# Rational expectations theory (1960)

Formulated by American economist John Muth (1930- ), rational expectations theory states that individuals and companies, acting with complete access to the relevant information, forecast events in the future without bias.

Errors in their forecasts are assumed to result from random events.

Rational expectations theory has emerged as an important aspect of new classical economics.

Also see: adaptive expectations, random walk hypothesis, new classical macroeconomics

## Theory

Rational expectations theory defines this kind of expectations as being the best guess of the future (the optimal forecast) that uses all available information. Thus, it is assumed that outcomes that are being forecast do not differ systematically from the market equilibrium results. As a result, rational expectations do not differ systematically or predictably from equilibrium results. That is, it assumes that people do not make systematic errors when predicting the future, and deviations from perfect foresight are only random. In an economic model, this is typically modelled by assuming that the expected value of a variable is equal to the expected value predicted by the model.

For example, suppose that P is the equilibrium price in a simple market, determined by supply and demand. The theory of rational expectations says that the actual price will only deviate from the expectation if there is an ‘information shock’ caused by information unforeseeable at the time expectations were formed. In other words, ex ante the price is anticipated to equal its rational expectation:

{\displaystyle P=P^{*}+\epsilon }
{\displaystyle E[P]=P^{*}}

where {\displaystyle P^{*}} is the rational expectation and {\displaystyle \epsilon } is the random error term, which has an expected value of zero, and is independent of {\displaystyle P^{*}}.

## Implications

Rational expectations theories were developed in response to perceived flaws in theories based on adaptive expectations. Under adaptive expectations, expectations of the future value of an economic variable are based on past values. For example, people would be assumed to predict inflation by looking at inflation last year and in previous years. Under adaptive expectations, if the economy suffers from constantly rising inflation rates (perhaps due to government policies), people would be assumed to always underestimate inflation. Many economists have regarded this as unrealistic, believing that rational individuals would sooner or later realize the trend and take it into account in forming their expectations.

The rational expectations hypothesis has been used to support some strong conclusions about economic policymaking. An example is the policy ineffectiveness proposition developed by Thomas Sargent and Neil Wallace. If the Federal Reserve attempts to lower unemployment through expansionary monetary policy economic agents will anticipate the effects of the change of policy and raise their expectations of future inflation accordingly. This in turn will counteract the expansionary effect of the increased money supply. All that the government can do is raise the inflation rate, not employment. This is a distinctly New Classical outcome. During the 1970s rational expectations appeared to have made previous macroeconomic theory largely obsolete, which culminated with the Lucas critique. However, rational expectations theory has been widely adopted and is considered an innocuous assumption in macroeconomics.[5]

If agents do not (or cannot) form rational expectations or if prices are not completely flexible, discretional and completely anticipated economic policy actions can trigger real changes.[6]

## Criticism

Rational expectations are expected values in the mathematical sense. In order to be able to compute expected values, individuals must know the true economic model, its parameters, and the nature of the stochastic processes that govern its evolution. If these extreme assumptions are violated, individuals simply cannot form rational expectations.[7]

### Testing empirically for rational expectations

Suppose we have data on inflationary expectations, such as that from the Michigan survey.[8] We can test whether these expectations are rational by regressing the actual realized inflation rate {\displaystyle I} on the prior expectation of it, X, at some specified lead time k:

{\displaystyle I_{t}=a+bX_{t-k}+\varepsilon _{t},}

where a and b are parameters to be estimated and {\displaystyle \varepsilon } is the error term. We can test the rationality of expectations by testing the joint null hypothesis that