“All agents inside the model, the econometrician, and God share the same model.”
“It has been standard for at least the past three decades to use models in which not only does the model give a complete description of a hypothetical world, and not only is this description one in which outcomes follow from rational behavior on the part of the decisionmakers in the model, but the decisionmakers in the model are assumed to understand the world in exactly the way it is represented in the model.”
1. Introduction
1Perhaps the first observation that one should make when talking about the role of expectations in economics is that this is not necessarily something which is related to time. As Frank Hahn [1983] said, “When an economist predicts that economies with price controls are highly likely to have black markets, no reference to time is needed.” (ibid: 77).
1.1. Atemporal expectations
2The use of “comparative statics” has a long history in the discipline. Answers to questions like, “what would happen if in the economy as it is if we modified some parameter?” make obvious sense and such exercises are commonplace. Yet, if instead of taking a deterministic view of the system one admits that it has a stochastic component, one could modify the question to ask, “what would you expect to happen?”. To all those who have studied probability theory this seemingly innocent modification opens a Pandora’s box of complications. It poses the question of the nature of uncertainty, which does not reside necessarily in meaningful probabilistic statements. This was the subject of debate and discussion in the interwar years and two of the leading protagonists were Knight and Keynes. The distinction that was made at the time was between risk and uncertainty. Knight argued that anything that involved a number of possible outcomes which were known and where it was possible to define the probabilities of each of them did not involve uncertainty and could be classified as “risk”. This is the sort of situation with which insurers have dealt for centuries. But situations in which one has incomplete knowledge of the set of possible outcomes and no meaningful way of specifying the probabilities involved should be considered as “uncertain”. Keynes made a similar distinction:
“By “uncertain” knowledge, let me explain, I do not mean merely to distinguish what is known for certain from what is only probable. The game of roulette is not subject, in this sense, to uncertainty; 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.”
4This quote is cited by Kay and King [2019] in their recent book on Radical Uncertainty which strongly recommends taking the Keynesian position when faced with the evolution of a complex system such as the modern socio-economic system. However, Keynes was very pragmatic and despite his recommendations he saw that it was unlikely to be followed, for as he says in the lines immediately following the above quote:
“Nevertheless, the necessity for action and for decision compels us as practical men to do our best to overlook this awkward fact and to behave exactly as we should if we had behind us a good Benthamite calculation of a series of prospective advantages and disadvantages, each multiplied by its appropriate probability, waiting to be summed.”
1.2. Probability and its limitations
6There is a widespread impression that once a statement becomes numerical it becomes precise and many individuals and institutions are victims of that illusion. This is not the place to go into the literature on the nature of probability and the long history of controversies over the very nature of the notion, but it is interesting to note in passing that Ramsey objected to Keynes’ definition of probability since he claimed that it was based on an ordinal concept rather than on a cardinal one and was thus, of use only in limited cases. That discussion, which did lead Keynes’ to modify, but not to fundamentally change his approach is thoroughly dealt with by Brady [2019]. The outcome of that debate was that, whilst Keynes remained convinced of the logical objections to standard tools to a world of radical uncertainty, analysts would, as he predicted, fall back on those tools.
7What is more, having taken that approach they will argue that their models are a “reasonable approximation of the truth” and that means that they are convinced that their probabilities and forecasts are also reasonable. However, one can nevertheless object that we “cannot derive a probability or a forecast, or a policy recommendation from a model; the probability is meaningful, the forecast accurate or the policy recommendation well founded, only within the context of the model” (Kay and King [2020]: 261).
8So, out of all this, come two clear conclusions. Economists make predictions both as to atemporal problems, such as “what would the result be if the world differed from its present state in a specific way?” and “temporal ones such as what will France’s GNP be next year?” It might, after the previous discussion, become clear that Yogi Berra’s observation was not the joke that it is usually made out to be. However, it might be that, at least when dealing with a process which unfolds over time, we can have recourse to a frequentist approach to probabilities with which many people are familiar.
9In what follows then, I will look at the problem of expectations about the future and their impact on the economy. In particular, I will discuss the nature of equilibrium in this context and then provide a critical view of the theory of rational expectations.
2. Expectations about the Future
10Macroeconomists, it would be fair to say, are mainly concerned with the evolution of certain aggregate variables. To predict those variables, they must make assumptions about the vision that the participants in the economy have of the future. This explains why economists are so preoccupied with people’s expectations about the evolution of their economic environment. But, think for a moment, in terms of the simplest model with which economics students are faced. There, such considerations do not enter. Each individual is faced with a set of alternatives from which they must choose that which they consider to be the best. The objective of the economist is then to see if the choices are mutually compatible. Stated like that, it is obvious that the problem may have no solution, because we have said nothing about how the choice sets are generated.
11However, now consider a situation in which the sets of alternatives with which the individuals are faced depend on some variable which is known to everyone. In economic models that variable is a vector of the prices of all goods, which determines the choice sets. Now, the question becomes, is there a price vector which generates choice sets for each individual such that the choices made by each individual are mutually compatible? This is an arid very theoretical question, which was posed by Walras and to which an abstract answer was given in 1926 by Wald. The context in Wald’s analysis is rarefied and is the simplest version of what has come to be known as the General Equilibrium model. It has a characteristic that is common to standard macroeconomic models, which is that people and firms know and accept the prices of all goods whether outputs or inputs. [2]
2.1. Equilibrium
12Now, come back to the problem that really interests us here, what is an equilibrium, if there is one, in a more “realistic” world? If what we are talking about is the evolution over time of the economy, then individuals will have to make choices not only for today but also for the future. This means that commodities that people consume, or firms produce, must be dated. People then have to choose what and when they wish to buy and consume at each date and firms similarly, for each date, now and in the future, have to choose what and when they wish to buy as inputs and sell as outputs.
