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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.

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One simple version of adaptive expectations is stated in the following equation, where ${\displaystyle p^{e}}$ is the next year's rate of inflation that is currently expected; ${\displaystyle p_{-1}^{e}}$is this year's rate of inflation that was expected last year; and ${\displaystyle p}$ is this year's actual rate of inflation:

${\displaystyle p^{e}=p_{-1}^{e}+\lambda (p-p_{-1}^{e})}$

where ${\displaystyle \lambda }$ 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.

${\displaystyle \lambda (p-p_{-1}^{e})}$

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:

${\displaystyle p_{t}^{e}=\lambda \sum _{j=0}^{\infty }(1-\lambda )^{j}p_{t-j}}$

where ${\displaystyle p_{t-j}}$ equals actual inflation ${\displaystyle j}$ 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]

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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.

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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 .

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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.

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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.

References

1. 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.
2. Mishkin, Frederic (2019). Economics of Money, Banking and Financial Markets (12 ed.). United States: Pearson. ISBN   978-0-13-473382-1.
3. Mollik, Andrea V. "Adaptive Expectations". Encyclopedia.com. Archived from the original on 2021-04-26. Retrieved 16 April 2021.
4. 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.

General references

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