# Rational expectations

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In economics, "rational expectations" are model-consistent expectations, in that agents inside the model are assumed to "know the model" and on average take the model's predictions as valid. [1] Rational expectations ensure internal consistency in models involving uncertainty. To obtain consistency within a model, the predictions of future values of economically relevant variables from the model are assumed to be the same as that of the decision-makers in the model, given their information set, the nature of the random processes involved, and model structure. The rational expectations assumption is used especially in many contemporary macroeconomic models.

Economics is the social science that studies the production, distribution, and consumption of goods and services.

In economics, an agent is an actor and more specifically a decision maker in a model of some aspect of the economy. Typically, every agent makes decisions by solving a well- or ill-defined optimization or choice problem.

A macroeconomic model is an analytical tool designed to describe the operation of the economy of a country or a region. These models are usually designed to examine the comparative statics and dynamics of aggregate quantities such as the total amount of goods and services produced, total income earned, the level of employment of productive resources, and the level of prices.

## Contents

Since most macroeconomic models today study decisions under uncertainty and over many periods, the expectations of individuals, firms, and government institutions about future economic conditions are an essential part of the model. To assume rational expectations is to assume that agents' expectations may be wrong, but are correct on average over time. In other words, although the future is not fully predictable, agents' expectations are assumed not to be systematically biased and collectively 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. in macroeconomics.

Statistical bias is a feature of a statistical technique or of its results whereby the expected value of the results differs from the true underlying quantitative parameter being estimated. The bias of an estimator of a parameter should not be confused with its degree of precision as the degree of precision is a measure of the sampling error. Mathematically Bias can be Defined as:

John Fraser Muth was an American economist. He is "the father of the rational expectations revolution in economics", primarily due to his article "Rational Expectations and the Theory of Price Movements" from 1961.

Deirdre McCloskey emphasizes that "rational expectations" is an expression of intellectual modesty: [3]

Deirdre Nansen McCloskey, is the Distinguished Professor of Economics, History, English, and Communication at the University of Illinois at Chicago (UIC). She is also adjunct professor of Philosophy and Classics there, and for five years was a visiting Professor of philosophy at Erasmus University, Rotterdam. Since October 2007 she has received six honorary doctorates. In 2013, she received the Julian L. Simon Memorial Award from the Competitive Enterprise Institute for her work examining factors in history that led to advancement in human achievement and prosperity. Her main research interests include the origins of the modern world, the misuse of statistical significance in economics and other sciences, and the study of capitalism, among many others.

Muth's notion was that the professors [of economics], even if correct in their model of man, could do no better in predicting than could the hog farmer or steelmaker or insurance company. The notion is one of intellectual modesty. The common sense is "rationality": therefore Muth called the argument "rational expectations".

Hence, it is important to distinguish the rational-expectations assumption from assumptions of individual rationality and to note that the first does not imply the latter. Rational expectations is an assumption of aggregate consistency in dynamic models. In contrast, rational choice theory studies individual decision making and is used extensively in, among others, game theory and contract theory. [4]

Rational choice theory, also known as choice theory or rational action theory, is a framework for understanding and often formally modeling social and economic behavior. The basic premise of rational choice theory is that aggregate social behavior results from the behavior of individual actors, each of whom is making their individual decisions. The theory also focuses on the determinants of the individual choices.

Game theory is the study of mathematical models of strategic interaction in between rational decision-makers. It has applications in all fields of social science, as well as in logic and computer science. Originally, it addressed zero-sum games, in which each participant's gains or losses are exactly balanced by those of the other participants. Today, game theory applies to a wide range of behavioral relations, and is now an umbrella term for the science of logical decision making in humans, animals, and computers.

In economics, contract theory studies how economic actors can and do construct contractual arrangements, generally in the presence of asymmetric information. Because of its connections with both agency and incentives, contract theory is often categorized within a field known as Law and economics. One prominent application of it is the design of optimal schemes of managerial compensation. In the field of economics, the first formal treatment of this topic was given by Kenneth Arrow in the 1960s. In 2016, Oliver Hart and Bengt R. Holmström both received the Nobel Memorial Prize in Economic Sciences for their work on contract theory, covering many topics from CEO pay to privatizations.

## 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.

In economics, economic equilibrium is a situation in which economic forces such as supply and demand are balanced and in the absence of external influences the (equilibrium) values of economic variables will not change. For example, in the standard textbook model of perfect competition, equilibrium occurs at the point at which quantity demanded and quantity supplied are equal. Market equilibrium in this case is a condition where a market price is established through competition such that the amount of goods or services sought by buyers is equal to the amount of goods or services produced by sellers. This price is often called the competitive price or market clearing price and will tend not to change unless demand or supply changes, and the quantity is called the "competitive quantity" or market clearing quantity. However, the concept of equilibrium in economics also applies to imperfectly competitive markets, where it takes the form of a Nash equilibrium.

