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So what are rational expectations exactly?

It seems that during the 1990s there was a ‘rational expectations revolution’, with a subsequent ‘change of paradigm’ in macroeconomics, which has been used to justify changes in economic policy (independence of Central Banks, state intervention reduced to a minimum, as having no effect since ‘rationally’ anticipated by economic agents). Every textbook, however elementary, was thus obliged to discuss this revolution: how could they not before such a discovery, one which has earned Lucas, Prescott and a few others the Nobel Prize? For the student, rational expectations, is a vague discourse illustrated by mysterious and incomprehensible mathematical abbreviations. But as is usual in this kind of situation - after having sat through classes in microeconomics, the student is resigned and makes do with learning by heart what he has been told.

One could, however, think that such an important concept, which deals with the behaviour of economic agents (i.e. you and I) would be accessible to intuition, and defined in consequence. However, this is none such case. If we refer to macroeconomic textbooks (oddly enough, this is where we find this ‘revolution‘, even though it is based on the choices of individuals) we generally find a trivial definition, of absolutely no interest, sometimes accompanied by incomprehensible formulae such as tE(pt+1| It), or obscure expressions such as ‘joint laws’ and ‘residual bias’.

To know what we are dealing with we must go back to its origins - to those who first formulated the concept in specialist journals. There we find that what we have is simply a self-fulfilling prophesy, where beliefs play a much greater role than rationality. This is a hypothesis that goes way back, and one that Keynes especially stressed. Nothing much new then, except? but for the mathematical jumble that goes with it.

Yet again students, and everyone else, are intimidated into believing something through their ignorance in mathematics, whilst behind all the maths is a simple and very old idea, of debatable interest.

A definition that is no definition

If there is one point where Clinton’s chief economist (Joseph Stiglitz) and that of Bush (Gregory Mankiw) concur, it is in the definition of rational expectations (science goes beyond political difference). Thus we read in the ‘glossary’ of Stiglitz’ Economic Principles , that

"the expectations of individuals are rational if they take fully into account the available and relevant information".

And in Mankiw’s Economic Principles that

"the hypothesis according to which the public uses all available and useful information to predict the future, including information concerning the policies to be carried out by the government in the future".

But why did we have to wait till the 1970s to suppose that economic agents ‘use all available information to predict the future’? Were they complete idiots before, on Wall Street and elsewhere? And what does “ take fully into account” mean ? Mystery. The student has to find his own way to try to understand. If he goes looking in other textbooks, the most advanced included, he will find everywhere the relation between rational expectations and the (‘full’ ’best’ or ’effective’) use of the information available. Thus we find in the ‘glossary’ of Robert Barro’s textbook Macroeconomics(1986) the following definition:

“ rational expectations : point of view according to which peoples make prognostics or estimations of unknown variables in the best way possible, using all available information at that moment ”

For his part David Romer writes, when he deals for the first time with the question of rational expectations in Advanced Macroeconomics (1990):

“ It is therefore natural to wonder what happens when investors formulate their expectations of the rate of change whilst using all the information publicly available - i.e. when their expectations are rational ” (p233)

Jeffrey Sachs and Eduardo Larrain (Macroeconomics, Prentice Hall, 1992) explain that

“ The general hypothesis that individuals make efficient use of all available information is known as the rational expectations hypothesis ”. p 40.

Olivier Blanchard and Daniel Cohen (Macroéconomie, 2002) having noted that:

“ People use all the information on the future, i.e. expectations are rational ”,

feel the need to specify that

“ this does not mean that people always make rational expectations but that the cases where rational expectation are a poor representation of reality are the exception ”

We are therefore before more than an assumption : a fact derived from reality, except in exceptional cases.

Another type of definition consists of alluding to the absence of “ systematic errors ”. Thus, according to the glossary of Paul Samuelson and William Nordhaus’ Economics (16th edition, 1998) :

“ expectations are said to be rational if they do not present systematic (or biased) errors and use all available information ”.

