Rational Expectations

Rational expectations is the hypothesis that people, firms and investors form their expectations about the future, for example about inflation, interest rates or prices, using all the information available to them and an accurate understanding of how the economy works. Individual forecasts can be wrong, but under rational expectations the errors are random: people do not keep making the same mistake in the same direction, because they would learn from it.

The idea was proposed by John Muth in 1961 and became the foundation of much of modern macroeconomics from the 1970s, through the work of Robert Lucas, Thomas Sargent, Neil Wallace and others. It is closely linked to the efficient market hypothesis in finance and to the Chicago school, and it reshaped thinking about the Phillips curve and central bank credibility.

Suppose a town council announces that the bridge toll will double next month. People who use the bridge do not wait until they see the higher bill; they change their plans now, perhaps moving trips forward or finding another route. They use what they know to anticipate the effect.

Rational expectations says people behave like that in the economy as a whole. If they understand that a central bank's policy will push prices up, they raise their price and wage demands in advance. That makes it hard for governments to fool people repeatedly, because people learn the rules of the game and adjust.

Under rational expectations the actual outcome equals people's expectation plus a random surprise:

• $x_{t+1}$ is the value of a variable, such as inflation, next period.
• $E_t[x_{t+1}]$ is the expectation formed today using all available information.
• $\varepsilon_{t+1}$ is the forecast error, which averages zero and cannot be predicted from today's information.

The older alternative, adaptive expectations, assumes people update forecasts only by looking at past errors: $\pi^{e}_{t} = \pi^{e}_{t-1} + \lambda\,(\pi_{t-1} - \pi^{e}_{t-1})$, where $\lambda$ is between 0 and 1. If people expected 2% inflation, inflation came in at 6% and $\lambda = 0.5$, the new expectation is $2 + 0.5 \times (6 - 2) = 4\%$. If inflation keeps rising, adaptive forecasters stay behind it year after year, a systematic error that rational expectations rules out.

Muth introduced the hypothesis in a 1961 article in Econometrica, applying it to markets for farm goods. In the early 1970s Robert Lucas used it to explain why the trade-off between inflation and unemployment seemed to vanish once inflation became persistent: if workers anticipate inflation, a central bank can lower unemployment only by surprising them, and it cannot do that systematically. This supported the idea of a natural rate of unemployment and the NAIRU.

In 1976 Lucas argued that large economic models estimated on past data would mislead policymakers, because the relationships they captured would change once people adjusted their expectations to a new policy. This "Lucas critique" pushed economists to build models from the decisions of individuals and firms. Sargent and Wallace's 1975 policy-ineffectiveness proposition went further, arguing that predictable monetary policy cannot affect output. Lucas received the Nobel Prize in economics in 1995 for developing and applying the hypothesis, and Sargent shared the 2011 prize with Christopher Sims for work on cause and effect in the macroeconomy.

• Credibility and rules. Finn Kydland and Edward Prescott (Nobel 2004) showed that a policymaker who can be expected to break promises will end up with higher inflation, an argument for independent central banks and inflation targeting.
• Expectations as a policy tool. Central banks now try to manage expectations through forward guidance and clear targets, a practice that assumes people pay attention to stated policy.
• Fiscal policy. Under rational expectations, households may save more in response to tax cuts financed by borrowing, the idea behind Ricardian equivalence.
• Modern models. New Keynesian models used by central banks combine rational expectations with sticky prices, so policy can affect output in the short run.

Critics argue that the hypothesis demands more knowledge and calculation than real people have. Behavioural economists document systematic biases, bounded rationality and money illusion, and surveys show that household inflation expectations often differ widely from forecasts and from each other. Keynesian economists also stress uncertainty that cannot be reduced to known probabilities. Supporters reply that rational expectations is a modelling discipline rather than a literal description, and that the alternative, assuming people make the same mistakes forever, is less plausible.

Researchers have developed middle-ground approaches, including adaptive learning, in which agents gradually learn the true model, and rational inattention, in which paying attention is costly. The 2008 crisis, which few models predicted, revived criticism of rational-expectations macroeconomics and of the related idea that financial markets always price risk correctly, a debate that continues in work on asset bubbles and animal spirits.

• The Nobel Prize: The Sveriges Riksbank Prize in Economic Sciences 1995 (Robert E. Lucas Jr.)
• The Nobel Prize: The Sveriges Riksbank Prize in Economic Sciences 2011 (Sargent and Sims)