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:

In microeconomics, supply and demand is an economic model of price determination in a market. It postulates that, holding all else equal, in a competitive market, the unit price for a particular good, or other traded item such as labor or liquid financial assets, will vary until it settles at a point where the quantity demanded will equal the quantity supplied, resulting in an economic equilibrium for price and quantity transacted.

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

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 as a modelling assumption even outside of New Classical macroeconomics [5] thanks to the work of New Keynesians such as Stanley Fischer.

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

${\displaystyle H_{0}:\quad a=0\quad {\text{and}}\quad b=1;}$

failure to reject this null hypothesis is evidence in favor of rational expectations. A stronger test can be conducted if the one above has failed to reject the null: the residuals of the above regression can themselves be regressed on other variables whose values are available to agents when they are forming the expectation. If any of these variables has a significant effect on the residuals, agents can be said to have failed to take them sufficiently into account when forming their expectations, leading to needlessly high variance of the forecasting residuals and thus more uncertainty than is necessary about their predictions, which hampers their effort to use the predictions in their economic choices for things such as money demand, consumption, fixed investment, etc.

## Notes

1. Snowdon, B., Vane, H., & Wynarczyk, P. (1994). A modern guide to macroeconomics. (pp. 236–79). Cambridge: Edward Elgar Publishing Limited.
2. Muth, John F. (1961). "Rational Expectations and the Theory of Price Movements" (PDF). Econometrica. 29 (3): 315–335. doi:10.2307/1909635. JSTOR   1909635. reprinted in Hoover, Kevin D., ed. (1992). The New Classical Macroeconomics, Volume 1. International Library of Critical Writings in Economics, vol. 19. Aldershot, Hants, England: Elgar. pp. 3–23. ISBN   978-1-85278-572-7.
3. McCloskey, Deirdre N. (1998). The Rhetoric of Economics (2 ed.). Univ of Wisconsin Press. p. 53. ISBN   978-0-299-15814-9.
4. Levine, David K. (2012-01-26). "Why Economists Are Right: Rational Expectations and the Uncertainty Principle in Economics". Huffington Post. Retrieved 2017-07-18.
5. Robert Skidelsky, The Return of the Master.
6. Galbács, Peter (2015). The Theory of New Classical Macroeconomics. A Positive Critique. Contributions to Economics. Heidelberg/New York/Dordrecht/London: Springer. doi:10.1007/978-3-319-17578-2. ISBN   978-3-319-17578-2.
7. Evans, G. W. and G. Ramey (2006) Adaptive Expectations, Underparameterization and the Lucas Critique. Journal of Monetary Economics, vol. 53, pp. 249-264.
8. "University of Michigan: Inflation Expectation". Economic Research, Federal Reserve Bank of St. Louis. January 1978.

## Related Research Articles

In economics, adaptive expectations is a hypothesized process by which people form their expectations about what will happen in the future based on what has happened in the past. For example, if inflation has been higher than expected in the past, people would revise expectations for the future.

Macroeconomics is a branch of economics dealing with the performance, structure, behavior, and decision-making of an economy as a whole. This includes regional, national, and global economies. Macroeconomists study aggregated indicators such as GDP, unemployment rates, national income, price indices, and the interrelations among the different sectors of the economy to better understand how the whole economy functions. They also develop models that explain the relationship between such factors as national income, output, consumption, unemployment, inflation, saving, investment, energy, international trade, and international finance.

Financial economics is the branch of economics characterized by a "concentration on monetary activities", in which "money of one type or another is likely to appear on both sides of a trade". Its concern is thus the interrelation of financial variables, such as prices, interest rates and shares, as opposed to those concerning the real economy. It has two main areas of focus: asset pricing and corporate finance; the first being the perspective of providers of capital, i.e. investors, and the second of users of capital.

New Keynesian economics is a school of contemporary macroeconomics that strives to provide microeconomic foundations for Keynesian economics. It developed partly as a response to criticisms of Keynesian macroeconomics by adherents of new classical macroeconomics.

Robert Emerson Lucas Jr. is an American economist at the University of Chicago, where he is currently the John Dewey Distinguished Service Professor Emeritus in Economics and the College. Widely regarded as the central figure in the development of the new classical approach to macroeconomics, he received the Nobel Prize in Economics in 1995 "for having developed and applied the hypothesis of rational expectations, and thereby having transformed macroeconomic analysis and deepened our understanding of economic policy". He has been characterized by N. Gregory Mankiw as "the most influential macroeconomist of the last quarter of the 20th century."

The Phillips curve is a single-equation economic model, named after William Phillips, describing an inverse relationship between rates of unemployment and corresponding rates of rises in wages that result within an economy. Stated simply, decreased unemployment, in an economy will correlate with higher rates of wage rises. Phillips did not himself state there was any relationship between employment and inflation; this notion was a trivial deduction from his statistical findings. Samuelson and Solow made the connection explicit and subsequently Milton Friedman and Edmund Phelps put the theoretical structure in place. In so doing, Friedman was to successfully predict the imminent collapse of Phillips' a-theoretic correlation.

