Economics Stack Exchange is a question and answer site for those who study, teach, research and apply economics and econometrics. It only takes a minute to sign up.
Sign up to join this community
I believe the rational expectations hypothesis says that agents in a model bear expectations that are the same as mathematical expectations.
Under what circumstances does this hypothesis become questionable? What are the usual arguments against this hypothesis?
The Rational Expectations Hypothesis (REH) is an hypothesis about aggregate expectations. I believe it is illuminating to post here a lengthy quote (part 2) from Muth (1961) paper where REH originated (bold letters are our emphasis):
2. THE "RATIONAL EXPECTATIONS" HYPOTHESIS
Two major conclusions from studies of expectations data are the following:
1. Averages of expectations in an industry are more accurate than naive models and as accurate as elaborate equation systems, although there are considerable cross-sectional differences of opinion.
2. Reported expectations generally underestimate the extent of changes that actually take place.In order to explain these phenomena, I should like to suggest that expectations, since they are informed predictions of future events, are essentially the same as the predictions of the relevant economic theory (We show in Section 5 that the hypothesis is consistent with these two phenomena). At the risk of confusing this purely descriptive hypothesis with a pronouncement as to what firms ought to do, we call such expectations "rational." It is sometimes argued that the assumption of rationality in economics leads to theories inconsistent with, or inadequate to explain, observed phenomena, especially changes over time (e.g., Simon 1959). Our hypothesis is based on exactly the opposite point of view: that dynamic economic models do not assume enough rationality.
The hypothesis can be rephrased a little more precisely as follows: that 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).
The hypothesis asserts three things: (1) Information is scarce, and the economic system generally does not waste it. (2) The way expectations are formed depends specifically on the structure of the relevant system describing the economy. (3) A "public prediction," in the sense of Grunberg and Modigliani (1954), will have no substantial effect on the operation of the economic system (unless it is based on inside information). This is not quite the same thing as stating that the marginal revenue product of economics is zero, because expectations of a single firm may still be subject to greater error than the theory.
It 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. ...
I believe that it should be clear from the above that:
1) REH is not an assertion about each separate individual, but about the properties of the "prevailing" expectation produced by the black-box combination of individual expectations. In other words the REH is assumed, without really making any assumptions about individual rationality.
2) It has as much to do with the "internal consistency" of the economic model itself, because by construction and without any economic assumptions, $E(X\mid I) = X+ e,\; E(e\mid I) =0 $.
The fact that the predominant economic model framework has been that of the "representative" (identical) consumer, nevertheless blurred the distinction between the aggregate expectation, and individual expectations on aggregate variables. This provided shallow "micro-foundations" to the REH, (shallow because it is not really micro-founded, that which essentially assumes away the need to aggregate), but also, it moved the debate into the arena of individual expectations formation and whether individuals use information efficiently or not, which raised valid objections as those mentioned in the answer by @EnergyNumbers.
But really, at the individual level, the hypothesis that individuals use the mathematical expected value comes essentially from Expected Utility theory, that predates the Rational Expectations, and has a debate on its own (also here in Economics.SE)
Another set of "arguments against" the REH (which gave very interesting literature), was collected early on in the book "Individual forecasting and aggregate outcomes - Rational Expectations examined" 1983 R. Frydman and E. Phelps (ed). Of which I mention two:
1) Being an equilibrium concept, REH requires co-ordination of expectations formation (which is really not that realistic) or properties of Nash-equilibrium: this last insight gave us "Eductive Expectations" and some really thoughtful works by Roger Guesnerie.
2) The second one, which became rather more widely spread than Eductive Expectations, is "Adaptive Learning" (see "Learning and Expectations in Macroeconomics" By Evans and Honkapohja, 2001).
Adaptive Learning pointed out that REH assumes that economic agents know the structure of their environment perfectly. So in Adaptive Learning models we have the first systematic approach to model uncertainty : as economists, so economic agents do not know the environment perfectly, and they have to estimate it and learn it gradually (hence "adaptive learning"). In this strand of literature, "learning" is done through econometric methods, mainly least-squares (which is a very intuitive least-distance mathematical approximation method). Roughly speaking, here agents' expectations are not the expected values, but the estimated expected values. This creates much more interesting and realistic dynamics, that some times may converge (someday) to an REH equilibrium (which makes Adaptive Learning a "selection mechanism" for the sometimes multiple REH equilibira), or to some other point, not predicted by REH.
Research into the issue of aggregate expectations formation and modeling is currently exploding, see for example another Frydman & Phelps (ed.) book, "Rethinking Expectations" (2012), in parallel with the emerging "Post-Walrasian" direction in Macroeconomics (see D. Colander (ed). Post-Walrasian Macroeconomics 2006).
We could expect the rational expectations hypothesis to hold, as long as errors were randomly distributed, without any systematic biases.
