Rational Expectations and the Standard Model of Social Ontology

Noah Smith has an interesting post where he refers to an article of Charles Manski about the rational expectations hypothesis (REH). Manski points out that in a stochastic environment it is highly unlikely that expectations are rational in the sense of the REH. However, he ultimately concludes that there are no better alternative. In this post, I want to point out that the REH is actually well in line with what the philosopher Francesco Guala calls in an article the “Standard Model of Social Ontology” (SMOSO), including the fact that it lacks empirical support. This somehow echoes Noah Smith’s conclusion that “rational Expectations can’t be challenged on data grounds”.

Guala characterizes the SMOSO by the following  three elements:

1) Reflexivity: Guala defines this as the fact that “social entities are constituted by beliefs about beliefs” (p. 961). A more general way to characterize reflexivity is that individuals form attitudes (mainly, beliefs) about the systems they are part of and thus attitudes about others’ attitudes. If it is assumed that these attitudes determine people’s actions and in turn, these actions determine the state of the system, then people’s attitudes determine the system. This may lead to the widely discussed phenomenon of self-fulfilling prophecies where the agents’ beliefs about others’ beliefs about the (future) state of the system bring the system to that state.

2) Performativity: it can be defined as the fact that the social reality is literally made by the agents’ attitudes and actions. The classical example is language: performative utterances like “I promise that Y” or “I make you man and wife” not only describe the social reality, they (in the appropriate circumstances) make it by creating a state of affairs that makes the utterance true. Other cases are for instance the fact that some pieces of paper are collectively regarded as money or the fact that raising one’s hand is regarded as a vote in favor of some proposition or candidate.

3) Collective intentionality: attitudes (in particular beliefs) constitutive of the social reality are in some way or another “collective”. Depending on the specific model, collective intentionality can refer to a set of individual attitudes (intentions, beliefs) generally augmented by an epistemic condition (usually, mutual or common knowledge of these attitudes) or a distinct collective attitude of the form “we intend to” or “we believe that”.

The three elements constitutive of the SMOSO are common to almost all the theories and models developed in social ontology and the philosophy of social science for the last thirty years. That does not mean that they fully determine the content of these theories and models: there are several and mutually exclusive accounts of collective intentionality, as well as there are different ways to account for performativity and reflexivity. Now, I want to suggest that many economic models using the REH fall within this general model of social ontology. The REH states that economic agents do not make systematic errors in the prediction of the future value of relevant economic variables. In other words, they make correct predictions on average. Denote X(t) the value of any economic variable you want (price, inflation, …) at time t and X(t+1)^ei the expected value of X at time t+1 according to agent i. Formally, an expectation corresponds to X(t+1)^ei = E[X(t)ΙI(t)^i] with I(t)^i the information available at t for i and E the expectation operator. The REH is the assumption that X(t+1) = X(t+1)^ei + Eu where u is an error term of mean 0. The proximity of the REH with the three elements of the SMOSO is more or less difficult to see but is nevertheless real.

The relationship between the REH and reflexivity is the easiest to state because discussions on rational expectations in the 1950s find their roots in the treatment of the reflexivity issue which itself originates in Oskar Morgenstern’s discussion of the “Holmes-Moriarty paradox”. Morgenstern was concerned with the fact that if the state of affairs that realizes depends on one’s beliefs about others’ beliefs about which state of affairs will realize, then it may be impossible to predict states of affairs. In 1950s, papers by Simon and by Modigliani and Grunberg tackle this problem. Using fixed-point techniques, they show that under some conditions, there is at least one solution x* = F(x*) such that the prediction x* regarding the value of some variable is self-confirmed by the actual value F(x*). In his article on rational expectations, Muth mentions as one of the characteristic of the REH the fact that a public prediction in the sense of Grunberg and Modigliani “will have no substantial effect on the operation of the economic system (unless it is based on inside information)”. So, the point is that a “rational prediction” should not change the state of the system.