13We thus have to attribute to both firms and consumers a considerable degree of knowledge about the future. They must know all the prices with which they will be faced in the future and those, in turn will determine their production possibilities, and profits, in the case of firms and income and the set of available choices in the case of consumers. Yet, what I have described is, at best, a skeletal model of the economy. Where do the prices come from, who sets them, and how are they modified? What is the horizon involved, do people live forever or do they have either a finite life or a stochastic duration? Furthermore, do people realise that the evolution of the economy will depend on the behaviour of the others and therefore think in strategic terms? (see e.g. Guesnerie [2005]). Much of the discussion in economics has been around how to answer these considerations but we are still left with individuals choosing over alternative streams of consumption and production. The constraints that are faced are usually given by prices and therefore the people involved must have a forecast of those prices or at least an understanding of the process governing the evolution of the economy. If that process is stochastic there must be sufficient structure in it to permit predictions. This clearly imposes heroic assumptions as to the capacity of people to calculate and understand not only their local situation but that of the economy as a whole.
2.1.1. Hayek’s Early Contribution
14But, the emphasis was not only on the attitudes of individuals and firms but also on defining an equilibrium which was consistent with those attitudes and the plans that they induced. Although this problem became a really central one in macroeconomics, it is worth recalling that F.A. Hayek had already defined the sort of equilibrium that could be envisaged. He said in a well-known article in 1937:
“For a society then we can speak of a state of equilibrium at a point of time – but it means only that compatibility exists between the different plans which the individuals composing it have made for action in time. And equilibrium will continue, once it exists, so long as the external data correspond to the common expectations of all the members of the society. The continuance of a state of equilibrium in this sense is then not dependent on the objective data being constant in an absolute sense and is not necessarily confined to a stationary process. Equilibrium analysis becomes in principle applicable to a progressive society and to those inter-temporal price relationships which have given us so much trouble in recent times.” [3]
16Here, Hayek was already ahead of his time since he did not assimilate his notion of an equilibrium consistent with expectations to a stationary environment but again, he goes on to mention an important idea which gets lost in our typical perfectly competitive models. That is the fact that one might reflect on how people take into account other people’s expectations. If one pursues this line, one is inevitably led to game theoretic reasoning and in many cases, as a number of distinguished game theorists have pointed out, to an infinite regress. These considerations were again made explicit by Hayek:
“These considerations seem to throw considerable light on the relationship between equilibrium and foresight, which has been somewhat hotly debated in recent times. It appears that the concept of equilibrium merely means that the foresight of the different members of the society is in a special sense correct. It must be correct in the sense that every person’s plan is based on the expectation of just those actions of other people which those other people intend to perform, and that all these plans are based on the expectation of the same set of external facts, so that under certain conditions nobody will have any reason to change his plans. Correct foresight is then not, as it has sometimes been understood, a precondition which must exist in order that equilibrium may be arrived at. It is rather the defining characteristic of a state of equilibrium. Nor need foresight for this purpose be perfect in the sense that it need extend into the indefinite future, or that everybody must foresee everything correctly. We should rather say that equilibrium will last so long as the anticipations prove correct, and that they need to be correct only on those points which are relevant for the decisions of the individuals.”
18Hayek, as we have suggested in a recent article (Bowles et al. [2017]) therefore, not only anticipated what we now term rational expectations but actually introduced a discussion as to the role of stationarity and persistence and strategic thinking.
2.1.2. Keynes’ approach
19This effort to incorporate various aspects of expectation formation and of their relation to equilibrium stands in stark contrast to the approach adopted by J.M. Keynes who was highly sceptical about the idea of consistent expectations and even about what that would that mean:
“The theory can be summed up by saying that, given the psychology of the public, the level of output and employment as a whole depends on the amount of investment. I put it in this way, not because this is the only factor on which aggregate output depends, but because it is usual in a complex system to regard as the causa causans that factor which is most prone to sudden and wide fluctuation. More comprehensively, aggregate output depends on the propensity to hoard, on the policy of the monetary authority as it affects the quantity of money, on the state of confidence concerning the prospective yield of capital assets, on the propensity to spend and on the social factors which influence the level of the money wage. But of these several factors it is those which determine the rate of investment which are most unreliable, since it is they which are influenced by our views of the future about which we know so little. This that I offer is, therefore, a theory of why output and employment are so liable to fluctuation.”
21Keynes, like Hayek, was ahead of his times in talking of the sources of fluctuations of output and employment in a “complex system”. But, writing in the same year as Hayek, he arrives at a very different position:
“The orthodox theory assumes that we have a knowledge of the future of a kind quite different from that which we actually possess. This false rationalization follows the lines of the Benthamite calculus. The hypothesis of a calculable future leads to a wrong interpretation of the principles of behaviour which the need for action compels us to adopt, and to an underestimation of the concealed factors of utter doubt, precariousness, hope and fear”
23Whilst Keynes had a view of people and firms as having a very limited idea of what the future holds and being heavily influenced by psychological factors in planning for and making their decisions, Hayek was looking for some sort of consistency even if he did not think that it would necessarily emerge. As Kay and King [2020] point out, economists have embarked on the search for a logically consistent equilibrium which takes little account of the radical uncertainty with which we are faced. Economic theory, as Leijonhufvud [1993] said deals with
24“Incredibly smart people in unbelievably simple situations, “while the real world is in fact, more accurately described as “believably simple people coping with incredibly complex situations” (ibid: 2).
