional asymmetric information and uncertainty (Dymski, 1994; Neal,

1996) that may imply financial fragility (Minsky, 1986) due to credit rationing. However a

variation on this theme is that borrowers and lenders both facing fundamental uncertainty leads

to asymmetric expectations that can generate credit rationing and other phenomena in credit

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markets that can generate macroeconomic fluctuations (Wolfson, 1996).

Ultimately, of course, Post Keynesians must face the implications of the deep assertion of

fundamental uncertainty by Keynes. Heiners (1983, 1989) arguments are comforting that people

will fall back on rules of thumb in moments of great uncertainty. But this is less useful when a

la Shackle it is the crucial decisions of people themselves that are bringing about the uncertainty.

There is the threat invoked by Coddington of a nihilism that cannot make any predictions even

for policy. Davidson, who has excoriated so many for not properly recognizing Keynesian

uncertainty, must also face this essential contradiction as he hopes for the successful

implementation of beneficial policy that requires some degree of forecasting and ergodicity. His

response (Davidson, 1996, p. 506) is to invoke Reinhold Neibuhrs Serenity Prayer: God

grant us the grace to accept with serenity the things that cannot be changed (immutable realities),

courage to change things that should be changed (mutable realities), and the wisdom to

distinguish the one from the other. This observer suspects that Keynes himself would have

found the line between these two to be uncertain.

IV. POLICY IMPLICATIONS AND CONCLUSIONS

Keynes viewed probability as a fundamentally subjective concept that depends on the logical

relations between possible events. Given that people base their expectations on the weightier of

probable events that foresee as possible, and that those perceptions depend greatly on what other

people expect, expectations can change very suddenly and the state of long term expectation is

fundamentally uncertain. With regard to probabilities themselves, Keynes distinguishes four

cases, that there are no probabilities at all (fundamental uncertainty), that there may be some

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partial ordering of probable events but no cardinal numbers can be placed on them, that there

may be numbers but they cannot be discovered for some reason, and that there may be numbers

but they are difficult to discover.

Post Keynesians have drawn on these different viewpoints in forming their views on the

nature of uncertainty and expectation formation. One line of argument emphasizes the element

of potential surprise associated with crucial decisions such as major capital investments. In this

view fundamental uncertainty is equated with free will and choice by decision makers.

Followers of this line also emphasize the unidirectional and irreversible nature of historical time.

Another line argues that the essence of fundamental uncertainty derives from nonergodicity of

time series and stochastic processes. Yet another emphasizes the nature of the interaction of

people in forming expectations and various complexities of group dynamics. In the face of this

uncertainty expectations are seen as arising from bounded rationality and conventions.

Many of these issues remain open to further research and debate with Post Keynesians clearly

offering important approaches, insights, and perspectives. The fundamental nature of

probability and stochastic processes may be the deepest such question that is far from closed.

The nature of how Keynesian uncertainty influences economic decision making is another issue

that could certainly see some further investigation. The question of how complexity in the

economic environment influences decision making and whether or not this leads to uncertainty

for ontological or epistemological reasons is one that remains very controversial and unresolved.

And the problem of how people actually form expectations and what kinds of conventions they

use and how these interact with the institutional structure of the economy is clearly an important

one that Post Keynesians have much to offer in resolving. However, one thing that is certain

20

regarding the views of the various Post Keynesians about Keynesian uncertainty and its

implications for expectation formation it is that it is utterly incompatible with the rational

expectations hypothesis.

The Post Keynesian perspectives on uncertainty and expectations formation are central to the

development of Post Keynesian views of macroeconomic policy. Of course, the rejection of

rational expectations coincides with a rejection of the policy ineffectiveness arguments of the

New Classical school. But, the arguments of the New Keynesian school that emphasize the

significance of sticky prices and wages are also seen as inadequate as they also draw on rational

expectations. Fundamental uncertainty is seen as implying the possibility of long-run

unemployment even in a world of perfect competition and fully flexible prices and wages.

Uncertainty leads to liquidity preference and the non-neutrality of money in the long run. Most

importantly, uncertainty and the associated instability of expectations is seen as underpinning the

instability of investment, which in turn is the main key to more general macroeconomic

instability.

