Consider the following first-order VAR model of stationary variables:

\[\begin{aligned}& y_{t}=\delta_{11} y_{t-1}+\delta_{12} x_{t-1}+v_{t}^{y} \\& x_{t}=\delta_{21} y_{t-1}+\delta_{22} x_{t-1}+v_{t}^{x}\end{aligned}\]

Under the assumption that there is no contemporaneous dependence, determine the impulse responses, four periods after a standard deviation shock for

a. \(y\) following a shock to \(y\)

b. \(y\) following a shock to \(x\)

c. \(x\) following a shock to \(y\)

d. \(x\) following a shock to \(x\)