Recall that lecture examined the following model:
\(\displaystyle \begin{equation} y_t=E_{t-1}[y_{t+1}^\beta]e_t \label{3} \end{equation} \begin{equation} s.t. \hspace{.2in} \stackrel{lim}{_{j\rightarrow\infty}}E_{t-1}[y_{t+j}]=\bar{y} \label{4} \end{equation}\)
\(\displaystyle \mathrm{where} $e_t$ is normally distributed with mean equal to one and variance equal to $\sigma_{e}^{2}$, and $|\beta|\neq1$.\)
\(\displaystyle \mbox{Prove that the results from lecture do not depend on the assumption that the mean of} $e_t$ equals one.\)
Sometimes it is easier to guess and verify a model's reduced form, rational expectations solution before analyzing its stability (i.e reversing Steps 5 and 6 from lecture).
Step 5: diagonalize the system and check for unique equilibrium
Step 6: Impose stability condition and derive solution
I need some clue how to go about this proof. do i need to provide more about the results from lecture first?
\(\displaystyle \begin{equation} y_t=E_{t-1}[y_{t+1}^\beta]e_t \label{3} \end{equation} \begin{equation} s.t. \hspace{.2in} \stackrel{lim}{_{j\rightarrow\infty}}E_{t-1}[y_{t+j}]=\bar{y} \label{4} \end{equation}\)
\(\displaystyle \mathrm{where} $e_t$ is normally distributed with mean equal to one and variance equal to $\sigma_{e}^{2}$, and $|\beta|\neq1$.\)
\(\displaystyle \mbox{Prove that the results from lecture do not depend on the assumption that the mean of} $e_t$ equals one.\)
Sometimes it is easier to guess and verify a model's reduced form, rational expectations solution before analyzing its stability (i.e reversing Steps 5 and 6 from lecture).
Step 5: diagonalize the system and check for unique equilibrium
Step 6: Impose stability condition and derive solution
I need some clue how to go about this proof. do i need to provide more about the results from lecture first?