Hayek, Radner and Rational-Expectations Equilibrium

In revising my paper on Hayek and Three Equilibrium Concepts, I have made some substantial changes to the last section which I originally posted last June. So I thought I would post my new updated version of the last section. The new version of the paper has not been submitted yet to a journal; I will give a talk about it at the colloquium on Economic Institutions and Market Processes at the NYU economics department next Monday. Depending on the reaction I get at the Colloquium and from some other people I will send the paper to, I may, or may not, post the new version on SSRN and submit to a journal.

In this section, I want to focus on a particular kind of intertemporal equilibrium: rational-expectations equilibrium. It is noteworthy that in his discussions of intertemporal equilibrium, Roy Radner assigns a meaning to the term “rational-expectations equilibrium” very different from the one normally associated with that term. Radner describes a rational-expectations equilibrium as the equilibrium that results when some agents can make inferences about the beliefs of other agents when observed prices differ from the prices that the agents had expected. Agents attribute the differences between observed and expected prices to the superior information held by better-informed agents. As they assimilate the information that must have caused observed prices to deviate from their expectations, agents revise their own expectations accordingly, which, in turn, leads to further revisions in plans, expectations and outcomes.

There is a somewhat famous historical episode of inferring otherwise unknown or even secret information from publicly available data about prices. In 1954, one very rational agent, Armen Alchian, was able to identify which chemicals were being used in making the newly developed hydrogen bomb by looking for companies whose stock prices had risen too rapidly to be otherwise explained. Alchian, who spent almost his entire career at UCLA while moonlighting at the nearby Rand Corporation, wrote a paper at Rand listing the chemicals used in making the hydrogen bomb. When news of his unpublished paper reached officials at the Defense Department – the Rand Corporation (from whose files Daniel Ellsberg took the Pentagon Papers) having been started as a think tank with funding by the Department of Defense to do research on behalf of the U.S. military – the paper was confiscated from Alchian’s office at Rand and destroyed. (See Newhard’s paper for an account of the episode and a reconstruction of Alchian’s event study.)

But Radner also showed that the ability of some agents to infer the information on which other agents are causing prices to differ from the prices that had been expected does not necessarily lead to an equilibrium. The process of revising expectations in light of observed prices may not converge on a shared set of expectations of future prices based on common knowledge. Radner’s result reinforces Hayek’s insight, upon which I remarked above, that although expectations are equilibrating variables there is no economic mechanism that tends to bring expectations toward their equilibrium values. There is no feedback mechanism, corresponding to the normal mechanism for adjusting market prices in response to perceived excess demands or supplies, that operates on price expectations. The heavy lifting of bringing expectations into correspondence with what the future holds must be done by the agents themselves; the magic of the market goes only so far.

Although Radner’s conception of rational expectations differs from the more commonly used meaning of the term, his conception helps us understand the limitations of the conventional “rational expectations” assumption in modern macroeconomics, which is that the price expectations formed by the agents populating a model should be consistent with what the model itself predicts that those future prices will be. In this very restricted sense, I believe rational expectations is an important property of any model. If one assumes that the outcome expected by agents in a model is the equilibrium predicted by the model, then, under those expectations, the solution of the model ought to be the equilibrium of the model. If the solution of the model is somehow different from what agents in the model expect, then there is something really wrong with the model.

What kind of crazy model would have the property that correct expectations turn out not to be self-fulfilling? A model in which correct expectations are not self-fulfilling is a nonsensical model. But there is a huge difference between saying (a) that a model should have the property that correct expectations are self-fulfilling and saying (b) that the agents populating the model understand how the model works and, based know their knowledge of the model, form expectations of the equilibrium predicted by the model.

Rational expectations in the first sense is a minimal consistency property of an economic model; rational expectations in the latter sense is an empirical assertion about the real world. You can make such an assumption if you want, but you can’t credibly claim that it is a property of the real world. Whether it is a property of the real world is a matter of fact, not a methodological imperative. But the current sacrosanct status of rational expectations in modern macroeconomics has been achieved largely through methodological tyrannizing.

In his 1937 paper, Hayek was very clear that correct expectations are logically implied by the concept of an equilibrium of plans extending through time. But correct expectations are not a necessary, or even descriptively valid, characteristic of reality. Hayek also conceded that we don’t even have an explanation in theory of how correct expectations come into existence. He merely alluded to the empirical observation – perhaps not the most faithful description of empirical reality in 1937 – that there is an observed general tendency for markets to move toward equilibrium, implying that, over time, expectations somehow do tend to become more accurate.

It is worth pointing out that when the idea of rational expectations was introduced by John Muth (1961), he did so in the context of partial-equilibrium models in which the rational expectation in the model was the rational expectation of the equilibrium price in a particular market. The motivation for Muth to introduce the idea of a rational expectation was the cobweb-cycle model in which producers base current decisions about how much to produce for the following period on the currently observed price. But with a one-period time lag between production decisions and realized output, as is the case in agricultural markets in which the initial application of inputs does not result in output until a subsequent time period, it is easy to generate an alternating sequence of boom and bust, with current high prices inducing increased output in the following period, driving prices down, thereby inducing low output and high prices in the next period and so on.

