Do people have rational expectations?

6 Nov, 2013 at 11:23 | Posted in Economics | 2 Comments

Yesterday — in an article in The Fiscal Times — Mark Thoma tries to answer the question “Do people have rational expectations?” His answer goes like this (emphasis added):

Rational expectations attempts to avoid [the mistakes made by earlier expectational theories] by assuming people optimally incorporate all available information into their expectations …

The rationality assumption is reasonable in some cases. For example, even young children have rational expectations in the sense that economists use the term. Think, for example, of a game where a parent is tickling a child and following a fixed rule. Tickle the armpit, tickle the knee, tickle the armpit, tickle the knee, and so on in a repeating pattern.

If the child is following the simplest type of adaptive expectations in trying to cover up and avoid being tickled, i.e. expect whatever happened last period, he or she will always be one step behind and will never block a tickle. But if the child understands the rule the parent is following and also fully understands the nature of the game, it is easy to rationally anticipate where the next tickle attempt will be and take evasive action.

The assumption of rational expectations is still present in most models today. But is it proper to assume that, like the child playing the tickle game, people fully understand the policy rules that monetary and fiscal policymakers are using to stimulate or slow down the economy? …

I think it’s a stretch to assume that people have this knowledge, but there are two responses to the objection that the economy is too complex for individuals to understand in the sense that rational expectations requires. The first is an “as if” argument … The other argument is that although individuals may not get things exactly correct, markets aggregate information efficiently, e.g. individual errors average out at the market level …

Rational expectations are important for two reasons. First, they serve as a “perfect case” benchmark … Assuming rational expectations is like assuming a perfect vacuum in physics – it provides a baseline that can be augmented with real-world features. Second, there are cases – simple games and financial markets for example – where the assumption of rational expectations may be approximately satisfied. But it’s a mistake, I think, to assume that rational expectations apply in all other settings or to the economy as a whole.

Although there is quite a lot of healthy skepticism on the rational expectations hypothesis (REH) here that I agree with, I still think that Thoma’s picture of the extent to which the assumption of rational expectations is useful and valid, is inadequate and unwarranted.

Let me elaborate a little on why I think so.

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 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 – and this goes for Thoma too.

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. Of course, 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 world of REH, learning is like being better and better at reciting the complete works of Shakespeare by heart – or at hitting bull’s eye when playing dart. It presupposes that we have a complete list of the possible states of the world and that by definition mistakes are non-systematic (which, strictly seen, follows from the assumption of “subjective” probability distributions being equal to the “objective” probability distribution). This is a rather uninteresting and trivial kind of learning. It is a closed world learning, synonymous to improving one’s adaptation to a world which is fundamentally unchanging. But in real, open world situations, learning is more often about adapting and trying to cope with genuinely new phenomena.

In the real world, it is not possible to just 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 — to use Thoma’s own word — “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.

Now Thoma says that assuming rational expectations

is like assuming a perfect vacuum in physics – it provides a baseline that can be augmented with real-world features.

But 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.

The perhaps most problematic part of Thoma’s argument is that he maintains — with the help of his “tickling game” — that young children in it (emphasis added)

have rational expectations in the sense that economists use the term.

But 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 ratinal 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.

Thoma maintains that

Rational expectations are important for two reasons. First, they serve as a “perfect case” benchmark … Second, there are cases – simple games and financial markets for example – where the assumption of rational expectations may be approximately satisfied.

As I have tried to argue here, there is no support for this conviction at all. On the contrary. 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.