The policy implications arising from these problems certainly include active monetary and

fiscal policies. But they also include deeper and more fundamental institutional and structural

changes in the economy. Thus, Post Keynesians argue for the development of institutions that

can provide more general anchors for economic decision making. Those that have been

suggested include various kinds of incomes policies to stabilize the wage and price process,

indicative planning to more broadly coordinate expectations formation, and a variety of

mechanisms to stabilize investment, including a more substantial role for government in the

process of investment.

21

There have been a variety of incomes policies suggested by many Post Keynesian economists

over the years. Prominent have been proposals for tax incentive plans, wage incentive plans,

full-blown wage and price controls, or economy-wide collective collective bargaining. All of

these involve a degree of direct government in the wage and price setting process, with tax

breaks being given to industries that restrain prices or wages and tax hikes facing those that

excessively raise them. A market-oriented such plan was proposed by Lerner and Colander

(1980). Such plans have not been implemented seriously anywhere. Wage and price controls

have been used in many countries, but except in wartime seem to break down after several years.

Economy-wide wage bargaining, sometimes labeled corporatism, has been extensively used in

several Scandinavian countries and in Austria for extended periods of time with much success in

terms of keeping down inflation while avoiding excessive unemployment. A good discussion

of this latter system and its actual functioning can be found in Pekkarinen, Pohjola, and

Rowthorn (1992).

Indicative planning has not always been associated with Post Keynesianism, although as

noted above, Keynes has long been thought to have advocated it in certain of his writings.

Advocacy of this approach, in which government gets leading decision makers together to

jointly plan expected growth but without any command coercion to follow the plan, has been

been more a feature of French Keynesians. Although it has fallen out of fashion to a large

degree, indicative planning has been successfully used in the past in France, Japan, South Korea,

and some other countries, with India being a prominent ongoing practitioner. A discussion of

French indicative planning can be found in Estrin and Holmes (1983) while Meade (1970)

provides a more general discussion within a broader Keynesian context, and Frank and Holmes

22

(1990) present it in the context of a complex economy with multiple equilibria.

As regards government involvement in investment, this can cover a range of possible

activities, including subsidies or public works programs tied to business cycles, with Sweden

having a fund for social investment tied to the state of the economy, to a variety of more direct

or indirect methods of controlling investment, including more direct control of the banking

system, although this can lead to the problem of crony capitalism, if managed poorly. Keynes

spoke eloquently, if rather vaguely, regarding this issue near the end of his General Theory (p.

378):

Furthermore, it seems unlikely that the influence of banking policy on the rate of interest

will be sufficient by itself to determine an optimum rate of investment. I conceive, therefore,

that a somewhat comprehensive socialisation of investment will prove the only means of

securing an approximation to full employment; though this need not exclude all manner of

compromises and devices by which public authority will co-operate with private initiative. But

beyond this no obvious case is made out for a system of State Socialism which would embrace

most of the economic life of the community. It is not the ownership of the instruments of

production which it is important for the State to assume. If the State is able to determine the

aggregate amount of resources devoted to augmenting the instruments and the basic rate of

reward to those who own them, it will have accomplished all that is necessary.

Thus, finally, for Post Keynesians more generally, overcoming the destabilizing tendencies

arising from fundamental uncertainty in economic decisionmaking by whatever reasonable and

23

appropriate means is probably the central problem facing macroeconomic policymakers.

NOTES

1. For discussions of implications of this non-comparability idea, especially to the debate over econometrics between Keynes and Tinbergen, see Rowley and Hamouda (1987) and O'Donnell (1990).

2. An exception to this is in the infinite dimensional case. When rolling a die with an infinite number of sides there may be no convergence of Bayesian priors on "objective posteriors" (Diaconis and Freedman, 1986). Poirier (1988) that some Bayesians are fully subjective in the sense of Keynes.

3. Shackle is one of the rare Post Keynesians who is also admired by Austrian economists (O'Driscoll and Rizzo, 1985).

4. Estrin and Holmes (1985) critique Coddington's critique of Keynes and argue that Keynes saw indicative planning as an appropriate response to uncertainty based on his 1926 The End of Laissez-Faire (1973, Vol. IX).

5. An incomplete list of those citing Davidson's argument includes Rutherford (1984), Weisman (1984), Gowdy (1985-86), Rowley and Hamouda (1987), Lawson (1988), Carvalho (1988), Carter (1991-92), McKenna and Zannoni (1993), Neal (1996), and Rosser (1998, 1999).

