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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?

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I guess one argument would be that expectations are much more complicated than an equation with a few variables. You could argue that the assumptions made in these rational models are unfounded. The Austrian school argues this with Neoclassicals quite a bit. – rosenjcb Nov 19 '14 at 22:12
Shouldn't it be the evidence against rational expectation hypothesis? I suppose that one can do a calibration theorem like argument, but in the end is evidence what could be put against a hypothesis. – user157623 Nov 19 '14 at 23:11
I think rational expectations phrased in another way is helpful for me to understand what it is. A model is a probability distribution over sequences of outcomes. Rational expectations is when the agents have the same probability distribution over outcomes as the model. – cc7768 Mar 26 '15 at 14:03

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):

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).

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+1: I liked the reference to adaptive learning. I'll have to take a look at that book. – jmbejara Nov 20 '14 at 3:26

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:

  1. 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.

  2. 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.

  3. 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.

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Nice summary. Also, just wanted to add a thought: perhaps we're terrible at predicting tail events because it it really hard to estimate tail events. If we want to estimate the shape of the tails of distributions of, say, GDP growth, we don't have very many tail events to estimate it with. – jmbejara Nov 20 '14 at 3:28
I recently read a paper that dealt with the consequences of very imperfect computation of the probability of tail events. You might find it interesting: "Understanding Uncertainty Shocks and the Role of Black Swans," by Orlik and Veldkamp. – jmbejara Nov 20 '14 at 3:41
@jmbejara oooh, that does look interesting, thank you - I'll work through that later today, all being well. – EnergyNumbers Nov 20 '14 at 4:18
If the guy's poetry was good, and someone who was familiar with its quality would be willing to pay \$1 to hear it, is there any reason to believe that the same person would be unwilling to listen if paid \$1 to do so, assuming the person truthfully believed that the \$1 would incur no obligation beyond listening to poetry for which he would have been willing to pay \$1? – supercat Dec 4 '14 at 16:55
The Orlik and Veldkamp paper is quite good. One observation -- I'm not sure your first bullet point is a very good argument against rational expectations because I'm not sure that would be considered a violation of rational expectations. That is more an argument against certain utility functions (which is still an important topic to think about). – cc7768 Mar 26 '15 at 13:42

We could expect the rational expectations hypothesis to work, as long as it exists, which is not always the case.

This example is borrowed from Beth Allen(1998).

In a 2 by $2$ by $2$ exchange economy, there're two inhabitants, trader I and trader II, two states, $\Omega = \{\omega_1,\omega_2\}$, and two types of commodities $a$ and $b$. A common prior distribution, $p(\omega_1)=p(\omega_2)=\frac {1}{2}$ is assumed. Trader I's and trader II's knowledge can be represented as $\mathscr{P}_I = \{\{\omega_1\}, \{\omega_2\}\}$ and $\mathscr{P}_{II} =\{\{\omega_1, \omega_2\}\}$ respectively. Their preferences are state-dependent, which are two random variables: $$V_{I}( \cdot )(x) = \chi_{\{ \omega_1\}}( 2 \ln {(3+x_a)} + \ln {(3+x_b)})+\chi_{\{ \omega_2\}}( \ln {(3+x_a)} + 2\ln {(3+x_b)}) $$ $$V_{II}( \cdot )(x) = \chi_{\{ \omega_1\}}( \ln {(3+x_a)} + 2\ln {(3+x_b)})+\chi_{\{ \omega_2\}}( 2\ln {(3+x_a)} + \ln {(3+x_b)}) $$

Observation: Since it's static pure exchange economy, lending is meaningless. An equilibrium point belongs to a subset of $M = \{(p,x^i) \mid x_a^i+p x_b^i = 0 \}$ for $i = I, II$.

Thus, an equilibrium can be characterized as a random variable, $$(P, X) : \Omega \to M$$. Let $\mathscr {P}$ be a partition such that $\sigma{(\mathscr {P})} = \sigma(P)$.

Definition: A rational expectations equilibrium is $(\hat P,\hat X)$ such that $$\hat {X} = \operatorname{argmax}_{\{ X \mid (1,\hat{P}) \cdot X(\omega_j) = 0, j = 1, 2\}} \Bbb {E}( V_i \mid \mathscr{P} \vee \mathscr{P}_i)$$for $i = I, II$.

Suppose that trader II obtains extra information from $P$, i.e. $P(\omega_1) \neq P(\omega_2)$.At each state, two traders' constrained optimization problems become symmetric. Then at both state the relative price is $1$, which can't give out any new information to trader II. So it can't be an $\sf R.E.E$.

Suppose that trader II doesn't obtain extra information from $P$, i.e. $P(\omega_1) = P(\omega_2)$. Then at $\omega_1$, the optimization problem faced by them are $$\max_{M} 2 \ln {(3+x_a)} + \ln {(3+x_b)} $$ $$\max_{M} 1.5 \ln {(3-x_a)} +1.5 \ln {(3-x_b)} $$

Some calculation yields $P(\omega_1) = \frac{5}{7}$. By symmetry, at $\omega_2$, $P(\omega_2) = \frac{1}{P(\omega_1)} = \frac{7}{5}$, which contradicts with the premise. The above discussion exhausts all possible situations. So we can't have an $\mathsf{R.E.E}$ in this economy.

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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. .

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I don't think I understand this. So for example, all financial agents understand the market, but econometricians don't? – Lasse Mar 26 '15 at 7:00
The idea that economic agents knows something that the econometrician is guessing at is a reasonably common modeling choice. See for example A Markov model of heteroskedasticity, risk, and learning in the stock market or Exporting and productivity – BKay Mar 26 '15 at 9:29
From working 3 years in the financial sector I have seen anything but rationality from economic agents :) – Lasse Mar 26 '15 at 9:34

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