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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 people want to create an expectation of the inflation rate in the future, they can refer to past inflation rates to infer some consistencies and could derive a more accurate expectation the more years they consider.

One simple version of adaptive expectations is stated in the following equation, where is the next year's rate of inflation that is currently expected; is this year's rate of inflation that was expected last year; and is this year's actual rate of inflation:

where is between 0 and 1.^{ [1] } This says that current expectations of future inflation reflect past expectations and an "error-adjustment" term, in which current expectations are raised (or lowered) according to the gap between actual inflation and previous expectations. The error-adjustment term, also called *partial adjustment*, allows for variations in inflation rates over the previous years, especially years that have abnormally high or low rates.

The above term is the *partial adjustment* error term, this term allows for variances that occur between actual values and expected values. The importance of considering the error prevents over and under expecting values of in the above example inflation rates. The adjustment means that the expectation can tend toward the direction of the future expected value that would be closer to the actual value, this allows a prediction to be made and consideration to be added or removed so as to be accurate of the future expectation. This consideration or error term is what allows the predicted value to be adaptable, thus creating an equation that is *adaptive* of the expectation being inferred.

The theory of adaptive expectations can be applied to all previous periods so that current inflationary expectations equal:

where equals actual inflation years in the past.^{ [2] } The adding of a time series portion to the expectation equations accounts for multiple previous years and their respective rates in forecasting like the above example of the future inflation rate. Thus, current expected inflation reflects a weighted average of all past inflation rates, where the weights get smaller and smaller as we move further in to the past. The initial previous year has the highest weighting and the subsequent years take lesser weighting the further back the equation accounts for.

When an agent makes a forecasting error (as in incorrectly recording a value or mistyping), the stochastic shock will cause the agent to incorrectly forecast the price expectation level again even if the price level experiences no further shocks, since the previous expectations only ever incorporates part of their errors. The backward nature of expectation formulation and the resultant systematic errors made by agents (see cobweb model) had become unsatisfactory to economists such as John Muth, who was pivotal in the development of an alternative model of how expectations are formed, called rational expectations. The use of rational expectations have largely replaced adaptive expectations in macroeconomic theory since its assumptions rely on an optimal expectations approach which is consistent with economic theory. However, it must be stressed that confronting adaptive expectations and rational expectations aren't necessarily justified by either use, in other words, there are situations in which following the adaptive scheme is a rational response.

The first use adaptive expectations hypothesis was to describe agent behavior in *The Purchasing Power of Money* by Irving Fisher (1911), then later used to describe models such as hyperinflation by Philip Cagan (1956).^{ [3] } Adaptive expectations were instrumental in the consumption function (1957) and Phillips curve outlined by Milton Friedman. Friedman suggests that workers form adaptive expectations of the inflation rate, the government can easily surprise them through unexpected monetary policy changes. As agents are trapped by the money illusion, they are unable to correctly perceive price and wage dynamics, so based on Friedman's theory, unemployment can always be reduced through monetary expansions. If the government chooses to fix a low unemployment rate the result is an increasing level of inflation for an extended period of time. However, in this framework, it is clear why and how adaptive expectations are problematic. Agents are arbitrarily supposed to ignore sources of information which, otherwise, would affect their expectations. For example, government announcements are such sources. Agents are expected to modify their expectations and break with the former trends when changes in economic policy necessitate it. This is the reason why the theory of adaptive expectations is often regarded as a deviation from the rational tradition of economics.^{ [4] }

In economics, **inflation** is an increase in the general price level of goods and services in an economy. When the general price level rises, each unit of currency buys fewer goods and services; consequently, inflation corresponds to a reduction in the purchasing power of money. The opposite of inflation is deflation, a decrease in the general price level of goods and services. The common measure of inflation is the **inflation rate**, the annualized percentage change in a general price index. As prices faced by households do not all increase at the same rate, the consumer price index (CPI) is often used for this purpose. The employment cost index is also used for wages in the United States.

**Rational expectations** is an economic theory used to explain how individuals make predictions about the future based on all available information. It states that individuals will also learn from past trends and experiences in order to make the best possible prediction about what will happen. They could be wrong sometimes, but that, on average, they will be correct.

**New Keynesian economics** is a school of 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.

The **Phillips curve** is an economic model, named after William Phillips, that predicts a correlation between reduction in unemployment and increased rates of wage rises within an economy. While Phillips himself did not state a linked relationship between employment and inflation, this was a trivial deduction from his statistical findings. Paul Samuelson and Robert Solow made the connection explicit and subsequently Milton Friedman and Edmund Phelps put the theoretical structure in place.

In financial mathematics and economics, the **Fisher equation** expresses the relationship between nominal interest rates and real interest rates under inflation. Named after Irving Fisher, an American economist, it can be expressed as **real interest rate ≈ nominal interest rate − inflation rate.** In more formal terms, where equals the real interest rate, equals the nominal interest rate, and equals the inflation rate, the Fisher equation is . It can also be expressed as or .

