Rational Expectations

What the hypothesis claims

Suppose at time t agents need to forecast some variable x at time t+1. Let E(x_{t+1} | I_t) denote the conditional expectation given information set I_t. The rational expectations hypothesis says agents' subjective forecast equals this mathematical expectation:

E*(x_{t+1}) = E(x_{t+1} | I_t)

Two things follow. First, the forecast error x_{t+1} − E*(x_{t+1}) has mean zero — agents are not systematically too high or too low. Second, the forecast error is uncorrelated with anything in I_t — agents have wrung all useful information out of what they knew. If correlation existed, agents could have improved the forecast for free.

The hypothesis does not claim agents are infallible, telepathic, or unbiased in psychological judgment. It claims they don't make systematic, exploitable mistakes — because if they did, somebody would notice and exploit them, eliminating the bias. It is an equilibrium concept about forecasting, not a cognitive theory.

Muth's original 1961 paper was about commodity prices and went largely unnoticed. Lucas's adaptation (1972, 1976) made it the central assumption of a generation of macro models. The result was the New Classical revolution and, through it, the modern Dynamic Stochastic General Equilibrium (DSGE) framework that central banks use today.

The Lucas critique (1976)

Lucas's 1976 paper "Econometric Policy Evaluation: A Critique" is among the most influential papers in postwar economics. The argument:

1. Macroeconomists in the 1960s built large structural models — like the Federal Reserve's MPS model — by estimating equations on historical data: consumption depends on income, investment depends on interest rates, and so on.
2. They used these estimated equations to predict the effect of new policy. "If the Fed raises rates 1%, our model predicts unemployment rises 0.4%."
3. Lucas pointed out the flaw: the estimated equations weren't structural. They reflected the historical policy regime under which agents' expectations had formed. Change the policy, and rational agents change their behavior — which means the equation's estimated parameters shift.
4. So a model fit on the 1950s-60s monetary regime would predict the wrong response to 1970s policy. The estimated coefficients aren't deep parameters; they're regime-dependent reduced forms.

The 1970s gave Lucas his proof. The Phillips curve (a stable trade-off between inflation and unemployment) had been used as a policy tool: more inflation, less unemployment. When governments tried to exploit it, the trade-off vanished. Stagflation — high inflation and high unemployment — wasn't supposed to be possible. But Lucas's framework predicted exactly this: if agents anticipated the inflationary policy, they'd embed it in wage demands and price-setting, neutralizing its real effect.

The critique left three options for macro modelers: (1) abandon policy evaluation; (2) build models from microfoundations — preferences, technology, information — so that the deep parameters are policy-invariant; (3) ignore the critique. The profession picked option 2. The DSGE framework is the result.

Expectations theories compared

	Adaptive expectations	Rational expectations	Bounded rationality	Behavioral expectations	Learning models	Heterogeneous agent
Information used	Past values only	Full information set	Limited subset	Salient cues + biases	Past + updating rule	Mixed across agents
Errors are unbiased	No (lag bias)	Yes	Approximately	No (systematic biases)	Eventually yes	Aggregate yes, individual no
Forward-looking	No	Yes	Partially	Limited	Yes (with delay)	Mixed
Knows the model	No	Yes	Approximately	No	Learns it	Some do
Empirical fit	Pre-1970s	Strong on equilibrium asset prices	Better in surveys	Best on bubbles, crashes	Good on convergence	Best on dispersion
Used in DSGE	Rarely	Standard	Increasingly	Sometimes	Sometimes	Frontier

Rational expectations is the benchmark; the other rows are deviations from or supplements to it.

Counterarguments

Behavioral departures. Decades of survey research show forecasts are systematically biased. The Survey of Professional Forecasters consistently underweights structural breaks; consumer inflation expectations are anchored to recent gas prices; investors over-extrapolate trends. Tversky and Kahneman's work on heuristics gave these patterns a cognitive foundation that rational expectations cannot accommodate.

The information problem. Rational expectations requires agents to know the true model. In real economies, the model itself is contested — Keynesian, monetarist, New Classical, MMT, all claim to be the truth. If agents disagree on the model, they disagree on the rational forecast, and aggregation becomes complicated.

Learning instead of knowing. A literature on adaptive learning (Evans & Honkapohja) argues agents learn the model from data, converging to rational expectations only asymptotically. Out of equilibrium — say, after a regime change — behavior looks adaptive, not rational. The 2008 crisis and its aftermath fit this picture: forecasters needed years to absorb the new policy regime.

Sunspots and self-fulfilling beliefs. Multiple rational-expectations equilibria can exist for the same fundamentals. Which one prevails depends on coordination — bank runs, currency crises, asset bubbles can all be rational-expectations equilibria selected by belief, not by structure. This generality blunts the criterion's predictive bite.

Variants

• Adaptive learning: Agents update beliefs each period using a recursive least-squares-like rule. Converges to rational expectations under stability conditions (Evans-Honkapohja E-stability).
• Near-rational expectations: Agents use simple heuristics that get most of the way to the rational forecast at lower cognitive cost (Akerlof-Yellen).
• Bayesian rational expectations: Replaces "knows the true model" with "has a prior over models and updates rationally" (Hansen-Sargent on robust control and ambiguity).
• Sticky information: Agents update slowly because gathering information is costly (Mankiw-Reis 2002).
• Rational inattention: Agents face a Shannon-information capacity constraint and choose what to focus on (Sims 2003).
• Heterogeneous expectations: A fraction of agents use rational expectations; others use simple rules. Equilibria depend on the mix (Brock-Hommes 1997).

Common pitfalls

• Reading "rational" as "always correct". Forecast errors are routine; the hypothesis only forbids systematic, predictable errors.
• Assuming agents know each other's forecasts. Rational expectations is consistent with private information — different agents can have different (but each unbiased) forecasts.
• Using rational expectations naively after a regime change. The Lucas critique cuts both ways: a model assuming rational expectations must specify the policy rule. Change the rule, change the equilibrium.
• Ignoring the equilibrium-selection problem. When multiple rational-expectations equilibria exist, theory alone can't say which one obtains.
• Conflating rational expectations with efficient markets. Efficient-markets is a stronger claim about asset prices reflecting all information; rational expectations is a weaker claim about forecast unbiasedness. Markets can be informationally efficient without rational expectations being a good description of every individual.