Adaptive expectations

In economics , adaptive expectations are expectations that are formed from past values. They are the result of a learning behavior in which individuals compare their previous expectations with reality and adjust accordingly. This situation can occur when the time to produce a commodity is long, as is the case with many agricultural products.

definition

Furthermore, let the expectation with regard to any economic quantity, the earlier expectation regarding this quantity and the realization in a period . If the expectation is adaptive, then it is proportional to the error in predicting the price in the previous period: ${\displaystyle x_{t+1}^{e}}$ ${\displaystyle x_{t}^{e}}$ ${\displaystyle x_{t}}$ ${\displaystyle t}$

${\displaystyle x_{t+1}^{e}=x_{t}^{e}+\lambda (x_{t}-x_{t}^{e})}$.

There is a number between zero and one that describes the strength of the error correction: If the value is zero, no error correction takes place; if the value is one, the previous expectation is completely revised. ${\displaystyle \lambda }$

By recursion of the above formula, i.e. repeated insertion, one obtains the following expression:

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

Thus the current expectation corresponds to a weighted arithmetic mean of all previous realizations.

meaning

Depending on the type of underlying stochastic process, adaptive expectations can match rational expectations . Under the strong assumption that the underlying economic model is known, rational expectations are superior to adaptive ones. If the underlying model is unknown, adaptive expectations have the advantage that they avoid permanent errors in the expectation formation.

Individual evidence

1. ↑ George G. Judge, R. Carter Hill, W. Griffiths, Helmut Lütkepohl , TC Lee. Introduction to the Theory and Practice of Econometrics. 2nd Edition. John Wiley & Sons, New York / Chichester / Brisbane / Toronto / Singapore 1988, ISBN 0-471-62414-4 , p. 735.
2. ↑ George G. Judge, R. Carter Hill, W. Griffiths, Helmut Lütkepohl, TC Lee. Introduction to the Theory and Practice of Econometrics. 2nd Edition. John Wiley & Sons, New York / Chichester / Brisbane / Toronto / Singapore 1988, ISBN 0-471-62414-4 , p. 735.
3. ↑ Evans, GW and G. Ramey (2006) Adaptive Expectations, Underparameterization and the Lucas Critique. Journal of Monetary Economics, Vol. 53, pp. 249-264.