2.2. Modern Rational Expectations Theory
25But dealing with the problems of Keynesian radical uncertainty lost out to those who sought a mathematically consistent equilibrium concept. This resulted in the modern rational expectations hypothesis the father of which is usually considered to be Thomas Muth who worked simultaneously on it with Herbert Simon, his colleague. The problem that interested them at the time was not so much how individuals make their decisions but rather, how firms do so. This might seem to be a more tractable problem. Yet, given that firms change in ownership, structure and even goals, over time, the task of anticipating all this is also heroic. Thus, the problem to be tractable has, somehow to be simplified. Muth [1961] in an article which has become the basic reference for the rational expectations’ literature, was explicit:
“I should like to suggest that expectations, since they are informed predictions of future events are essentially the same as the predictions of the relevant economic theory. At the risk of confusing this purely descriptive hypothesis with a pronouncement as to what firms ought to do, we call such expectations “rational””.
27What Muth is suggesting is that there is a commonly accepted economic theoretical model which captures the evolution of the economy and, at an equilibrium, people should form their expectations consistently with that model. This was, of course, extremely convenient for economists who now only had to require agents to have expectations consistent with the model that the economists proposed. How and why they should do so was left unexplained. In other words, Muth saw clearly that specifying the expectations as being consistent with the evolution of the economy was simply a way of closing the model. However, Muth here was thinking on the theoretical plane and was well aware of what sort of assumptions were necessary for this and he, himself, questioned the empirical value of this exercise when he said that “To make dynamic economic models complete various expectational formulae have been used. There is, however, little evidence to suggest that the presumed relations bear a resemblance to the way the economy works” (Ibid: 315).
28The simplest interpretation of Muth’s approach is that it is essentially a way to close the model by simply assuming that everyone has expectations that are consistent with the “real” process that governs the evolution of the economy. Either this is just an assumption, and one looks for expectations that would achieve this, or one tries to explain how individuals would come to hold such expectations.
2.2.1. Heterogeneous expectations
29Although the idea of common expectations is convenient for the modeler, there is a wealth of evidence suggesting that people hold diverse expectations, and that this is indeed a reason for much of the trade on financial markets. Muth [1961] was well aware of this, but in his seminal article showed that he was not totally convinced by the idea that differences in individual expectations might matter. In fact, he thought that, in general, such differences should cancel out. He said specifically that,
“Allowing for cross-sectional differences in expectations is a simple matter, because their aggregate affect is negligible as long as the deviation from the rational forecast for an individual firm is not strongly correlated with those of the others. Modifications are necessary only if the correlation of the errors is large and depends systematically on other explanatory variables.”.
31This is an appeal to the idea of independence and some sort of law of large numbers but long before Muth, this idea was questioned.
2.2.2. Herd Behaviour
32From Poincaré [1908] on, people’s tendency to herd in their expectations has been emphasized, in contradiction to Bachelier and the Efficient Markets Hypothesis. Bachelier in his thesis argued that people in a financial market look at their own information, independently of what others are doing, and act upon it. Their actions influence the prices of assets, and, in this way, their hitherto private, information becomes public. But Poincaré [1908] who had been the referee for Bachelier’s thesis, argued that, despite the elegance of Bachelier’s mathematical reasoning, his result, which constitutes the basis of much work on efficient markets, was empirically unjustified:
“When people are in close contact with each other they no longer decide randomly and independently of each other. Many factors come into play, and they disturb people, shifting them one way and then the other, but there is one thing that they will not destroy and that is people’s tendency to behave like sheep. It is that which will always persist”.
34What Poincaré is referring to, the simple fact that peoples’ actions are often strongly influenced by others when they are in a group, and that the group, will tend to herd on one opinion or choice, whatever its rationale, has been widely discussed by economists as a source of bubbles, (see e.g., Banerjee [1992], Bikhchandani et al. [1992, 1998]). Again, it is worth noting that the reason that people herd may not be because of any lack of rationality it may even be the case that individuals attribute too much rationality to others and therefore infer from the actions of the latter that they dispose of some information which makes their action rational.
35So here the difficulty is not that agents are too different but that they may herd on a single opinion and that the effect will be that they arrive at a common view of the future but that this view will not be rational in the sense that theorists are positing. The private information which was supposed to be transmitted through a common signal, is not used by the individuals as they follow the common behaviour of a group. This idea is reinforced by Cars Hommes (2012) who has examined the experimental evidence for Rational Expectations and shows that when there is positive feedback such a notion is inconsistent with the evidence. What is meant by positive feedback here, is that when an action is taken by someone it increases the pay-off from taking it. The classic example is when the purchase of an asset increases the price of that asset. When there is negative feedback as, for example, when going to a crowded beach, the feedback is negative and herd behaviour does not continue.
2.2.3. Differing beliefs
36Another objection to the Rational Expectations Hypothesis is that people may use different implicit, or explicit, algorithms to form their expectations from the same information and that this may destroy the formation of the common rational view:
“(But) once the theoretical door is opened to one or more hypotheses of optimality in the expectations formation of the individual agents, the implied behaviour of the (otherwise identical), model is often found to be wrenched into directions far from the behaviour implied by the rational expectations hypothesis. In short, Pandora’s box of disequilibrium behaviour is opened up”.