It is the same for Michael Burda and Charles Wyplosz who write in their treatise Macroeconomics :

“ rational expectations hypothesis : hypothesis asserting that agents evaluate future events using all available information efficiently so that they do not make systematic forecasting errors ” (p 543)

It is useless to speak here of all other textbooks which unanimously take up these terms (or expressions) such as ‘use available information’, ‘efficiently’, without ‘systematic errors’ etc.

The Maths

Often, following this kind of definition which is not a definition, we are the beneficiary of incomprehensible mathematical abbreviation. It is thus that Romer, after the couplet “ best use of available information” explains that:

“ Lucas’ second postulate is very important : it assumes that producers rationally determine the conditional expectation of ri for a given pi. In other words, Lucas supposes that E(ri| pi) is equal to the true expectation of ri, knowing pi and the true joint law of the two variables ”.

What does this mean? What is a ‘true’ expectation’s ‘true law’? What does the mysterious symbol E(ri| pi) mean? If we don’t understand, we wonder how producers do, and (“ rationally ”) determine the ‘true law’. All of which does not stop Romer following this up with:

“ Today the hypothesis of rational expectations seems no more curious than the hypothesis of maximisation of individual utility. However, when it was introduced by Lucas, it was very controversial ”.

We understand why it was very controversial : there is an enormous difference between knowing one’s tastes (one’s utility function) and knowing the true laws which govern the economy with its multitude of agents interacting with their different tastes and beliefs.

Sachs and Larrain also hit us with the “ true” model, 400 pages after defining the rational expectations as the ‘best’ use of available information :

“ Lucas and Sargent proposed that workers and firms behave as they understand the ‘true’ model of the economy and base their forecast of inflation in that model, rather than adaptative. This approach was christened rational expectations on the grounds that it would be rational for economic agents to form their expectations based upon their ‘model’ of the economy ” (p 462).

Indeed, If we want to understand what rational expectations are exactly, we have to go back to the texts of those who introduced the concept. We observe that we are far from the “ best use of available information ”…

Self-fulfilling expectations

Thomas Sargent, one of the first to use the hypothesis of rational expectations, wrote in The Concise Encyclopedia of Economics (on-line):

“ The concept of rational expectations asserts that outcomes do not differ systematically (ie. regularly or predictably) from what people expected them to be ”.

In a series of lectures (The Arne Ryder Lectures) published under the title Bounded Rationality in Macroeconomics (Oxford University Press) Sargent specifies:

“ The idea of rational expectations has two components : first, that each person’s behavior can be described as the outcome of maximising an objective function subject to perceived constraints and second, that the constraints perceived by everybody in the system are mutually consistent ” (p 6).

We note that there is nothing in these definitions regarding the “ the best use of available information ”. On the contrary, we see the concepts of “ perceived constraints ” and of consistency of these constraints. Sargent specifies on this:

“ In an economic system, the decisions of one person form parts of the constraints upon others, so that consistency, at least implicitly, requires people to be forming beliefs about others’ decisions, about their decision processes, and even about their beliefs ” (p 6).

Thus, the hypothesis of rational expectations - which, according to Romer, “seems no more curious than the hypothesis of individual maximisation ” - brings the beliefs of each individual as to what other people will do into play, but also about other’s beliefs when they take their decisions! For expectations to be effectively ‘rational’, it is necessary for all these beliefs, and beliefs of beliefs, to be correct (or “true”), that is, compatible ! We understand that this totally mind-blowing hypothesis has provoked, to say the least, some reticence… Sargent is aware of this, and therefore asks the question: “ Why do economists adopt the hypothesis of rational expectations? ” He responds:

“ As models in which people’s behavior depends on their perceptions can produce so many possible outcomes, they are useless as instruments for generating predictions ”.