6. The concept of ergodicity is often associated with that of stationarity of a time series. In fact, an ergodic system will be stationary. However, some stationary systems may be nonergodic, such as limit cycles or other kinds of cyclical fluctuations that can arise from well-known Keynesian models such as that of Hicks (1950) in which a multiplier-accelerator framework is placed within a context of floors and ceilings to investment. Thus, nonstationarity is a sufficient, but not a necessary condition for nonergodicity.

7. This extends the argument of Mandelbrot (1963) that unusual events can be modeled by assuming asymptotically infinite variances. Mirowski (1990) sees this approach as the fountainhead of fundamental uncertainty.

8. This implies an infinite regress problem in decision making when one is taking into account the behavior of other agents that can imply undecidability (Binmore, 1987; Lipman, 1991; Koppl and Rosser, 2000). Conlisk (1996) notes that such infinite regresses can arise when one is contemplating how to economize on information searches or calculations. Is it worth economizing on economizing on economizing…? (Raiffa, 1968). This is undecidable and can be viewed as an ontological problem that must be avoided by making a decision "on intuitive grounds" (Johansen, 1977), that is, by relying ultimately on "animal spirits."

9. See Rosser (2000) for extended and more general discussion of issues raised in this statement. Brock (1993) provides an alternative approach to sudden changes in group dynamics based on the mean-field approach used in statistical mechanics.

10. Glickman (1994) and Davidson (1996) question the usual approach to discussions of speculative bubbles because they reject the concept of a fundamental value against which a bubble can be defined and measured.

24

11. Chaotic dynamics involve sensitive dependence on initial conditions that imply that a small initial error can lead to a wide deviation of outcomes. These have been argued to undermine the possibility of rational expectation (Grandmont, 1985; Rosser, 1996) and to represent an independent source of Keynesian uncertainty, along with other kinds of complex dynamics (Rosser, 1998, 1999). Davidson (1996) argues that chaotic dynamics also represent merely another epistemological problem of calculating an immutably given equilibrium. However, the calculations involved here require infinite information which makes this into a problem of "effectively ontological" uncertainty (Rosser, 1998).

12. See Sent (1996) for a critique of Sargent's views.

REFERENCES

Akerlof, G.A. “Procrastination and Obedience.” American Economic Review, 1991, 81, 1-19.

Arestis, P. Post-Keynesian Economics: Towards Coherence. Cambridge Journal of Economics, 1996, 20, 111-135.

Azariadis, C. Self-Fulfilling Prophecies. Journal of Economic Theory, 1981, 25, 380-396.

Bausor, R. Time and the Structure of Economic Analysis. Journal of Post Keynesian Economics, 1982-83, 5, 163-179.

_______. “Toward a Historically Dynamic Economics: Examples and Illustrations.” Journal of Post Keynesian Economics, 1984, 6, 360-376.

Bowman, D. and Faust, J. Options, Sunspots, and the Creation of Uncertainty. Journal of Political Economy, 1997, 105, 957-975.

Brock, W.A. “Pathways to Randomness in the Economy: Emergent Nonlinearity and Chaos in Economics and Finance.” Estudios Económicos, 1993, 8, 3-55.

_________ and Hommes, C.H. A Rational Route to Randomness. Econometrica, 1997, 65, 1059-1095.

Carabelli, A. On Keyness Method. London, UK: Macmillan, 1988.

Carter, M. Uncertainty, Liquidity and Speculation. Journal of Post Keynesian Economics, 1991-92, 14, 169-182.

Carvalho, F.J.C. de Keynes on Probability, Uncertainty, and Decision Making. Journal of Post Keynesian Economics, 1988, 11, 66-81.

Cass, D. and Shell, K. Do Sunspots Matter? Journal of Political Economy, 1983, 91, 193-227.

25

Christiano, L.J. and Eichenbaum, M. Unit Roots in Real GNP: Do We Know, and Do We Care? Carnegie-Rochester Series on Public Policy, 1990, 32, ed. by A.H. Meltzer, 7-61.

Coddington, A. Deficient Foresight: A Troublesome Theme in Keynesian Economics. American Economic Review, 1982, 72, 480-487.

