# Rational expectations

Rational expectations is a hypothesis in economics which states that agents' predictions of the future value of economically relevant variables are not systematically wrong in that all errors are random. Equivalently, this is to say that agents' expectations equal true statistical expected values. An alternative formulation is that rational expectations are model-consistent expectations, in that the agents inside the model assume the model's predictions are valid.[1] The rational expectations assumption is used in many contemporary macroeconomic models, game theory and applications of rational choice theory.

Since most macroeconomic models today study decisions over many periods, the expectations of workers, consumers and firms about future economic conditions are an essential part of the model. How to model these expectations has long been controversial, and it is well known that the macroeconomic predictions of the model may differ depending on the assumptions made about expectations (see Cobweb model). To assume rational expectations is to assume that agents' expectations may be individually wrong, but are correct on average. In other words, although the future is not fully predictable, agents' expectations are assumed not to be systematically biased and use all relevant information in forming expectations of economic variables.

This way of modeling expectations was originally proposed by John F. Muth (1961)[2] and later became influential when it was used by Robert Lucas, Jr. and others. Modeling expectations is crucial in all models which study how a large number of individuals, firms and organizations make choices under uncertainty. For example, negotiations between workers and firms will be influenced by the expected level of inflation, and the value of a share of stock is dependent on the expected future income from that stock.

## Theory

Rational expectations theory defines this kind of expectations as being identical to 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 actual price is equal to its rational expectation:

$P=P*+\epsilon$
$E[P]=P*$

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

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. This may be regarded as unrealistic - surely rational individuals would sooner or later realize the trend and take it into account in forming their expectations?

The hypothesis of rational expectations addresses this criticism by assuming that individuals take all available information into account in forming expectations. Though expectations may turn out incorrect, they will not deviate systematically from the expected values.

The rational expectations hypothesis has been used to support some radical 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 throughout modern macroeconomics as a modelling assumption thanks to the work of New Keynesians such as Stanley Fischer.

Rational expectations theory is the basis for the efficient market hypothesis (efficient market theory). If a security's price does not reflect all the information about it, then there exist "unexploited profit opportunities": someone can buy (or sell) the security to make a profit, thus driving the price toward equilibrium. In the strongest versions of these theories, where all profit opportunities have been exploited, all prices in financial markets are correct and reflect market fundamentals (such as future streams of profits and dividends). Each financial investment is as good as any other, while a security's price reflects all information about its intrinsic value.

## Criticisms

The models of Muth and Lucas (and the strongest version of the efficient-market hypothesis) assume that at any specific time, a market or the economy has only one equilibrium (which was determined ahead of time), so that people form their expectations around this unique equilibrium.[citation needed] Muth's math (sketched above) assumed that P* was unique. Lucas assumed that equilibrium corresponded to a unique "full employment" level (potential output) -- corresponding to a unique NAIRU or natural rate of unemployment. If there is more than one possible equilibrium at any time then the more interesting implications of the theory of rational expectations do not apply. In fact, expectations would determine the nature of the equilibrium attained, reversing the line of causation posited by rational expectations theorists.

A further problem relates to the application of the rational expectations hypothesis to aggregate behavior. It is well known that assumptions about individual behavior do not carry over to aggregate behavior (Sonnenschein-Mantel-Debreu theorem). The same holds true for rationality assumptions: Even if all individuals have rational expectations, the representative household describing these behaviors may exhibit behavior that does not satisfy rationality assumptions (Janssen 1993). Hence the rational expectations hypothesis, as applied to the representative household, is unrelated to the presence or absence of rational expectations on the micro level and lacks, in this sense, a microeconomic foundation.

It can be argued that it is difficult to apply the standard efficient market hypothesis (efficient market theory) to understand the stock market bubble that ended in 2000 and collapsed thereafter; however, advocates[who?] of rational expectations say that the problem of ascertaining all the pertinent effects of the stock-market crash is a great challenge.[citation needed]

Furthermore, social scientists in general criticize the movement of this theory into other fields such as political science. In his book Essence of Decision, political scientist Graham T. Allison specifically attacked the rational expectations theory.

Some economists now use the adaptive expectations model, but then complement it with ideas based on the rational expectations theory. For example, an anti-inflation campaign by the central bank is more effective if it is seen as "credible," i.e., if it convinces people that it will "stick to its guns." The bank can convince people to lower their inflationary expectations, which implies less of a feedback into the actual inflation rate. (An advocate of Rational Expectations would say, rather, that the pronouncements of central banks are facts that must be incorporated into one's forecast because central banks can act independently). Those studying financial markets similarly apply the efficient-markets hypothesis but keep the existence of exceptions in mind.