# Expectations, Rational

RATIONAL EXPECTATIONS: DEFINITIONS AND DEFENSES

ARGUMENTS AGAINST RATIONAL EXPECTATIONS

BIBLIOGRAPHY

A basic postulate of economics is that people do the best with what they have (Maddock and Carter 1982). Applied to the formation of expectations (or economic beliefs), the theory of rational expectations, first proposed by John Muth in 1961, assumes that agents acquire and process information rationally. Since the 1970s, this theory has been used to model phenomena as diverse as aggregate supply, exchange rates, consumption, and economic cycles. A number of important empirical predictionsabout exchange rates (Frankel and Rose 1995) and the term structure of interest rates (Mankiw and Miron 1986), for exampleemploy rational expectations as a key assumption.

## RATIONAL EXPECTATIONS: DEFINITIONS AND DEFENSES

Definitionally, a rational expectation is the best guess about an unknown variable, using all available information. Where the unknown variable is random (such as the exchange rate in k periods time represented in equations by (yt + k ) the rational expectation is the mean of the variable (i.e., the mathematical expectation E (yt + k ) equal to the integral of all possible values of yt + k, weighted by their probabilities). The rational expectation is calculated using information up to the current period t, and so it is sometimes written as Et (yt + k ) (k > 0). Obtaining the mathematical expectation within a model context requires knowing the full structure of the model. If information is costly to collect, then rational expectations cannot strictly be rational, as was recognized soon after rational expectations was proposed. In other words, assuming a positive marginal cost to information and a decreasing marginal benefit, the information collected will fall short of the information required to understand the full system.

The economics literature either ignores this problem for simplicity, or it acknowledges that expectations are formed on the basis of sample information. In the latter case, the rational expectation can be defined as an estimator of an unknown variable with desirable statistical properties, such as minimum forecast error (in the case of a random variable) or unbiasedness and efficiency (in the case of an unknown parameter). Alternatively, mirroring the use of estimators in classical inference, changes in beliefs about unknown parameters can be modeled by statistical hypothesis testing (Menzies and Zizzo 2005).

It is assumed that people do not make systematic errors when predicting the future, so the rational expectation of a random variable is the mean represented by Et (yt + k ). In other words, departures from perfect foresight (that is, from Et (yt + k ) = yt + k ) are a random process with a zero mean. Mathematically, rational expectations are modeled by making the outcome yt + k equal to the rational expectation, plus a random error u t + k representing ignorance, mistakes, and other influence only revealed in k periods time: yt + k = Et (yt + k ) + u t + k.

As an example of rational expectations at work, if all agents hold rational expectations, if transactions costs are small, and if agents are unconcerned about risk, then the socalled efficient market hypothesis holds. If a securitys price does not reflect all the information available about it, then someone can buy (or sell) the security to make a profit, thus driving the price toward the rational expectation. If all profit opportunities are eliminated, prices in financial markets fully reflect fundamentals (e.g., future interest rates, profits, or dividends).

Rational expectations have a number of advantages as a modeling tool. First, they are conceptually simple. Second, they prevent economic theorists from introducing ad hoc influences via arbitrary expectations mechanisms. Third, they create simple model solutions. Fourth, there is a close correspondence between the properties of random errors arising from the rational expectations (u above) and the random errors assumed in empirical work.

There are many ways of defending the notion that agents have rational expectations, based on rationality (rational agents should use all the available information in the most efficient way), macro-aggregation (rational expectations allow for mistakes, as long as they are not systematic mistakes), and evolutionary dynamics arguments (agents without rational expectations would be driven out of the market by more rational agents, who would be able to bankrupt them on the basis of their superior use of information). Even if these arguments are not accepted, however, mainstream economists could also claim that the parsimony and tractability of rational expectations justifies their use. While this is unlikely on its own to be sufficient to accept rational expectations as scientifically valid, it may be more palatable if one can claim that a lack of realism is an acceptable price when parsimony and tractability are matched by significant predictive power. The argument has also been made that it would not be safe to make policy on the basis of the assumption that policymakers have superior knowledge about how the economy works, and that macroeconomic models should therefore employ rational expectations (Sorensen and WhittaJacobsen 2005).

