Consider the following two-variable VAR model with one lag and no intercept:

\[ \begin{aligned} & Y_{t}=\beta_{11} Y_{t-1}+\gamma_{11} X_{t-1}+u_{1 t} \\ & X_{t}=\beta_{21} Y_{t-1}+\gamma_{21} X_{t-1}+u_{2 t} \end{aligned} \]

a. Show that the iterated two-period ahead forecast for \(Y\) can be written as \(Y_{t \mid t-2}=\delta_{1} Y_{t-2}+\delta_{2} X_{t-2}\), and derive values for \(\delta_{1}\) and \(\delta_{2}\) in terms of the coefficients in the VAR.

b. In light of your answer to (a), do iterated multi-period forecasts differ from direct multi-period forecasts? Explain.