The hypothesis becomes problematic, if we find systematic biases.
We have found some systematic biases, thanks to behavioural economics experiments, and studies of risk.
Some systematic biases:
We are not asymmetric with regards to losses and gains: the disutility of a loss is higher than the utility of a gain of the same nominal price - if you give me £10, then take £10 away, I feel hard done by, even though I've come out of it at net £0 difference.
We are systematically terrible at assessing very low probability events. For two reasons. One is that there is evidence that we're simply poor calculators when it comes to very small probabilities, even with perfect information about the statistical distribution (ref to follow if I remember). And the other is exactly as jmbejara has noted in the comments: inference about tails of distributions is hard, because there's very little empirical data available to infer from; and small errors in the inference get turned into very consequences by the end of the calculation, because of the nature of very long, very thin tails.
We are susceptible to price anchoring: our expectations of final price are influenced by the first price we hear. Most memorably illustrated by Dan Ariely's experiment on valuing his reading of his own poetry: he gave members of his class each a piece of paper, containing a price for his poetry reading, to assess its value. What he didn't tell the class, was that some of the bits of paper explained that the price was what the student would be asked to pay, to hear Dan's poetry reading; and the others explained that the price was what Dan would pay to the student, if they sat through his poetry reading. From each group, he found students willing to accept the price they were given. So he established that his poetry reading had both a positive and a negative price. Illustrating both price anchoring and multiple mutually-inconsistent equilibria.
Rational expectations seems to have a similar joint hypothesis problem as the efficient market hypothesis. In the efficient market hypothesis, this means "If efficiency is rejected, this could be because the market is truly inefficient or because an incorrect equilibrium model has been assumed." Similarly here, if rational expectations is rejected this could be because rational expectations is truly false or that the model of rational expectations is incorrect.
For a contrived example of this consider what happens if agents know the the true distributions of shocks in the economy but the econometrician does not. If the econometrician guesses the wrong process for these shocks and discovers that agents are not rationally expecting this incorrect process. This clearly does not constitute a rejection of rational expectations even though that is often what is claimed. .
One of the challenges to rational expectations is that it must be the case that the first moment exists for the variable of interest. This cannot be the case either for equity or equity-like investments, or economic growth.
The assumption is that the marginal expectation, or possibly the average expectation is equal to the true value at some limit. For some equations, such as $x_{t+1}=Rx_t+\varepsilon_{t+1}, R>1$ then while the maximum likelihood estimator and the mvue is the least squares estimator, the test statistic for $\hat{R}-R$ is the Cauchy distribution which has no mean. See
White, J.S. (1958) The Limiting Distribution of the Serial Correlation Coefficient in the Explosive Case. The Annals of Mathematical Statistics, 29, 1188-1197
or
Harris, D.E.(2017) The Distribution of Returns. Journal of Mathematical Finance, 7, 769-804.
As a consequence, if it is true that $R$ is truly known with perfect certainty by all actors except the economist measuring the behavior of $x_{t+1}$, then the economist has no test that can ever be performed validly to determine whether the hypothesis is either true or false because the statistic is the mean of a distribution that notoriously has no mean. You cannot accept or reject any null hypothesis because there is no power to test the hypothesis in the first place, regardless of sample size including having an infinite sample.
In the Harris paper above, the equation does have a Bayesian solution, but that rejects the rational expectations model as no Bayesian solution with a proper prior is unbiased. R must be greater than one as who would invest money if they believed the future would be worse tomorrow so all models with capital in it must lack a mean and a variance.
Rational expectations should hold when one is playing roulette or parimutuel horse racing. Indeed, there is literature showing this to be the case that is quite credible. Those models have finite variance so they behave well.
It isn't that people are biased or anything like that. Models where $R$ is greater than one have no solution. The White paper above is effectively a non-existence proof. So, for macroeconomics, the best refutation is that there is a non-existence proof for the expectations.
The simplest and most persuasive argument against REH is that it assumes that "the market" can predict the future (literally). There is no difference between subjective and objective expectations in the long run, because subjective expectations converge to objective expectations.
A more theoretically grounded reason is due to game theorists. It has been demonstrated that when individuals follow rational choice theory, economic models that assume the REH yield results that are inconsistent with the REH whenever at least one agent has non-rational expectations. See M.C.W. Janssen, Microfoundations, Tinbergen Institute Discussion Paper (TI 2006-041/1) for literature.
So, although others have argued that REH is only about "the market" (aggregate) and not about the individuals, if we allow any individual to have non-rational expectations, the model becomes inconsistent with rational choice theory. In this sense RE is all or nothing - either REH holds and all individuals have RE or REH does not hold and only some individuals have RE. Unless, of course, we are willing to venture into the land of heuristics, bounded rationality etc. to salvage REH.