38This problem is raised by Woodford [2011] when he argues that even though the economist may be able to define a situation in which the agents in his model understand the workings of that model and behave so as to achieve an equilibrium, such an equilibrium may not be realized because the individuals whose behaviour the model is supposed to describe, actually believe in a different model. Woodford says
“This postulate of “rational expectations,” as it is commonly though rather misleadingly known, is the crucial theoretical assumption behind such doctrines as “efficient markets” in asset pricing theory and “Ricardian equivalence” in macroeconomics. It is often presented as if it were a simple consequence of an aspiration to internal consistency in one’s model and/or explanation of people’s choices in terms of individual rationality, but in fact it is not a necessary implication of these methodological commitments. It does not follow from the fact that one believes in the validity of one’s own model and that one believes that people can be assumed to make rational choices, that they must be assumed to make the choices that would be seen to be correct by someone who (like the economist) believes in the validity of the predictions of that model. Still less would it follow, if the economist herself accepts the necessity of entertaining the possibility of a variety of possible models, that the only models that she should consider are ones in each of which, everyone in the economy is assumed to understand the correctness of that particular model, rather than entertaining beliefs that might (for example) be consistent with one of the other models in the set that she herself regards as possibly correct.
2.2.4. Self-fulfilling beliefs
40This reveals yet another difficulty with the formation of expectations. Indeed, there is, an old literature (see Bray [1982], Kirman [1975, 1983], Woodford [1990]) which shows that individuals who believe in a “wrong” model, can, by behaving in a way consistent with their beliefs, produce outcomes which confirm those beliefs. For example, they may come to believe that changes in fundamental economic variables are driven by sunspots and coordinate successfully on that belief which then becomes self-fulfilling. This may happen even if there is no connection initially between sunspots and economic variables. In this case it is clear that there is no reason for those beliefs to be “rational”. The idea that agents may rationally coordinate on wrong beliefs is inescapable.
2.3. Stationarity
41The only way that rational expectations could be rational is if there was some sort of stationarity characterizing the stochastic process which governs the evolution of the economy. Hendry and Mizon [2010]) two leading econometricians, argued that it is irrational to assume rational expectations when there are changes in the data generating process of the economy. Indeed, in a world in which the economic environment is constantly changing, it would not be, even, from an econometric point of view, rational to hold this sort of expectations. If the process governing the economy contains what are called “structural breaks”, points in time where there is a discontinuous change in the evolution of the economy, it is not reasonable, from a purely econometric point of view, to simply condition on past information to predict the future. As Hendry and Mizon [2010] say:
“The mathematical derivations of dynamic stochastic general equilibrium (DSGE) models and new Keynesian Phillips curves (NKPCs), both of which incorporate “rational expectations”, fail to recognize that when there are unanticipated changes, conditional expectations are neither unbiased nor minimum mean-squared error (MMSE) predictors, and that better predictors can be provided by robust devices. As a consequence, the law of iterated expectations then does not hold as an intertemporal relation unless all distributional shifts are perfectly anticipated by all economic agents, a possibility contradicted by the recent financial crisis. Further, given the prevalence of such changes, learning about the post-change scenario is both difficult, and itself generates further non-stationarities”.
43Without going into technical details, the idea can be simply explained. In a world where the economy moves forward along a path from which it deviates from time to time, one could over time come to learn the distribution of the deviations. In other words, in the long run one would have a correct view of the probabilities of shocks or deviations from the “steady state path”. But what if that path itself changes randomly, as we might well expect it to, in the complex modern world? In that case simply conditioning on past experience is an unsatisfactory way of forming expectations. Yet the two dominant macroeconomic models, widely used as a basis for policy purposes, are based on the assumption that agents do just this and those authors who consider adaptive learning which might converge to Rational Expectations do not take such structural breaks into account.
44But this is not the end of the criticisms which can be levelled at the Rational Expectations Hypothesis. Perhaps even more destructive are the arguments raised by Bookstaber [2017a]. He argues that we can identify four phenomena endemic to financial crises, but which also characterize economic crises in general: the emergence phenomenon, the phenomenon of non-ergodicity, radical uncertainty, and computational irreducibility. We should examine each of these in turn in relation to Rational Expectations, and this will be the objective of the next subsection.
2.4. Fundamental Problems
2.4.1. Emergence
45The properties of a system are said to be emergent when their dynamics cannot be predicted from the sum or average of the behaviour of individuals. To cite Phil Anderson, a Nobel prize physicist in well-known paper in Science;
“The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe. In fact, the more the elementary particle physicists tell us about the nature of the fundamental laws, the less relevance they seem to have to the very real problems of the rest of science much less to those of society… Instead, at each level of complexity entirely new properties appear and the understanding of the new behaviours requires research which I think is as fundamental in its nature as any other.”
47This observation flies in the face of much of modern economic theory which is based on the idea that a thorough knowledge of the behaviour of individuals will permit us to understand the evolution of the economy. Indeed, Lucas and his followers have argued that one should only make assumptions about individuals, and this would effectively rule out looking at properties which might only emerge as the scale of the economy increases and this is true for most modern macroeconomic models which incorporate Rational Expectations.
2.4.2. Non ergodicity
48This problem is related to that raised earlier of non-stationarity. It essentially says that even observing the economy over a very long time will not teach you about the probability distribution at any one point in time. This is a characteristic of markets in general and financial markets in particular. In an evolving system, the probabilities of events, even when they can be defined, change over time, in large part because, we as humans change and we change the economy and markets. We can no longer use extrapolations from the past, which makes forecasting a more than hazardous task and partly explains the significant forecasting errors in economics. A report by the Geneva Association of Insurers recently acknowledged this problem and proposes to substantially modify the calculations of insurance premiums.