Thus to arrive at these oft mentioned predictions, the most improbable situation is assumed : all agents are identical and have the same (self-fulfilling) beliefs. Then to get us to swallow it whole, they talk about macroeconomics….

As for Muth, the first to have used the expression “ rational expectations ” (in Rational Expectations and the Theory of Price Movements, Econometrica, 1961). He describes them as

“ informed of future events, that is to say, they are essentially the same as the predictions of the relevant economic theory ” (p 316)

Whilst saying that this means:

“ expectations of firms (or, more generally, the subjective probability distribution of outcomes) tend to be distributed, for the same information set, about the prediction f the theory (or the “objective” probability distribution of outcomes)”(p 316).

Thus, the ‘subjective’ and ‘objective’ probability distributions of relevant variables are the essential concepts. If Muth talks of ‘objective’ distributions in inverted commas, it is because he cannot that observed ‘real’ situations are the result of decisions taken by agents, and therefore of their beliefs concerning the ‘true model’ of the economy.

Lucas and Prescott, in the other seminal text on rational expectations Investment under uncertainty, Econometrica 1971) introduced them as follows:

“ the actual and anticipated prices have the same probability distribution, so that price expectations are rational ” (their italics, p 660).

They also write:

“ Thus we surrender, in advance, any hope of shedding light in the process by which firms translate current information into price forecasts ”.

Further on they also write

“ We assume that expectations of firms are rational, or that the anticipated price at time t is the same function of (u1, …, ut) as is the actual price. That is, we assume that firms know the true distribution of prices for all future periods ” (p664).

Lucas and Prescott do not use inverted commas here when they talk about the ‘true’ law of probability, which is, however, the result of the actions of firms. But Lucas does so elsewhere. For example, in Asset Prices in an Exchange Economy (Econometrica, 1978) he writes about rational expectations that it is « the hypothesis that agents ‘know’ the ‘true’ probability distribution of future prices.» (p 1444). There is, in the same paper, a non-ambiguous definition on rational expectations, without inverted commas :

“ The assumption of rational expectations : the market clearing price function p implied by consumer behavior is assumed to be the same as the price function p on which consumer decisions are based ” (p 1431).

We are some ( a long ? ) way from textbooks’ " best use of available information”…

What rationality?

When Muth introduces the expression “ rational expectations ”, he does so to set himself apart from those who use in their models a formula ‘a priori’ to calculate expected variables (for instance, extrapolated or adaptive expectations formulas), a formula which does not take into account accumulated experience, and which should be revised - if individuals are rational. We can therefore legitimately contest the procedure consisting of the use of a formula which, in prolonging an outmoded trend, leads to systematic errors. Rational individuals will, at any time, observe the present situation, taking into account past experience, and make consequent predictions. But that nowhere implies that these predictions are “ correct ” - or self-fulfilling. What is most probable, is that they will continue to be mistaken, and will constantly modify the model which serves them in their prediction-making. Lucas, Prescott, but also Sargent, however, advance (but not with too much conviction) that in the ‘long-term’ this process will stop, the probability distributions of expected and actual values being therefore equal. But this is a pure petition of principle, based on the idea, nowhere proven, that the economy must always after a certain period of adjustment, return to equilibrium (to this it is often added the pre-emptory, or woeful argument “ otherwise, we can do nothing ” - implicitly meaning that we can no longer construct models).

Assuming that equilibrium is achieved - the forecasts are self-fulfilling - there is no reason to qualify this as ‘rational’, since it is the result of beliefs which do not necessarily generates optimum states, in the way that economists mean (game theorists? particularly stress this point). Keynes, among others, and for a long time, also stressed this point. He did not assume, obviously, as Muth, Lucas, Prescott and our “ new macro-economists ” do, that the model which the agents believe in is Walrasian, and where, at the same time, they behave as price takers and propose (equilibrium) prices, so that they engender a Pareto optimal allocation. That is completely crazy, but doesn’t stop them getting Nobel Prizes!

 
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