Muth argued that rational producers would not respond to price signals in a way that led to consistently mistaken expectations, but would base their price expectations on more realistic expectations of what future prices would turn out to be. In his microeconomic work on rational expectations, Muth showed that the rational-expectation assumption was a better predictor of observed prices than the assumption of static expectations underlying the traditional cobweb-cycle model. So Muth’s rational-expectations assumption was based on a realistic conjecture of how real-world agents would actually form expectations. In that sense, Muth’s assumption was consistent with Hayek’s conjecture that there is an empirical tendency for markets to move toward equilibrium.

So, while Muth’s introduction of the rational-expectations hypothesis was an empirically progressive theoretical innovation, extending rational-expectations into the domain of macroeconomics has not been empirically progressive, rational-expectations models having consistently failed to generate better predictions than macro-models using other expectational assumptions. Instead, a rational-expectations axiom has been imposed as part of a spurious methodological demand that all macroeconomic models be “micro-founded.” But the deeper point – one that Hayek understood better than perhaps anyone else — is that there is a difference in kind between forming rational expectations about a single market price and forming rational expectations about the vector of n prices on the basis of which agents are choosing or revising their optimal intertemporal consumption and production plans.

It is one thing to assume that agents have some expert knowledge about the course of future prices in the particular markets in which they participate regularly; it is another thing entirely to assume that they have knowledge sufficient to forecast the course of all future prices and in particular to understand the subtle interactions between prices in one market and the apparently unrelated prices in another market. It is those subtle interactions that allow the kinds of informational inferences that, based on differences between expected and realized prices of the sort contemplated by Alchian and Radner, can sometimes be made. The former kind of knowledge is knowledge that expert traders might be expected to have; the latter kind of knowledge is knowledge that would be possessed by no one but a nearly omniscient central planner, whose existence was shown by Hayek to be a practical impossibility.

The key — but far from the only — error of the rational-expectations methodology that rules modern macroeconomics is that rational expectations somehow cause or bring about an intertemporal equilibrium. It is certainly a fact that people try very hard to use all the information available to them to predict what the future has in store, and any new bit of information not previously possessed will be rapidly assessed and assimilated and will inform a possibly revised set of expectations of the future. But there is no reason to think that this ongoing process of information gathering and processing and evaluation leads people to formulate correct expectations of the future or of future prices. Indeed, Radner proved that, even under strong assumptions, there is no necessity that the outcome of a process of information revision based on the observed differences between observed and expected prices leads to an equilibrium.

So it cannot be rational expectations that leads to equilibrium, On the contrary, rational expectations are a property of equilibrium. To speak of a “rational-expectations equilibrium” is to speak about a truism. There can be no rational expectations in the macroeconomic except in an equilibrium state, because correct expectations, as Hayek showed, is a defining characteristic of equilibrium. Outside of equilibrium, expectations cannot be rational. Failure to grasp that point is what led Morgenstern astray in thinking that Holmes-Moriarty story demonstrated the nonsensical nature of equilibrium. It simply demonstrated that Holmes and Moriarity were playing a non-repeated game in which an equilibrium did not exist.

To think about rational expectations as if it somehow results in equilibrium is nothing but a category error, akin to thinking about a triangle being caused by having angles whose angles add up to 180 degrees. The 180-degree sum of the angles of a triangle don’t cause the triangle; it is a property of the triangle.

Standard macroeconomic models are typically so highly aggregated that the extreme nature of the rational-expectations assumption is effectively suppressed. To treat all output as a single good (which involves treating the single output as both a consumption good and a productive asset generating a flow of productive services) effectively imposes the assumption that the only relative price that can ever change is the wage, so that all but one future relative prices are known in advance. That assumption effectively assumes away the problem of incorrect expectations except for two variables: the future price level and the future productivity of labor (owing to the productivity shocks so beloved of Real Business Cycle theorists).

Having eliminated all complexity from their models, modern macroeconomists, purporting to solve micro-founded macromodels, simply assume that there are just a couple of variables about which agents have to form their rational expectations. The radical simplification of the expectational requirements for achieving a supposedly micro-founded equilibrium belies the claim to have achieved anything of the sort. Whether the micro-foundational pretense affected — with apparently sincere methodological fervor — by modern macroeconomics is merely self-delusional or a deliberate hoax perpetrated on a generation of unsuspecting students is an interesting distinction, but a distinction lacking any practical significance.

Four score years since Hayek explained how challenging the notion of intertemporal equilibrium really is and the difficulties inherent in explaining any empirical tendency toward intertempral equilibrium, modern macroeconomics has succeeded in assuming all those difficulties out of existence. Many macroeconomists feel rather proud of what modern macroeconomics has achieved. I am not quite as impressed as they are.