Impulse response functions?
Start by establishing $ \epsilon _1 = \epsilon , \epsilon_{t&gt;1}=0$ . Now, epsilon will be your impulse.
You can calculate an expression for $A_t,\bar{A}_t\ \forall t$ . From here, you can either:


Work recursively with each variable and provide an analytic function for them, for every moment on time.
Calculate a value if you are simulating it, using the policy functions at each step.



Notice that, if you log-linearized your equations, $\epsilon=1$ would mean a 1% deviation from the steady state.