In economics, a model is a theoretical construct representing economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified, often mathematical, framework designed to illustrate complex processes. Frequently, economic models posit structural parameters. A model may have various exogenous variables, and those variables may change to create various responses by economic variables. Methodological uses of models include investigation, theorizing, and fitting theories to the world.

Neutrality of money is the idea that a change in the stock of money affects only nominal variables in the economy such as prices, wages, and exchange rates, with no effect on real variables, like employment, real GDP, and real consumption. Neutrality of money is an important idea in classical economics and is related to the classical dichotomy. It implies that the central bank does not affect the real economy by creating money. Instead, any increase in the supply of money would be offset by a proportional rise in prices and wages. This assumption underlies some mainstream macroeconomic models. Others like monetarism view money as being neutral only in the long-run.

The cobweb model or cobweb theory is an economic model that explains why prices might be subject to periodic fluctuations in certain types of markets. It describes cyclical supply and demand in a market where the amount produced must be chosen before prices are observed. Producers' expectations about prices are assumed to be based on observations of previous prices. Nicholas Kaldor analyzed the model in 1934, coining the term "cobweb theorem", citing previous analyses in German by Henry Schultz and Umberto Ricci.

Thomas John "Tom" Sargent is an American economist, who is currently the W.R. Berkley Professor of Economics and Business at New York University. He specializes in the fields of macroeconomics, monetary economics and time series econometrics. As of 2014, he ranks fourteenth among the most cited economists in the world. He was awarded the Nobel Memorial Prize in Economics in 2011 together with Christopher A. Sims for their "empirical research on cause and effect in the macroeconomy".

The policy-ineffectiveness proposition (PIP) is a new classical theory proposed in 1975 by Thomas J. Sargent and Neil Wallace based upon the theory of rational expectations, which posits that monetary policy cannot systematically manage the levels of output and employment in the economy.

George Lennox Sharman Shackle was an English economist. He made a practical attempt to challenge classical rational choice theory and has been characterised as a "post-Keynesian", though he is influenced as well by Austrian economics. Much of his work is associated with the Dempster–Shafer theory of evidence.

The Lucas islands model is an economic model of the link between money supply and price and output changes in a simplified economy using rational expectations. It delivered a new classical explanation of the Phillips curve relationship between unemployment and inflation. The model was formulated by Robert Lucas, Jr. in a series of papers in the 1970s.

Dynamic stochastic general equilibrium modeling is a method in macroeconomics that attempts to explain economic phenomena, such as economic growth and business cycles, and the effects of economic policy, through econometric models based on applied general equilibrium theory and microeconomic principles.

New classical macroeconomics, sometimes simply called new classical economics, is a school of thought in macroeconomics that builds its analysis entirely on a neoclassical framework. Specifically, it emphasizes the importance of rigorous foundations based on microeconomics, especially rational expectations.

Macroeconomic theory has its origins in the study of business cycles and monetary theory. In general, early theorists believed monetary factors could not affect real factors such as real output. John Maynard Keynes attacked some of these "classical" theories and produced a general theory that described the whole economy in terms of aggregates rather than individual, microeconomic parts. Attempting to explain unemployment and recessions, he noticed the tendency for people and businesses to hoard cash and avoid investment during a recession. He argued that this invalidated the assumptions of classical economists who thought that markets always clear, leaving no surplus of goods and no willing labor left idle.

The Lucas aggregate supply function or Lucas "surprise" supply function, based on the Lucas imperfect information model, is a representation of aggregate supply based on the work of new classical economist Robert Lucas. The model states that economic output is a function of money or price "surprise". The model accounts for the empirically based trade off between output and prices represented by the Phillips curve, but the function breaks from the Phillips curve since only unanticipated price level changes lead to changes in output. The model accounts for empirically observed short-run correlations between output and prices, but maintains the neutrality of money in the long-run. The policy ineffectiveness proposition extends the model by arguing that, since people with rational expectations cannot be systematically surprised by monetary policy, monetary policy cannot be used to systematically influence the economy.

In economic theory and econometrics, the term heterogeneity refers to differences across the units being studied. For example, a macroeconomic model in which consumers are assumed to differ from one another is said to have heterogeneous agents.

## References

• Hanish C. Lodhia (2005) "The Irrationality of Rational Expectations – An Exploration into Economic Fallacy". 1st Edition, Warwick University Press, UK.
• Maarten C. W. Janssen (1993) "Microfoundations: A Critical Inquiry". Routledge.
• John F. Muth (1961) "Rational Expectations and the Theory of Price Movements" reprinted in The new classical macroeconomics. Volume 1. (1992): 3–23 (International Library of Critical Writings in Economics, vol. 19. Aldershot, UK: Elgar.)
• Thomas J. Sargent (1987). "Rational expectations," The New Palgrave: A Dictionary of Economics , v. 4, pp. 76–79.
• N.E. Savin (1987). "Rational expectations: econometric implications," The New Palgrave: A Dictionary of Economics , v. 4, pp. 79–85.