## ARGUMENTS AGAINST RATIONAL EXPECTATIONS

There are a number of contrary views on rational expectations, however. First, rational expectations are rational only if collecting and processing information is costless in money and time, let alone cognitive effort. If agents are only boundedly rational, information collection and processing costs will be larger and will induce shortcuts in the use of information. Second, the theory of rational expectations assumes that agents not only hold a model of the economy, but that this model of the economy is correct. This is in stark contrast with the fact that disagreement exists within the economics profession on how the economy works. Further multiple models are normally used in practical policymaking. Interesting variations of rational expectations build on the assumption that agents do not know exactly how the economy works, so that they need to make hypotheses on models (or parameters of models) of how the economy works (Goldberg and Frydman 1996; Menzies and Zizzo 2005).

Third, there has been no general proof of the evolutionary dynamics argument. Indeed, there are models showing how lessthanrational agents may survive when mixed up with rational agents (e.g., noise trader models in finance; Shleifer 2000). Fourth, the usefulness argument is virtually unfalsifiable. This is because tests of rational expectations are also joint tests of the models they are embedded in, and because of the difficulty in identifying rational expectations relative to alternatives in regression analysis. Therefore, failures of rational expectations can be, and often are, blamed on other hypotheses (see, for example, Gerlach and Smets 1997 in relation to the term structure of interest rates), though the problem may ultimately lie in the model of expectation formation.

Fifth, in experimental settings, rational expectations predictions are not rejected as null hypotheses in some contexts, but the most common outcome is that individuals do not hold rational expectations. In addition, experimental research often finds either underutilization or overutilization of prior beliefs (Camerer 1995). These systematic empirical failures cannot be reconciled with the macroaggregation argument.

Finally, if conservativeness in policymaking is considered desirable in the face of an uncertain economy, then it should be modeled explicitly (e.g., in the objective function), rather than by postulating an incorrect model of expectation formation. Doing otherwise may be counterproductive, and it may make it more difficult to provide an accurate account of the economy. Notwithstanding these points, however, the notion of rational expectations remains the mainstream conceptualization of expectations formation in economic modeling.

## BIBLIOGRAPHY

Camerer, Colin. 1995. Individual Decision Making. In The Handbook of Experimental Economics, eds. John H. Kagel and Alvin E. Roth, 587703. Princeton, NJ: Princeton University Press.

Evans, George, and Sepo Honkapohja. 2001. Learning and Expectations in Macroeconomics. Princeton, NJ: Princeton University Press.

Frankel, Jeffrey A., and Andrew K. Rose. 1995. Empirical Research on Nominal Exchange Rates. In The Handbook of International Economics, eds. Gene Grossman and Kenneth Rogoff, 16891729. Amsterdam: Elsevier.

Gerlach, Stefan, and Frank Smets. 1997. The Term Structure of EuroRates: Some Evidence in Support of the Expectations Hypothesis. Journal of International Money and Finance 16 (2): 305321.

Goldberg, Michael D., and Roman Frydman. 1996. Imperfect Knowledge and Behavior in the Foreign Exchange Market. Economic Journal 106 (437): 869893.

Maddock, Rodney, and Michael Carter. 1982. A Childs Guide to Rational Expectations. Journal of Economic Literature 20 (1): 3951.

Mankiw, N. Gregory, and Jeffrey A. Miron. 1986. The Changing Behaviour of the Term Structure of Interest Rates. Quarterly Journal of Economics 101 (2): 211228.

Menzies, Gordon D., and Daniel J. Zizzo. 2005. Inferential Expectations. Working Paper no. 12. Canberra: Australian National University, Centre for Applied Macroeconomics.

Muth, John F. 1961. Rational Expectations and the Theory of Price Movements. Econometrica 29 (3): 315335.

Shleifer, Andrei. 2000. Inefficient Markets: An Introduction to Behavioral Finance. Oxford: Oxford University Press.

Sorensen, Peter Birch, and Hans Jorgen WhittaJacobsen. 2005. Introducing Advanced Macroeconomics: Growth and Business Cycles. London: McGrawHill.

Gordon Douglas Menzies

Daniel John Zizzo

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