In finance, **arbitrage pricing theory (APT)** is a multi-factor model for asset pricing which relates various macro-economic (systematic) risk variables to the pricing of financial assets. Proposed by economist Stephen Ross in 1976, it is widely believed to be an improved alternative to its predecessor, the Capital Asset Pricing Model (CAPM). APT is founded upon the law of one price, which suggests that within an equilibrium market, rational investors will implement arbitrage such that the equilibrium price is eventually realised. As such, APT argues that when opportunities for arbitrage are exhausted in a given period, then the expected return of an asset is a linear function of various factors or theoretical market indices, where sensitivities of each factor is represented by a factor-specific beta coefficient or factor loading. Consequently, it provides traders with an indication of ‘true’ asset value and enables exploitation of market discrepancies via arbitrage. The linear factor model structure of the APT is used as the basis for evaluating asset allocation, the performance of managed funds as well as the calculation of cost of capital. Furthermore, the newer APT model is more dynamic being utilised in more theoretical application than the preceding CAPM model. A 1986 article written by Gregory Connor and Robert Korajczyk, utilised the APT framework and applied it to portfolio performance measurement suggesting that the Jensen coefficient is an acceptable measurement of portfolio performance.

A **macroeconomic model** is an analytical tool designed to describe the operation of the problems of 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.

The **Hodrick–Prescott filter** is a mathematical tool used in macroeconomics, especially in real business cycle theory, to remove the cyclical component of a time series from raw data. It is used to obtain a smoothed-curve representation of a time series, one that is more sensitive to long-term than to short-term fluctuations. The adjustment of the sensitivity of the trend to short-term fluctuations is achieved by modifying a multiplier .

In economics, **money illusion**, or **price illusion**, is a cognitive bias where money is thought of in nominal, rather than real terms. In other words, the face value of money is mistaken for its purchasing power at a previous point in time. Viewing purchasing power as measured by the nominal value is false, as modern fiat currencies have no intrinsic value and their real value depends purely on the price level. The term was coined by Irving Fisher in *Stabilizing the Dollar*. It was popularized by John Maynard Keynes in the early twentieth century, and Irving Fisher wrote an important book on the subject, *The Money Illusion*, in 1928.

**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.

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.

In macroeconomics, the **classical dichotomy** is the idea, attributed to classical and pre-Keynesian economics, that real and nominal variables can be analyzed separately. To be precise, an economy exhibits the classical dichotomy if real variables such as output and real interest rates can be completely analyzed without considering what is happening to their nominal counterparts, the money value of output and the interest rate. In particular, this means that real GDP and other real variables can be determined without knowing the level of the nominal money supply or the rate of inflation. An economy exhibits the classical dichotomy if money is neutral, affecting only the price level, not real variables. As such, if the classical dichotomy holds, money only affects absolute rather than the relative prices between goods.

The **veil of money** is the property assumed by some economists whereby money is a commodity like other commodities – such as oil or gold or food – as opposed to its having special properties.

**Quantal response equilibrium** (**QRE**) is a solution concept in game theory. First introduced by Richard McKelvey and Thomas Palfrey, it provides an equilibrium notion with bounded rationality. QRE is not an equilibrium refinement, and it can give significantly different results from Nash equilibrium. QRE is only defined for games with discrete strategies, although there are continuous-strategy analogues.

**Dynamic stochastic general equilibrium** modeling is a macroeconomic method which is often employed by monetary and fiscal authorities for policy analysis, explaining historical time-series data, as well as future forecasting purposes. DSGE econometric modelling applies general equilibrium theory and microeconomic principles in a tractable manner to postulate economic phenomena, such as economic growth and business cycles, as well as policy effects and market shocks.

**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.

The **random walk model of consumption** was introduced by economist Robert Hall. This model uses the Euler numerical method to model consumption. He created his consumption theory in response to the Lucas critique. Using Euler equations to model the random walk of consumption has become the dominant approach to modeling consumption.

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.

The **Taylor contract** or **staggered contract** was first formulated by John B. Taylor in his two articles, in 1979 "Staggered wage setting in a macro model". and in 1980 "Aggregate Dynamics and Staggered Contracts". In its simplest form, one can think of two equal sized unions who set wages in an industry. Each period, one of the unions sets the nominal wage for two periods. This means that in any one period, only one of the unions can reset its wage and react to events that have just happened. When the union sets its wage, it sets it for a known and fixed period of time. Whilst it will know what is happening in the first period when it sets the new wage, it will have to form expectations about the factors in the second period that determine the optimal wage to set. Although the model was first used to model wage setting, in new Keynesian models that followed it was also used to model price-setting by firms.

- ↑ Evans, G.W.; Honkapohja, S. (2001). "Expectations, Economics of".
*International Encyclopedia of the Social & Behavioral Sciences*. pp. 5060–5067. doi:10.1016/B0-08-043076-7/02245-2. ISBN 978-0-08-043076-8. - ↑ Mishkin, Frederic (2019).
*Economics of Money, Banking and Financial Markets*(12 ed.). United States: Pearson. ISBN 978-0-13-473382-1. - ↑ Mollik, Andrea V. "Adaptive Expectations".
*Encyclopedia.com*. Archived from the original on 2021-04-26. Retrieved 16 April 2021. - ↑ 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.

- Evans, George W.; Honkapohja, Seppo (2001-01-28).
*Learning and Expectations in Macroeconomics*. Princeton University Press. ISBN 978-0-691-04921-2.

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