Colander, D. (ed.), Beyond Microfoundatoins” Post Walrasian Macroeconomics. Cambridge, UK: Cambridge University Press, 1996.

Conlisk, J. Why Bounded Rationality? Journal of Economic Literature, 1996, 34, 669-700.

Cooper, R. and John, A. Coordinating Coordination Failures. Quarterly Journal of Economics, 1988, 103, 441-465.

Davidson, P. 1978. Money and the Real World, 2nd edition. London, UK: Macmillan.

_________. Rational Expectations: A Fallacious Foundation for Studying Crucial Decision-Making Processes. Journal of Post Keynesian Economics, 1982-83, 5, 182-197.

_________. Is Probability Theory Relevant for Uncertainty? Journal of Economic Perspectives, 1991, 5(1), 129-143.

_________. Post Keynesian Macroeconomic Theory. Aldershot, UK: Edward Elgar, 1994.

_________. Reality and Economic Theory.” Journal of Post Keynesian Economics, 1996, 18, 479-508.

Davis, J.B. Keyness Philosophical Development. Cambridge, UK: Cambridge University Press, 1993.

Diaconis, P. and Freedman, D. “On the Consistency of Bayes Estimates.” Annals of Statistics, 1986, 14, 254-278.

Dymski, G. Asymmetric Information, Uncertainty, and Financial Structure. In G.Dymski and R. Pollin (eds.), New Perspectives in Monetary Macroeconomics: Explorations in the Tradition of Hyman P. Minsky. Ann Arbor, MI: University of Michigan Press, 1994

Eichner, A. (ed.) A Guide to Post-Keynesian Economics. Armonk, NY: M.E. Sharpe, 1979

Estrin, S. and Holmes, P. French Planning in Theory and Practice. Cambridge, MA: Harvard University Press, 1983.

_______ and ________. 1985. Uncertainty and Economic Planning. Journal of Post Keynesian

26

Economics, 1985, 7, 463-473.

Flood, R.P. and Garber, P.M. Speculative Bubbles, Speculative Attacks, and Policy Switching. Cambridge, MA: MIT Press, 1994.

Frank, J. and Peter Holmes, P. A Multiple Equilibrium Model of Indicative Planning. Jounral of Comparative Economics, 1990, 14, 791-806.

Galbraith, J.K. The Great Crash, 1929. Boston: Houghton Mifflin, 1954.

Gardenfors, P. and Sahlin, N.-E. Unreliable Probabilities, Risk Taking, and Decision-Making. Synthèse, 1982, 53, 471-487.

Georgescu-Roegen, N. The Entropy Law and the Economic Process. Cambridge, MA: Harvard University Press, 1971.

Glickman, M. “”The Concept of Information, Intractable Uncertainty, and the Current State of the ‘Efficient Markets’ Theory.” Journal of Post Keynesian Economics, 1994, 16, 325-349.

Gowdy, J.M. “Expectations and Predictability.” Journal of Post Keynesian Economics, 1985-86, 8, 192-200.

Grandmont, J.-M. On Endogenous Competitive Business Cycles. Econometrica, 1985, 53, 995-1045.

______________. 1998. Expectations Formation and Stability of Large Socioeconomic Systems. Econometrica, 1998, 66, 741-781.

Guesnerie, R. Successes and Failures in Coordinating Expectations. European Economic Review, 1993, 37, 243-268.

Heiner, R.A. “The Origin of Predictable Behavior.” American Economic Review, 1983, 73, 560-595.

_________. The Origin of Predictable Dynamic Behavior. Journal of Economic Behavior and Organization, 1989, 12, 233-258.

Hicks, J.R. A Contribution to the Theory of the Trade Cycle. Oxford, UK: Oxford University Press, 1950.

________. Causality in Economics. New York: Basic Books, 1979.

Hommes, C.H. and Rosser, J.B., Jr. “Consistent Expectations Equilibria and Complex Dynamics in Renewable Resource Markets.” Macroeconomic Dynamics, 2000, forthcoming.

27

______________. and Sorger, G. 1998. Consistent Expectations Equilibria, Macroeconomic Dynamics 1998, 2, 287-321.

Johansen, L. Lectures on Macroeconomic Planning. Part 1. General Aspects. Amsterdam: North-Holland, 1977.

Kahneman, D., Slovic, P. and Tversky, A. (eds.) Judgment under Uncertainty: Heuristics and Biases. Cambridge, UK: Cambridge University Press, 1982.