2.4.3. Radical Uncertainty
49Uncertainty is said to be radical when it cannot be probabilized and when it concerns events whose existence is not currently known, (the unknown unknowns problem) and this brings us directly back to Kay and King [2020]. In such circumstances, for example, when situations which we have not even envisaged emerge, the only pragmatic answer may be to simply say, “we do not know”.
2.4.4. Computational Irreducibility
50Finally, our economic system is so complex and there are so many feedback effects that we cannot build a “scientific” model of the system as a whole. Computationally irreducible systems have outcomes that cannot be summarized by equations of motion. Instead, they must be experienced, or in the case of models, simulated, period by period in order to find out what actually happens.
51All of this would suggest that theoretical models of systems which are built on the Rational Expectations Hypothesis are unlikely to have much traction. This is reflected in the remarks of a number of leading policy makers.
2.5. Policy makers’ scepticism
52As former Federal Reserve chairman Paul Volcker, said explicitly “it’s clear that among the causes of the recent financial crisis was an unjustified faith in rational expectations [and] market efficiencies.” New York Review of Books Nov. 24th, 2011. This scepticism had been already expressed by Trichet [2010], the governor of the European Central Bank at the time said that “We may need to consider a richer characterisation of expectation formation. Rational expectations theory has brought macroeconomic analysis a long way over the past four decades. But there is a clear need to re-examine this assumption”. Finally, once can also mention Bernanke [2010] who, in direct reference to the Rational Expectations Hypothesis said, “The best approach for dealing with this uncertainty is to make sure that the system is fundamentally resilient and that we have as many fail-safes and back-up arrangements as possible.” Interview with the IHT May 17th [2010]
53These were all reactions to the financial crisis of 2008 but why this disillusionment? Theoretical models seemed to work relatively well during calm periods, so much so that before 2008 a number of economists spoke of the “great moderation”. As always, however, when the crisis arrived, policy makers based their actions on “judgment and experience” to quote Jean-Claude Trichet. But, as Greg Mankiw, then President of the Council of Economic Advisers in the United States, said already in 2006, before the onset of the crisis “The fact that modern macroeconomic research has been very little used to determine economic policy is prima facie evidence that it is not of great use in this activity” (ibid: 43).
54The sentiment seems to be that we have pushed ahead with making our existing models more technically sophisticated but that the increased mathematical difficulty has done little to help policymakers. One reaction might be to take one of Kay and King’s recommendations seriously and just to admit that to echo Keynes, we simply do not know. This approach will not be easy to sell to policymakers nor, indeed to the public at large. An alternative would be to follow Bernanke’s advice and to try to make the system as resilient as possible. But, to make the system resilient requires understanding the way in which it evolves and much of what has gone before suggests that this is far from being a trivial matter.
55However, as one of the authors of Kay and King [2020] is well aware from his period as Governor of the Bank of England, policymakers do have to make decisions even in the face of radical uncertainty. This does not take anything away from the other message of the book, which is that, if possible, it is always useful to ask, “what is going on here?” But, having said that and observing that people in all walks of life do, in fact, take decisions in radically uncertain situations it is worth asking how they set about it.
3. An Alternative Approach
56I will suggest in the last part of this paper that we should fundamentally change the way we think about the problem of expectations in our economic models and instead of peopling the models with Leijonhufvud’s “incredibly smart people” we should actually look at how ordinary individuals, firms and institutions make decisions in our complex system. This was already proposed by Herb Simon in the ‘80s:
“A very natural next step for economics is to maintain expectations in the strategic position they have come to occupy, but to build an empirically validated theory of how attention is in fact directed within a social system, and how expectations are, in fact, formed. Taking that next step requires that empirical work in economics take a new direction, the direction of micro-level investigation proposed by Behavioralism” .
58But if we are to understand how collective phenomena emerge, we have not only to analyse individual behaviour but also the environment in which that behaviour is situated.
3.1. The economy as a complex system
59We should start from the idea that the economy is a complex system and that macroeconomic activity emerges from the interaction between economic actors. Contrary to what is assumed in traditional models, this activity cannot be thought of as the result of the choices of a representative or average individual. In such a system, macroeconomic behaviour is fundamentally different from that of individuals as the earlier quote from Anderson indicates. Trying to model agents with heterogeneous characteristics and their interactions in a changing environment, with the sort of mathematical tools that we have been using, for the reasons given earlier, is a vain endeavour. We have then to abandon building tractable models which can be solved and accept that complex systems have to be analysed with computational models and simulated. But as Bookstaber says, by adopting this approach and “embracing the notion of complexity we come to the end of the theory”. This assertion will provoke a very strong reaction among economists who continue to assert, as Walras did in his time, that theoretical economics is on its way to becoming a science “as incontrovertible as astrophysics”. Nevertheless, as Frank Hahn, one of the major theoretical economists of the 20th century, when asked in 1991 to predict the future of economics in the 21st century, said,
“But wildly complex systems need simulating… But while there will be work for the computer scientist, I very much doubt that economists will be able to establish general propositions in any but very special examples. Again, I do not judge – simulation, especially when based on good data, is a perfectly respectable and probably fruitful activity.” .
61It is in answer to this challenge that agent-based modelling has been developed. In such models we have to specify how individuals behave and the structure of interactions in which they are embedded.
