Consider the following model $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } X _ { t } ^ { e } + u _ { t }$ where the superscript "e" indicates expected values. This may represent an example where consumption depends on expected, or "permanent," income. Furthermore, let expected income be formed as follows:
$$X _ { t } ^ { e } = X _ { t - 1 } ^ { e } + \lambda \left( X _ { t } - X _ { t - 1 } ^ { e } \right) ; \quad 0

Question

Consider the following model $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } X _ { t } ^ { e } + u _ { t }$ where the superscript "e" indicates expected values. This may represent an example where consumption depends on expected, or "permanent," income. Furthermore, let expected income be formed as follows:
$$X _ { t } ^ { e } = X _ { t - 1 } ^ { e } + \lambda \left( X _ { t } - X _ { t - 1 } ^ { e } \right) ; \quad 0 < \lambda < 1$$ (a)In the above expectation formation hypothesis, expectations are formed at the end of the
period, say the $31 ^ { \text {st } }$ of December, if you had annual data.Give an intuitive explanation for
this process.

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The Answer of Consider the following model $Y _ { t } = \beta _ { 0 } + \beta _ { 1 } X _ { t } ^ { e } + u _ { t }$ where the superscript "e" indicates expected values. This may represent an example where consumption depends on expected, or "permanent," income. Furthermore, let expected income be formed as follows:
$$X _ { t } ^ { e } = X _ { t - 1 } ^ { e } + \lambda \left( X _ { t } - X _ { t - 1 } ^ { e } \right) ; \quad 0 < \lambda < 1$$ (a)In the above expectation formation hypothesis, expectations are formed at the end of the
period, say the $31 ^ { \text {st } }$ of December, if you had annual data.Give an intuitive explanation for
this process.

Consider the Following Model Yt=β0+β1Xte+utY _ { t } = \beta _ { 0 } + \beta _ { 1 } X _ { t } ^ { e } + u _ { t }Yt​=β0​+β1​Xte​+ut​

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