The relationship of the REH with performativity and collective intentionality is more difficult to characterize. Things are somewhat clearer however once we realize that the REH implies mutual consistency of the agents’ beliefs and actions (see this old post by economist Rajiv Sethi which makes this point clearly). This is due to the fact that in an economic system, the value X(t+1) of some economic variable at time t+1 will depend on the decisions si made by thousands of agents at t, i.e. X(t+1) = f(s1(t), s2(t), …, sn(t)). Assuming that these agents are rational (i.e. they maximize expected utility), the agent’s decisions depend on their conjectures X(t+1)^ei about the future value of the variable. But then this implies that one’s conjecture X(t+1)^ei is a conjecture about others’ decisions (s1(t), …, si-1(t), si+1(t), …, sn(t)) for any given functional relation f, and thus (assuming that rationality is common knowledge) a conjecture about others’ conjectures (X(t+1)^e1, …, X(t+1)^ei-1, X(t+1)^ei+1, …, X(t+1)^en). Since others’ conjectures are also conjectures about conjectures, we have an infinite chain of iterated conjectures about conjectures. Mutual consistency implies that everyone maximizes his utility given others’ behavior. In general, this will also imply that everyone forms the same, correct conjecture, which is identical to the REH in the special case where all agents have the same information since we have X(t+1) = X(t+1)^ei for all agent i. As Sethi indicates in his post, this is equivalent to what Robert Aumann called the “Harsanyi doctrine” or more simply, the common prior assumption: any disagreement between agents must come from difference in information.

In itself, the relationship between the REH and the common prior assumption is interesting. Notably, if we consider that the common prior assumption is difficult to defend on empirical grounds, this should lead us to consider the REH with suspicion. But it also helps to make the link with the SMOSO. Regarding performativity, we have to give up the assumption (standard in macroeconomics) that the equilibrium is unique, i.e. there are at least two values X(t+1)* and X(t+1)** for which the agents’ plans and conjectures are mutually consistent. Now, any public announcement of the kind “the variable will take value X(t+1)* (resp. X(t+1)**)” is self-confirming. Moreover, this is common knowledge.[1] The public announcement play the role of a “choreographer” (Herbert Gintis’ term) that coordinates the agents’ plans. This makes the link with collective intentionality. It is tempting to interpret the common prior assumption as some kind of “common mind hypothesis”, as if the economic agents were collectively sharing a worldview. Of course, as indicated above, it is also possible to adopt a less controversial interpretation by seeing this assumption as some kind of tacit agreement involving nothing but a set of individual attitudes. The way some macroeconomists defend the REH suggests a third interpretation: economic agents are able to learn about the economic world and this learning generates a common background. In game-theoretic terms, we could also say that agents are learning to play a Nash equilibrium (or a correlated equilibrium).

This last point is interesting when it is put in perspective with Guala’s critique of the SMOSO. Guala criticizes the SMOSO for its lack of empirical grounding. For instance, discussions about collective intentionality are typically conceptual, but almost never build on empirical evidence. Most critics of the REH in economics make a similar point: the REH is made for several reasons (essentially conceptual and theoretical) but has no empirical foundations. The case of learning is particularly interesting: since the 1970s, one of the “empirical” defenses of the REH has been the casual claim that “you can’t fool people systematically”. This is the same as to say that on a more or less short term, people learn how the economy works. This is a pretty weak defense, to say the least. Economists actually do not know how economic agents are learning, what is the rate of the learning process, and so on. Recently, a literature on learning and expectations has been developing, establishing for instance the conditions of convergence to rational expectations. As far as I can tell, this literature is essentially theoretical but is a first step to provide more solid foundations to REH… or to dismiss it. The problem of the empirical foundations for any assumption regarding how agents form expectations is likely to remain though.

Note

[1] Going a little further, it can be shown that if the public announcement is made on the basis of a probabilistic distribution p where each equilibrium is announced with probability p(X(t+1)*), then p also defines a correlated equilibrium in the underlying game, i.e. agents behave as if they were playing a mixed strategy defined by p.

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