3.2. The Behaviour and Expectations of Individuals in Simulated Models
62As mentioned earlier, we would like the individuals to have rather simple behaviour, for example to follow simple rules or heuristics and the complex aggregate behaviour to emerge from their interaction. Bookstaber in modelling financial markets (see e.g. Bookstaber [2017b]) observes that there are rather few major actors in financial markets and that the rules and strategies that they follow can be deduced from their decisions. Given this the modelling task is greatly facilitated by incorporated those rules into models. Furthermore, these actors are often explicit about their behaviour in order to attract investors, and the rules that they publish can be compared with their empirically observed behaviour. Although Bookstaber’s analysis has been largely focused on financial markets, the principles that he invokes can apply to any sort of socio-economic interaction. However, in observing the behaviour of actors in a specific market one’s model becomes specific to that market and one has to be careful about generalizing to other situations.
63Another approach is to think of simple but plausible heuristics for decision making and then let the actors in a model learn to use those rules which have been most beneficial in the past, to quote Lucas [1986]:
“In general terms, we view or model an individual as a collection of decision rules (rules that dictate the action to be taken in given situations) and a set of preferences used to evaluate the outcomes arising from particular situation-action combinations. These decision rules are continuously under review and revision; new decision rules are tried and tested against experience, and rules that produce desirable outcomes supplant those that do not. I use the term “adaptive” to refer to this trial-and- error process through which our modes of behaviour are determined.”
65Note that this is paradoxical for someone who is regarded as a major figure in the Real Business Cycle and Dynamic Stochastic General Equilibrium, movement where Rational Expectations play a fundamental role. Although the use and changes in the use of rules may lead to satisfactory behaviour and, in some eyes might even converge to “as if” optimization, they, in no way, involve expectations or predictions in the normal sense.
66This is why one could equally apply it to insects or animals who evolve, in some eyes, to optimal adaptation. Having rational expectations means then, having adapted from experience to the environment, which includes the behaviour of others. This is the basic argument underlying Evans and Honkopoja [2001]. Indeed, in many agent-based models, individuals simply learn from previous experience but do not actively contemplate the future. This has been the basis of some criticism, on the grounds that we are dealing with humans who have the unique capacity to use the past to plan for and make decisions about actions which will have consequences in the future. This is why, presumably, despite La Fontaine the idea that ants plan in this way for the future is not a good analogy for human behaviour. Thus, it might be said, in building models in which people simply learn which actions or rules have been good in the past we miss something important about how people actually survive in a constantly changing complex environment.
67Rather than attributing some arbitrary and abstract optimization process involving predicting the future and taking the appropriate optimal action we should study the behaviour of individuals in such circumstances and, for example, study the neurological activity involved. We might, in particular, see if individuals use simple heuristics to handle this difficult task in a complex environment. This is the approach taken by Gigerenzer and Gaissmaier [2011] for example. As those authors say, heuristics often involve ignoring information which might be thought of as pertinent. Heuristics are short cuts to achieving something without doing the calculations involved in solving the complete problem with which one is faced. Think of Gigerenzer’s most famous example which is a heuristic called “the gaze heuristic” for someone running to catch a ball. Rather than trying to calculate where the ball will fall, the runner should fix her gaze on the ball, start running, and adjust her running speed so that the angle of gaze remains constant. This will do the job though not as well, some critics say, as Gigerenzer claims. But as Gigerenzer and Gray [2017] say, “… a major lesson is that complex problems do not generally require complex solutions. Rather, they can often be solved by simple heuristics. Animals and humans tend to find these solutions”
3.3. The use of heuristics rather than analysis to anticipate future developments
68This takes us back to a longstanding debate on whether not only humans but even animals have the capacity to foresee and to prepare for the future. While Hume was convinced that they do, Pascal took the opposite position and claimed to have proved that animals could not anticipate and protect against future occurrences for example. This debate has continued to the present day and, if anything has led to the conclusion, as some of the examples that I will discuss show, that animals do somehow come to behave in an anticipatory manner. But they surely do not do so by solving some complicated intertemporal maximisation problem. Following up on this we might ask, if we observe humans and even animals, managing to handle problems which might, at first sight, require complicated calculations and predictions should we not try to understand how they achieve their goals. Or, to use Gigerenzer’s term, what heuristic they use?
69Once one understands the nature of the hypotheses that underly the Rational Expectations hypothesis, the natural reaction is to argue that humans are not capable of such reasoning, nor do they, in fact, reason in a way which would even permit them to learn the nature of the stochastic processes governing the evolution over time of the environment within which they function. So, rather than attributing remarkable cognitive capacity to humans, we then have to explain how they and even animals do find a way of anticipating and preparing for future events. The notion that animals may have the capacity to do this has received a lot of opposition particularly from biologists. It seems that there is, among the proponents of the argument that humans are uniquely endowed with certain anticipatory reasoning, an a priori, acceptance of a fundamental difference between humans and other species without any justification as to why this should be the case. Suddendorf and Corballis [1997] for example, explain that “The ability to travel mentally in time constitutes a discontinuity between ourselves and other animals.” (ibid: 163) and specify that “Mental time travel comprises the mental reconstruction of personal events from the past (episodic memory) and the mental construction of possible events in the future” (ibid: 133).
70The retrospective component can be defined, according to Tulving [1985]. as follows: “Episodic memory receives and stores information about temporally dated phases or events, and temporal-spatial relations among those events”. The prospective component is described by Suddendorf and Corballis as follows: “… animals other than humans cannot anticipate future need or drive states and are therefore bound to a present that is defined by their current motivational state. We shall refer to this as the Bischof-Köhler hypothesis…” ( [1997]: 142).