Katzner, D.W. “The Firm under Conditions of Ignorance and Historical Time.” Journal of Post Keynesian Economics, 1990, 13, 125-145.

Keynes, J.M. Treatise on Probability, 1921, reprinted in Collected Writings, Vol. VIII. New York: St. Martins Press, 1973.

__________. Obituary of Francis Ysidro Edgeworth.” 1924, reprinted in Collected Writings, Vol. X. New York: St. Martins Press, 1973.

__________. The End of Laissez-Faire. 1926, reprinted in Collected Writings, Vol. IX. New York: St. Martins Press, 1973.

__________. Essays in Biography. 1931, reprinted in Collected Writings, Vol. X. New York: St. Martins Press, 1931.

__________. The General Theory of Employment, Interest and Money. London: Macmillan, 1936, reprinted in Collected Writings, Vol. VII. New York: St. Martins Press, 1973.

__________. The General Theory of Employment, Quarterly Journal of Economics, 1937, 51, 209-223, reprinted in Collected Writings, Vol. XIV, New York: St. Martins Press, 1973.

Kindleberger, C.H. Manias, Panics, and Crashes, 3d ed. New York: Basic Books, 1999.

Knight, F.H. Risk Uncertainty and Profit. Chicago: University of Chicago Press, 1921.

Koppl, R. and Rosser, J.B., Jr. “Everything I Might Say Will Already Have Passed Through Your Mind.” Mimeo, Fairleigh Dickinson University and James Madison University, 2000.

Kregel, J.A. Economic Methodology in the Face of Uncertainty: The Modelling Methods of Keynes and the Post-Keynesians. Economic Journal, 1976, 86, 209-225.

Lawson, T. Probability and Uncertainty in Economic Analysis. Journal of Post Keynesian Economics, 1988, 11, 38-65.

28

Lerner, A. and Colander, D. MAP: A Market Anti-Inflation Plan. New York: Harcourt Brace Jovanovich, 1980.

Lipman, B.L. “How to Decide How to Decide How to…: Modeling Limited Rationality.” Econometrica, 1991, 59, 1105-1125.

Loasby, B.J. Choice, Complexity, and Ignorance. Cambridge, UK: Cambridge University Press, 1976.

Loretan, M. and Phillips, P.C.B. Testing the Covariance Stationarity of Heavy-Tailed Time Series: An Overview of the Theory with Applications to Several Financial Datasets . Journal of Empirical Finance, 1994, 1, 211-248.

Lucas, R.E., Jr. Expectations and the Neutrality of Money. Journal of Economic Theory, 1972, 4, 103-124.

Mandelbrot, B.B. “The Variation of Certain Speculative Prices.” Journal of Business, 1963, 36, 394-419.

McKenna, E.J. and Zannoni, D.C. Philosophical Foundations of Post Keynesian Economics. Journal of Post Keynesian Economics, 1993, 15, 395-407.

Meade, J.E. The Theory of Indicative Planning. Manchester, UK: University of Manchester Press, 1970.

Mirowski, P.J. "From Mandelbrot to Chaos in Economic Theory." Southern Economic Journal, 1990, 57, 289-307.

Minsky, H.P. Stabilizing an Unstable Economy. New Haven, CT: Yale University Press, 1986.

Muth, J.F. Rational Expectations and the Theory of Price Movements. Econometrica, 1961, 29, 315-335.

Neal, P. “Keynesian Uncertainty in Credit Markets.” Journal of Post Keynesian Economics, 1996, 18, 397-418.

Neumann, J. von and Morgenstern, O. The Theory of Games and Economic Behavior. Princeton, NJ: Princeton University Press, 1944.

ODonnell, R.M. Keynes on Mathematics: Philosophical Foundations and Economic Applications. Cambridge Journal of Economics, 1990, 14, 29-47.

O’Driscoll, G.P. and Rizzo, M.J. The Economics of Time and Ignorance. New York: Blackwell, 1985.

29

Pekkarinen, J., Pohjola, M., and Rowthorn, B. (eds.) Social Corporatism: A Superior Economic System? Oxford, UK: Clarendon Press, 1992.

Poirier, D.J. Frequentist and Subjectivist Perspectives on the Problems of Model Building in Economics. Journal of Economic Perspectives, 1988, 2(1), 121-144.

