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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