71The “mental time travel hypothesis” claims that animals, unlike humans, cannot mentally travel backwards in time to recollect specific past events (episodic memory) or forwards to anticipate future needs (future planning). Indeed. until recently, there was little evidence in animals for either ability. But some experiments on memory in food caching birds, however, question this as in one study that shows that western scrub jays form integrated, flexible, trial-unique memories of what they hid, where and when. Moreover, these birds can adjust their caching behaviour in anticipation of future needs. As Correia et al. [2007] say,
“According to the Bischof-Köhler hypothesis, only humans can dissociate themselves from their current motivation and take action for future needs: other animals are incapable of anticipating future needs, and any future-oriented behaviours they exhibit are either fixed action patterns or cued by their current motivational state. The results described here suggest that the jays can spontaneously plan for tomorrow without reference to their current motivational state, thereby challenging the idea that this is a uniquely human ability”.
73Indeed, more recent research suggests that some animals have elements of both episodic-like memory and future planning. Apes produce tools for future use which may be unrelated to current needs, (Bräuer, J., & Call, J. [2015]). A male chimpanzee has been observed to systematically collect stones to throw at future spectators, (Osvath, M. [2009] and orang-utans make calls to indicate to other orang-utans where they will travel to tomorrow, (van Schaik, C. P., et al. [2013])
74Finally, Laumer et al. [2019] have shown that orang-utans are capable of delaying satisfaction to obtain something better in the future, but can also, when faced with the choice between food now and a tool that will open a container in which there is better food later, learn to pick the tool.
75What all of this suggests is that we have a lot to learn about the sort of heuristics that are used to solve complex problems involving planning by ordinary humans and animals and that we should try to incorporate some of this into our models involving expectations. Just as we do not assume that a dog solves differential equations when it runs and catches a frisbee, one could try to capture the simple heuristics that individuals unknowingly use to prepare for the future. [4] Assuming that humans use heuristics to handle these problems allows us to escape from the rigid requirements for “rationality” that we usually impose.
4. Agent-Based Macro modelling
76At this point the reader may well enquire as to whether macro-models which incorporate the considerations that I have just discussed have been developed and how their analysis of empirical data compares to that of more conventional models such as DSGE for example. The answer to the first question, as to whether there are macroeconomic models in which the agents use simple heuristics to forecast, is affirmative, (see e.g. Delli Gatti et al. [2013], Colander and Kupers [2014] and the extensive bibliography provided by Testsfastion [5]) and the answer to the second is still subject to debate although governments and central banks are making increasing use of ABMs. From the previous discussion it should now be clear that the basis of this sort of model is to use agents who have quite simple rules of behaviour but whose interaction produces complex and sometimes unpredictable aggregate phenomena.
77The important feature of ABMs is that they explain the overall evolution of a system by simulating the behaviour of each individual agent within and then explicitly examining how the interaction of their micro-level behaviour leads to a macro-level picture. Each agent is a self-contained unit which follows a given set of behavioural rules. It is here that we see the difference between standard macroeconomic models and ABMs. Both adhere to the idea that we have to start with a specification of how individual agents behave and can thus be described as having “microfoundations” but the “bottom-up” approach in ABMs yields a very different picture simply because the aggregate behaviour emerges from the interaction between the rather simple agents rather than being the sum or average of sophisticated agents.
78However, ABMs should not be thought of as the simple transplantation of models such as the Ising model widely used in physics and other similar models in the sciences into economics. In economics, agent-level behaviour cannot be thought of as being known to the same level of accuracy as the laws of nature which govern the interactions between, for example, particles. In economics, the behaviour of individuals can change over time in response to their environment and as Murray Gell Mann once said, “imagine how difficult physics would be if particles could think!”. Whilst the standard assumptions on individuals in economics are accepted because they have been so widely used they are, nevertheless, based on the introspection of economists and not on observed behaviour, as many economists have pointed out [6]. But the rather different agent-level assumptions in ABMs have to be examined over the set of their parameter values in simulations to provide rigorous evidence as to their impact on aggregate outcomes.
79In reality, we know that there is a great deal of intrinsic uncertainty in the way in which agents behave, so at best, we can only hope to have some sort of probabilistic match for the aggregate behaviour of the system. The stochastic components possibly present in decision rules, expectations, and interactions will in turn imply that the dynamics of micro and macro variables can be described by stochastic processes. However, non-linearities which are typically present in the dynamics of ABM systems make it hard to analytically derive laws of motion. This suggests that the researcher must often resort to computer simulations in order to analyze the behavior of the ABM at hand. And even there, the detection of such “laws of motion” is no simple matter.
80If, as is undoubtedly the case, the process that generates the data, or, in other words, governs the dynamics of the system, is not ergodic then even matching the moments of the distribution of the aggregates becomes problematic. However, what this sort of model can do, is to reproduce the patterns that seem to emerge as the economy evolves, or as they are sometimes referred to, the stylized facts. While some may not see this as sufficient, the assumptions made in standard models suggest an implausible level of precision. An ABM is a way to generate many possible, plausible realizations of variables in exactly the same manner as different possible price paths are generated in Monte Carlo option pricing. Or one can say that, in comparison with the results from more standard models, ABMs have less bias but, at the cost of higher variance.
81To see how one can handle a socio-economic environment of which, by assumption, the participants have local and limited knowledge, I will now sketch the basic features of such models when they have been used in macroeconomics [7].