Raiffa, H. Decision Analysis: Introductory Lectures on Choices under Uncertainty. Reading, MA: Addison-Wesley, 1968.

Robinson, J. History versus Equilibrium. London, UK: Thames Papers in Political Economy, 1974.

Rosser, J.B. Jr. “Chaos Theory and Rationality in Economics.” In L.D. Kiel and E. Elliott (eds.), Chaos Theory in the Social Sciences: Foundations and Applications. Ann Arbor, MI: University of Michigan Press, 1996.

___________. “Speculations on Nonlinear Speculative Bubbles.” Nonlinear Dynamics, Psychology, and Life Sciences, 1997, 1, 175-200.

___________. Complex Dynamics in New Keynesian and Post Keynesian Economics, in R.J. Rotheim (ed.), New Keynesian Economics/Post Keynesian Alternatives. London, UK: Routledge, 1998.

___________. On the Complexities of Complex Economic Dynamics, Journal of Economic Perspectives, 1999, 13(4), 169-192.

___________. From Castastrophe to Chaos: A General Theory of Economic Discontinuities, Vol. I: Mathematics, Microeconomics, Macroeconomics, and Finance, 2d ed. Boston: Kluwer Academic Publishers, 2000.

Rotheim, R.J. Keynes and the Language of Probability and Uncertainty. Journal of Post Keynesian Economics, 1988, 11, 82-99.

Rowley, R. and Hamouda, O. “Troublesome Probability and Economics.” Journal of Post Keynesian Economics, 1987, 10, 44-64.

Runde, J. Keynesian Uncertainty and the Weight of Arguments. Economics and Philosophy, 1990, 6, 275-292.

______. Keynesian Uncertainty and Liquidity Preference. Cambridge Journal of Economics, 1994, 18, 129-144.

Rutherford, M. “Rational Expectations and Keynesian Uncertainty: A Critique.” Journal of Post

30

Keynesian Economics, 1984, 6, 377-387.

Sargent, T.J. Bounded Rationality in Macroeconomics. Oxford, UK: Clarendon Press, 1993.

Savage, L.J. The Foundations of Statistics. New York: Wiley, 1954.

Sent, M.-J. “Convenience: The Mother of all Rationality in Sargent.” Journal of Post Keynesian Economics, 1996, 19, 3-34.

Shackle, G.L.S. Uncertainty in Economics and Other Reflections. Cambridge, UK: Cambridge University Press, 1955.

____________. Decision, Order and Time in Human Affairs, 2d ed. Cambridge, UK: Cambridge University Press, 1969.

____________. Epistemics and Economics, A Critique of Economic Doctrines. Cambridge, UK: Cambridge University Press, 1972.

____________. Keynesian Kaleidics, the Evolution of a General Political Economy. Edinburgh, UK: Edinburgh University Press, 1974.

Shiller, R.J. Market Volatility. Cambridge, MA: MIT Press, 1989.

Sorger, G. “Imperfect Foresight and Chaos: An Example of a Self-Fulfilling Mistake.” Journal of Economic Behavior and Organization, 1998, 33, 363-383.

Thaler, R.H. The Winners Curse: Paradoxes and Anomalies of Economic Life. Princeton, NJ: Princeton University Press, 1994.

Tobin, James. 1959. Liquidity Preference as Behavior towards Risk, Review of Economic Studies 25, 65-86.

Vercelli, A. Methodological Foundations of Macroeconomics. Cambridge, UK: Cambridge University Press, 1991.

Vickers, D. Financial Markets in the Capitalist Process. Philadelphia, PA: University of Pennsylvania Press, 1978.

________. “Time, Ignorance, Surprise, and Economic Decisions.” Journal of Post Keynesian Economics, 1986, 9, 48-57.

Weisman, D.L. Tobin on Keynes: A Suggested Interpretation. Journal of Post Keynesian Economics, 1984, 6, 411-420.

31

Williams, E.E. and Findlay, III, M.C. Risk and the Role of Failed Expectations in an Uncertain World. Journal of Post Keynesian Economics, 1986, 9, 32-47.

Wolfson, M.H. A Post Keynesian Theory of Credit Rationing. Journal of Post Keynesian Economics, 1996, 18, 443-470.

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