On rational expectations and playing games of whack-a-mole (wonkish)

That is a clever argument. But it suffers from a fatal flaw. General equilibrium models of money do not have a unique equilibrium. They have many. This problem was first identified by the English economist Frank Hahn, and despite the best attempts of the rational expectations school to ignore the problem: it reappears with a alarming regularity. Rational expectations economists who deny an independent role for beliefs are playing a game of whack a mole …

This is not an esoteric point. It is at the core of the question that I pose at the beginning of this post: If the Fed raises the interest rate will it cause more or less inflation? And it is a point that policy makers are well aware of as this piece by Fed President Jim Bullard makes clear.

What is the solution? It is one thing to recognize that the world is random, and quite another to assume that we have perfect knowledge. If we place our agents in models where many different things can happen, we must model the process by which they form beliefs.

Roger Farmer

I agree with Farmer on most of his critique of rational expectations. But although multiplicity of equilibria certainly is one important criticism that can we waged against the Muth-Lucas idea, I don’t think it is the core problem with rational expectations.

Assumptions in scientific theories/models are often based on (mathematical) tractability (and so necessarily simplifying) and used for more or less self-evidently necessary theoretical consistency reasons. But one should also remember that assumptions are selected for a specific purpose, and so the arguments (in economics shamelessly often totally non-existent) put forward for having selected a specific set of assumptions, have to be judged against that background to check if they are warranted.

This, however, only shrinks the assumptions set minimally – it is still necessary to decide on which assumptions are innocuous and which are harmful, and what constitutes interesting/important assumptions from an ontological & epistemological point of view (explanation, understanding, prediction). Especially so if you intend to refer your theories/models to a specific target system — preferably the real world. To do this one should start by applying a Solowian Smell Test: Is the theory/model reasonable given what we know about the real world? If not, why should we care about it? If not – we shouldn’t apply it (remember time is limited and economics is a science on scarcity & optimization …)

As Farmer notices, the concept of rational expectations was first developed by John Muth in  an Econometrica article in 1961 — Rational expectations and the theory of price movements  — and later — from the 1970s and onward — applied to macroeconomics. Muth framed his rational expectations hypothesis (REH) in terms of probability distributions:

Expectations of firms (or, more generally, the subjective probability distribution of outcomes) tend to be distributed, for the same information set, about the prediction of the theory (or the “objective” probability distributions of outcomes).

But Muth was also very open with the non-descriptive character of his concept:

The hypothesis of rational expectations] does not assert that the scratch work of entrepreneurs resembles the system of equations in any way; nor does it state that predictions of entrepreneurs are perfect or that their expectations are all the same.

To Muth, its main usefulness was its generality and ability to be applicable to all sorts of situations irrespective of the concrete and contingent circumstances at hand.

Muth’s concept was later picked up by New Classical Macroeconomics, where it soon became the dominant model-assumption and has continued to be a standard assumption made in many neoclassical (macro)economic models – most notably in the fields of (real) business cycles and finance (being a cornerstone of the “efficient market hypothesis”).

REH basically says that people on the average hold expectations that will be fulfilled. This makes the economist’s analysis enormously simplistic, since it means that the model used by the economist is the same as the one people use to make decisions and forecasts of the future.

But, strictly seen, REH only applies to ergodic – stable and stationary stochastic – processes. If the world was ruled by ergodic processes, people could perhaps have rational expectations, but no convincing arguments have ever been put forward, however, for this assumption being realistic.

Of course you can make assumptions based on tractability, but then you do also have to take into account the necessary trade-off in terms of the ability to make relevant and valid statements on the intended target system. Mathematical tractability cannot be the ultimate arbiter in science when it comes to modeling real world target systems. One could perhaps accept REH if it had produced lots of verified predictions and good explanations. But it has done nothing of the kind. Therefore the burden of proof is on those who still want to use models built on utterly unreal assumptions.

In models building on REH it is presupposed – basically for reasons of consistency – that agents have complete knowledge of all of the relevant probability distribution functions. And when trying to incorporate learning in these models – trying to take the heat of some of the criticism launched against it up to date – it is always a very restricted kind of learning that is considered. A learning where truly unanticipated, surprising, new things never take place, but only rather mechanical updatings – increasing the precision of already existing information sets – of existing probability functions.