82Macroeconomic ABMs typically have the following structure. There is a population of agents (e.g., consumers, firms, banks, etc.), who may be linked together in a network, and whose characteristics and size may change or not in time. The evolution of the system is observed in discrete time steps, t = 1, 2,.... Each agent i has a finite vector of microeconomic characteristics (e.g., production, consumption, wealth, etc.) which may vary over time, and a vector of micro-economic parameters (e.g. mark-ups, propensity to consume, etc.). The economy as a whole may be characterized by a vector of macroeconomic parameters (which can include policy variables such as tax rates, or regulatory constraints). Initial conditions suchas wealth, technology, etc.) are set.
83At each time step a choice of the values of micro and macro parameters is made, and, one or more agents are chosen, either randomly or as a function of the state of the system, to update their micro economic variables. The agents who update according to the model specification may also, in addition to their own knowledge, collect information about the current and past state of a subset of other agents, whose identities will be determined by the network the links and interactions between agents. They can use their knowledge about their own history, their local environment, and as much information as they can gather about the state of the whole economy. They then use heuristics, routines, or other algorithmic behavioral rules to map their information into actions.
84All the components of the model, such as technologies, organizations, behaviour, and network links can evolve over time. After each updating round, a new set of micro-economic variables is fed into the economy for the next iteration: and aggregate variables are computed. The definitions of aggregate variables are similar to those of classic statistical aggregates (i.e., GDP, unemployment, etc.).
85What is meant by talking about the evolution of the state of the economy is the fact that all the variables in the model can vary over time and this is precisely why one cannot apply standard analytical tools nor econometrics to study the evolution of large ABM macroeconomic models. Indeed, one of the criticisms of ABMs is that they have too many degrees of freedom to be useful.
86To counter this, in Bookstaber and Kirman [2018] we suggest that one can make another step towards realism by somewhat reducing the complexity of the model. This can be done by incorporating the observed or announced heuristics used by some of the actors in the economy or market. Such information is available for large banks for example. For, as Bookstaber [2017] observes,
“Why start out by ignoring what’s there, plain as day, to see? There is only one financial system; if we are trying to understand financial crises, why not start with the object at hand? This is not just reasonable; if an ABM does not do this, if it runs as an abstract modeling exercise rather than capturing the messy reality, it is failing, it is not an ABM at all but instead a numerical approach to the deductive neo-classical models” .
88The disadvantage as many economists will remark, is that this makes the model much more specific, but when one is trying to explain a particular economic phenomenon, it may not be useful to try to develop abstract economic models which are not derived from, nor applicable to, the problem at hand. ABMs are, because of their specificity, better placed to produce-conditional forecasts, when one wants to examine a particular policy and its consequences. By their very construction they are context specific. Indeed, this is how epidemiologists use agent-based models, (see e.g. Hoertel et al. [2020] for a model of the Covid-19 pandemic). Rather than attempt to forecast the specific time that a virus outbreak will happen, they identify the risk factors for a virus to break out and subsequently spread. Of course, it is not difficult to see that ABMs nest DSGE models as a special case with little heterogeneity, no stock variables, and a particular set of assumptions about agent behaviour.
89In sum then, one can say that, ABMs will be of most use when analysing problems involving heterogeneity, complexity, non-linearity, emergence, heuristics, and specific rules for agents’ behaviour but that an evaluation of their capacity to fit the data accurately has to be measured by tools from the AI and Machine learning literature rather than those statistical or calibration methods most widely used in the macroeconomic literature (see e.g. Lamperti et al. [2018]).
5. Conclusion
90In this paper, I have raised some of the objections to the Rational Expectations Hypothesis and have suggested that it could only make sense in a relatively stationary environment precisely because the sort of sophisticated calculations which we attribute to the agents become infeasible in the world with which they are faced. As soon as there is radical uncertainty any attempt to plan for the future cannot be based on simple extrapolation of past experience. Yet, in a complex evolving world, individuals do manage to survive even if they do so without optimising or even behaving as if they maximise some objective function. Furthermore, in a system where individuals interact, they will face emergent properties and unintended consequences of their own acts. Our current models seem ill-adapted to such a world. We may do better to build computational models in which the individuals follow simple rules or heuristics. We will need to learn more from the abundant literature in other disciplines, about how these heuristics emerge and how robust they are both in human and in animal behaviour. But, to end on a positive note consider what Jean-Philippe Bouchaud, a professor of statistical physics at the École Normale and CEO of Capital Fund Management, France’s largest hedge fund, has to say,
91“Rather than aiming for precise numerical predictions based on unrealistic assumptions, economists should strive to build models that rely on plausible causal mechanisms and encompass all plausible scenarios, even when these scenarios cannot be fully characterised mathematically. A qualitative approach to the complexity of economics should be high on the research agenda. As Keynes said, it is better to be roughly right than exactly wrong.” J-P Bouchaud [2020].
Notes
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[2]
The assumption of price taking behaviour has been criticized as it does not specify how prices are set and in the majority of papers in macroeconomic theory, authors have fallen back on the comfortable assumption that the economy is already in an equilibrium state.
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[3]
Here Hayek, while being very careful about the definition of equilibrium, like so many economists, does not specify how such a situation is attained.
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[4]
This analogy was made in the economics context by Andy Haldane [2012] now Chief economist at the Bank of England.
- [5]
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[6]
See e.g. Lionel Robbins [1935], Tjalling Koopmans [1957], John Hicks [1956], and Werner Hildenbrand [1994];
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[7]
This is a sketch of the more complete and detailed account given in Dosi and Roventini [2019].
