David K Levine is totally wrong on the rational expectations hypothesis

14 Feb, 2012 at 17:04 | Posted in Economics | 1 Comment

In the wake of the latest financial crisis many people have come to wonder why economists never have been able to predict these manias, panics and crashes that haunt our economies.

In responding to these warranted wonderings, some economists – like renowned theoretical economist David K Levine in the article Why Economists Are Right: Rational Expectations and the Uncertainty Principle in Economics in the Huffington Post – have maintained that

it is a fundamental principle that there can be no reliable way of predicting a crisis.

To me this is a totally inadequate answer. And even trying to make an honour out of the inability of one’s own science to give answers to just questions, is indeed proof of a rather arrogant and insulting attitude.

The main reason Levine gives for his view is what he calls “the uncertainty principle in economics” and the “theory of rational expectations”:

In simple language what rational expectations means is ‘if people believe this forecast it will be true.’ By contrast if a theory is not one of rational expectations it means ‘if people believe this forecast it will not be true.’ Obviously such a theory has limited usefulness. Or put differently: if there is a correct theory, eventually most people will believe it, so it must necessarily be rational expectations. Any other theory has the property that people must forever disbelieve the theory regardless of overwhelming evidence — for as soon as the theory is believed it is wrong.

So does the crisis prove that rational expectations and rational behavior are bad assumptions for formulating economic policy? Perhaps we should turn to behavioral models of irrationality in understanding how to deal with the housing market crash or the Greek economic crisis? Such an alternative would have us build on foundations of sand. It would have us create economic policies and institutions with the property that as soon as they were properly understood they would cease to function.

These are rather preposterous allegations. To my knowledge, there is nobody among us economists that really advocates constructing models based on irrational expectations. And very few of us are not aware of the of effects that economic theory can have on the behaviour of economic actors.

So, to put it bluntly, Levine has totally failed to give a fair view of the state of play among contemporary economists on the issue of rational expectations. Let me try to sort it out just a little.

 

Rational expectations – a concept with a history

The concept of rational expectations was first developed by John Muth (1961) and later applied to macroeconomics by Robert Lucas (1972). In this way the concept of uncertainty as developed by Keynes (1921) and Knight (1921) was turned into a concept of quantifiable risk in the hands of neoclassical economics.

Muth (1961:316) 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 (1961:317) 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.

While Muth’s concept was later picked up by new classical macroeconomics in the hands of people like Robert Lucas and Eugene Fama, most of us thought it was such a patently ridiculous idea, that we had problems with really taking it seriously.

It is noteworthy that Lucas (1972) did not give any further justifications for REH, but simply applied it to macroeconomics. In the hands of Lucas and Sargent it was used to argue that government could not really influence the behavior of economic agents in any systematic way. In the 1980s it became a dominant model-assumption in the New Classical Macroeconomic models 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 in the “efficient market hypothesis”).

 

Keynes, genuine uncertainty and ergodicity

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.

The REH view is very different to the one we connect with John Maynard Keynes. According to Keynes (1937:113) we live in a world permeated by unmeasurable uncertainty – not quantifiable stochastic risk – which often force us to make decisions based on anything but rational expectations. Sometimes we “simply do not know.”

Keynes would not have accepted Muth’s view that expectations “tend to be distributed, for the same information set, about the prediction of the theory.” Keynes, rather, thinks that we base our expectations on the confidence or “weight” we put on different events and alternatives. To Keynes expectations are a question of weighing probabilities by “degrees of belief”, beliefs that have preciously little to do with the kind of stochastic probabilistic calculations made by the rational expectations agents modeled by Lucas et consortes.

In the real world, set in non-ergodic historical time, the future is to a large extent unknowable and uncertain.

REH only applies to ergodic – stable and stationary stochastic – processes. Economies in the real world are nothing of the kind. If the world was ruled by ergodic processes – a possibility utterly incompatible with the views of Keynes – 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 Levine too.

REH holds the view that people, on average, have the same expectations. Keynes, on the other hand, argued convincingly that people often have different expectations and informations, which constitutes the basic rational behind macroeconomic needs of coordination. Something that is rather swept under the rug by the extremely simple-mindedness of assuming rational expectations in representative actors models, which is so in vogue in New Classical Economics. But if all actors are alike, why do they transact? Who do they transact with? The very reason for markets and exchange seems to slip away with the sister assumptions of representative actors and rational expectations.

