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 Title: Adaptive expectations Author: World Heritage Encyclopedia Language: English Subject: Collection: MacRoeconomics Publisher: World Heritage Encyclopedia Publication Date:

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.

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

p^e = p^{e}_{-1} + \lambda (p - p^{e}_{-1})

where \lambda is between 0 and 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. This error-adjustment is also called "partial adjustment."

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

p^e = \lambda \sum_{j = 0}^{\infty} ((1-\lambda)^j p_j)

where p_j equals actual inflation j years in the past. Thus, current expected inflation reflects a weighted average of all past inflation, where the weights get smaller and smaller as we move further in the past.

Once a forecasting error is made by agents, due to a stochastic shock, they will be unable to correctly forecast the price level again even if the price level experiences no further shocks since they only ever incorporate part of their errors. The backward nature of expectation formulation and the resultant systematic errors made by agents (see Cobweb model) was 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. This has largely replaced adaptive expectations in macroeconomic theory since its assumption of optimality of expectations is consistent with economic theory.

Maurice Allais’s Hereditary, Relativist and Logistic (HRL) theory of monetary dynamics contains an original theory of expectations formation that is a genuine alternative to both adaptive and rational expectations.[1] Praised by Milton Friedman in 1968 with the following words: This work [the HRL formulation] introduces a very basic and important distinction between psychological time and chronological time. It is one of the most important and original paper that has been written for a long time … for its consideration of the problem of the formation of expectations.”[2] Allais’s contribution has nevertheless been “lost”: it has been absent from the debate about expectations.[3]

## References

1. ^ Allais, M. (1965), Reformulation de la théorie quantitative de la monnaie, Société d’études et de documentation économiques, industrielles et sociales (SEDEIS), Paris.
2. ^ Friedman, M. (1968), Factors affecting the level of interest rates, in Savings and residential financing: 1968 Conference Proceedings, Jacobs, D. P., and Pratt, R. T., (eds.), The United States Saving and Loan League, Chicago, IL, p. 375.
3. ^ Barthalon, E. (2014), Uncertainty, Expectations and Financial Instability, Reviving Allais’s Lost Theory of Psychological Time, Columbia University Press, New York.
• George W. Evans and Seppo Honkapohja (2001), Learning and Expectations in Macroeconomics. Princeton University Press, ISBN 978-0-691-04921-2.
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