Nothing really new happens in these ergodic models, where the statistical representation of learning and information is nothing more than a caricature of what takes place in the real world target system. This follows from taking for granted that people’s decisions can be portrayed as based on an existing probability distribution, which by definition implies the knowledge of every possible event (otherwise it is in a strict mathematical-statistically sense not really a probability distribution) that can be thought of taking place.

But in the real world it is – as shown again and again by behavioural and experimental economics – common to mistake a conditional distribution for a probability distribution. Mistakes that are impossible to make in the kinds of economic analysis that build on REH. On average REH agents are always correct. But truly new information will not only reduce the estimation error but actually change the entire estimation and hence possibly the decisions made. To be truly new, information has to be unexpected. If not, it would simply be inferred from the already existing information set.

In the real world, it is not possible to just assume — as Farmer puts it — “we do know the exact probability distribution of future events.” On the contrary. We can’t even assume that probability distributions are the right way to characterize, understand or explain acts and decisions made under uncertainty. When we simply do not know, when we have not got a clue, when genuine uncertainty prevail, REH simply is not  “reasonable.” In those circumstances it is not a useful assumption, since under those circumstances the future is not like the past, and henceforth, we cannot use the same probability distribution – if it at all exists – to describe both the past and future.

Although in physics it may possibly not be straining credulity too much to model processes as taking place in “vacuum worlds” – where friction, time and history do not really matter – in social and historical sciences it is obviously ridiculous. If societies and economies were frictionless ergodic worlds, why do econometricians fervently discuss things such as structural breaks and regime shifts? That they do is an indication of the unrealisticness of treating open systems as analyzable with frictionless ergodic “vacuum concepts.”

If the intention of REH is to help us explain real economies, it has to be evaluated from that perspective. A model or hypothesis without a specific applicability is not really deserving our interest. Without strong evidence all kinds of absurd claims and nonsense may pretend to be science. We have to demand more of a justification than rather watered-down versions of “anything goes” when comes to rationality postulates. If one proposes REH one also has to support its underlying assumptions. None is given. REH economists are not particularly interested in empirical examinations of how real choices and decisions are made in real economies. REH has been transformed from an – in principle – testable hypothesis to an irrefutable proposition.

As shown already by Paul Davidson in the 1980s, REH implies that relevant distributions have to be time independent (which follows from the ergodicity implied by REH). This amounts to assuming that an economy is like a closed system with known stochastic probability distributions for all different events. In reality it is straining one’s beliefs to try to represent economies as outcomes of stochastic processes. An existing economy is a single realization tout court, and hardly conceivable as one realization out of an ensemble of economy-worlds, since an economy can hardly be conceived as being completely replicated over time. It’s really straining one’s imagination trying to see any similarity between these modelling assumptions and children’s expectations in the “tickling game.” In REH we are never disappointed in any other way than as when we lose at the roulette wheels, since, as Muth puts it, “averages of expectations are accurate.” But real life is not an urn or a roulette wheel, so REH is a vastly misleading analogy of real-world situations. It may be a useful assumption – but only for non-crucial and non-important decisions that are possible to replicate perfectly (a throw of dices, a spin of the roulette wheel etc).

Most models building on rational hypothesis are time-invariant and so give no room for any changes in expectations and their revisions. The only imperfection of knowledge they admit of is included in the error terms, error terms that are assumed to be additive and to have a give and known frequency distribution, so that the models can still fully pre-specify the future even when incorporating these stochastic variables into the models.

If we want to have anything of interest to say on real economies, financial crisis and the decisions and choices real people make, it is high time to replace the rational expectations hypothesis with more relevant and realistic assumptions concerning economic agents and their expectations.

Any model assumption — such as ‘rational expectations’ — that doesn’t pass the real world Smell Test is just silly nonsense on stilts.

Suppose someone sits down where you are sitting right now and announces to me that he is Napoleon Bonaparte. The last thing I want to do with him is to get involved in a technical discussion of cavalry tactics at the battle of Austerlitz. If I do that, I’m getting tacitly drawn into the game that he is Napoleon. Now, Bob Lucas and Tom Sargent like nothing better than to get drawn into technical discussions, because then you have tacitly gone along with their fundamental assumptions; your attention is attracted away from the basic weakness of the whole story. Since I find that fundamental framework ludicrous, I respond by treating it as ludicrous – that is, by laughing at it – so as not to fall into the trap of taking it seriously and passing on to matters of technique.

Robert Solow