 

Mathematical tractability is not enough

In my view it is an enormous waste of intellectual power to build these kinds of models based on useless theories. Their marginal utility have long since passed over into the negative. That people are still more or less mindlessly doing this is a sign of an incredible intellectual hubris.

It would be far better to admit that we simply do not know about lots of different things, and that we should try to do as good as possible given this, rather than looking the other way and pretend that we are all-knowing rational calculators.

Models based on REH impute beliefs to the agents that is not based on any real informational considerations, but simply stipulated to make the models mathematically-statistically tractable.

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, like Levine, who still want to use models built on ridiculously unreal assumptions – models devoid of all empirical interest.

In reality, REH is a rather harmful modeling assumption, since it contributes to perpetuating the ongoing transformation of economics into a kind of science-fiction-economics. If economics is to guide us, help us make forecasts, explain or better understand real world phenomena, it is in fact next to worthless.

 

Learning and information

REH presupposes – 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 – built on REH – that Levine is such an adamant propagator for. 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 REH models new information is typically presented as something only reducing the variance of the parameter estimated. But if new information means truly new information it actually could increase our uncertainty and variance (information set (A, B) => (A, B, C)).

Truly new information give birth to new probabilities, revised plans and decisions – something the REH cannot account for with its finite sampling representation of incomplete information.

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.

REH presumes consistent behaviour, where expectations do not display any persistent errors. In the world of REH we are always, on average, hitting the bull’s eye. In the more realistic, open systems view, there is always the possibility (danger) of making mistakes that may turn out to be systematic. It is because of this, presumably, that we put so much emphasis on learning in our modern knowledge societies.

 

On risk, uncertainty and probability distributions

REH assumes that the expectations based on “objective” probabilities are the same as the “subjective” probabilities that agents themselves form on uncertain events. It treats risk and uncertainty as equivalent entities.

But 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 will not do. In those circumstances it is not a useful assumption. The reason is that 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.

There simply is no guarantee that probabilities at time 1 are the same as those at time 2. So when REH assumes that the parameter values on average are the same for the future and the past, one is – as Roman Frydman and Michael Goldberg (2007) forcefully argue – not really talking about uncertainty, but rather knowledge. But this implies that what we observe are realizations of pure stochastic processes, something, if we want to maintain this view, we really have to argue for.

In physics it may possibly not be straining credulity too much to model processes as ergodic – where time and history do not really matter – but in social and historical sciences it is obviously ridiculous. If societies and economies were 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 ergodic concepts.

The future is not reducible to a known set of prospects. It is not like sitting at the roulette table and calculating what the future outcomes of spinning the wheel will be.

We have to surpass REH and try to build economics on a more realistic foundation. A foundation that encompasses both ergodic and non-ergodic processes, both risk and genuine uncertainty. Reading Levine one comes to think of Robert Clower’s (1989:23) apt remark that

much economics is so far removed from anything that remotely resembles the real world that it’s often difficult for economists to take their own subject seriously.

 

Where is the evidence?

Instead of assuming REH to be right, one ought to confront the hypothesis with the available evidence. It is not enough to construct models. Anyone can construct models. To be seriously interesting, models have to come with an aim. They have to have an intended use. 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.

To say, as Prescott (1977:30) that

one can only test if some theory, whether it incorporates rational expectations or, for that matter, irrational expectations, is or is not consistent with observations

is not enough. Without strong evidence all kinds of absurd claims and nonsense may pretend to be science. We have to demand more of a justification than this rather watered-down version of “anything goes” when comes to rationality postulates. If one proposes REH one also has to support its underlying assumptions. None is given, which makes it rather puzzling how REH has become the standard modeling assumption made in much of modern macroeconomics. Perhaps the reason is, as Paul Krugman (2009) has it, that economists often mistake

beauty, clad in impressive looking mathematics, for truth.

But I think Prescott’s view is also the reason why REH economists are not particularly interested in empirical examinations of how real choices (cf Levine’s rather derogatory remarks on experimental and behavioural economics) and decisions are made in real economies. In the hands of Lucas et consortes REH has been transformed from an – in principle – testable hypothesis to an irrefutable proposition.

