Consider the Following Model $$Y _ { t } = \alpha _ { 0 } + \alpha _ { 1 } X _ { t } ^ { e } + u _ { t }$$

question 7

Essay

Consider the following model $$Y _ { t } = \alpha _ { 0 } + \alpha _ { 1 } X _ { t } ^ { e } + u _ { t }$$ t
where the superscript "e" indicates expected values.This may represent an example
where consumption depended on expected, or "permanent," income.Furthermore, let
expected income be formed as follows: $$X _ { t } ^ { e } = X _ { t - 1 } ^ { e } + \lambda \left( X _ { t - 1 } - X _ { t - 1 } ^ { e } \right) ; 0 < \lambda < 1$$ 1
This particular type of expectation formation is called the "adaptive expectations
hypothesis."
(a) In the above expectation formation hypothesis, expectations are formed at the beginning of the period, say the $1 ^ { \text {st } }$ of January if you had annual data. Give an intuitive explanation for this process.

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Definitions:

Errors

Mistakes or deviations from accuracy and correctness in action, calculation, opinion, or judgment.

Personal Attribution

The process by which individuals attribute causes to actions or events based on personal characteristics rather than situational factors.

Stable/Permanent

Characteristics or conditions that are constant, unchanging over time, and expected to stay the same indefinitely.

Primary

Pertaining to the first in order, importance, or time.