 

Rational expectations, the future and the end of history

REH basically assumes that all learning has already taken place. This is extremely difficult to vision tin reality, because that means that history has come to an end. When did that happen? It is indeed a remarkable assumption, since in our daily lives, most of us experience a continuing learning. It may be a tractable assumption, yes. But helpful to understand real-world economies? I’ll be dipped! REH models are not useful as-if representations of real-world target systems.

REH builds on Savage’s (1954) “sure thing principle,” according to which people never make systematic mistakes. They may “tremble” now and then, but on average, they always make the right, the rational, decision.

In REH agents know all possible outcomes. In reality, many of those outcomes are yet to be originated. The future is not about known probability distributions. It is not about picking the right ball from an urn. It is about new possibilities. It is about inventing new balls and new urns to put them in. If so, even if we learn, uncertainty does not go away. As G L S Shackle (1972:102) argued, the future

waits, not for its contents to be discovered, but for that content to be originated.

As shown already by Davidson (1983), REH implies that relevant distributions have to be time independent (which follows from the ergodicity implied by REH). But 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 (cf my critique of probabilistic econometrics in the tradition of Haavelmo in Pålsson Syll (2010)). 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.

In REH we are never disappointed in any other way than as when we lose at the roulette wheels, since “averages of expectations are accurate” (Muth 1961:316). 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).

 

REH and modeling aspirations of Nirvana

REH comes from the belief that to be scientific, economics has to be able to model individuals and markets in a stochastic-deterministic way. It’s like treating individuals and markets as the celestial bodies studied by astronomers with the help of gravitational laws. Unfortunately, individuals, markets and entire economies are not planets moving in predetermined orbits in the sky.

To deliver REH has to constrain expectations on the individual and the aggregate level to be the same. If revisions of expectations take place in the REH models they typically have to take in a known and pre-specified precise way. This squares badly with what we know to be true in real world, where fully specified trajectories of future expectations revisions are no-existent.

Most REH models 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 REH models can still fully pre-specify the future even when incorporating these stochastic variables into the models.

 

Aggregation and representative actors models

In the real world there are many different expectations and these cannot be aggregated in REH models without giving rise to inconsistency (acknowledged by Lucas (1995:225) himself). This is one of the main reasons for REH models being modeled as representative actors models. But this is far from being a harmless approximation to reality (cf Pålsson Syll (2010)). Even the smallest differences of expectations between agents would make REH models inconsistent, so when they still show up they have to be considered “irrational”.

It is not possible to adequately represent individuals and markets as having one single overarching probability distribution. Accepting that does not imply – as Levine seems to think – that we have to end all theoretical endeavours and assume that all agents always act totally irrationally and only are analyzable within behavioural economics. Far from it. It means we acknowledge diversity and imperfection, and that economic theory has to be able to incorporate these empirical facts in its models.

Incompatibility between actual behavior and REH behavior is not a symptom of “irrationality”. It rather shows the futility of trying to represent real-world target systems with models flagrantly at odds with reality.

 

Conclusion

Levine maintains that “the only robust policies and institutions – ones that we may hope to withstand the test of time – are those based on rational expectations – those that once understood will continue to function.” As I hope I have been able to show, there is really 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 place the rational expectations hypothesis where it belongs – in the dustbin of history.

Interestingly enough, the main developer of REH himself, Robert Lucas – in an interview with Kevin Hoover (http://econ.duke.edu/~kdh9/) – has himself had second-thoughts on the validity of REH:

Kevin Hoover: The Great Recession and the recent financial crisis have been widely viewed in both popular and professional commentary as a challenge to rational expectations and to efficient markets … I’m asking you whether you accept any of the blame … there’s been a lot of talk about whether rational expectations and the efficient-markets hypotheses is where we should locate the analytical problems that made us blind.

Robert Lucas: You know, people had no trouble having financial meltdowns in their economies before all this stuff we’ve been talking about came on board. We didn’t help, though; there’s no question about that. We may have focused attention on the wrong things, I don’t know.

I’m looking forward to see some future second-thoughts on the subject from Levine too. Better late than never.

 

References

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