Simultaneous shocks and multiple periods

My goal is to replicate an economy with a COVID shock and a transfer shock (to determine how transfers change equilibrium dynamics in a TANK model). To implement both shocks simultaneously, I use the same exogenous shock variable in both processes (as of now, I’m assuming this is the only way to do it, please help me out if there is another way). However, I aim for the transfers to be of the same magnitude for four periods (quarters) and zero afterward. How can I shock both variables simultaneously but at the same time achieve said specification for the time path of the transfers? Any help is very much appreciated. Thanks!

May I ask, how would you want to call that exogenous common shock in your model? As far as I know, the same shock can hit different things simultaneously, like an 'economy-wide productivity shock e^A_t hitting all sectors in a multi-sector DSGE model. For example, Y^1_t = A_t f(K^1_t, L^1_t), Y^2_t = A_t f(K^2_t, L^2_t), where A_t affects both sectors (A_t = \rho A_{t-1} + e^A_t). I think if you can convince people that there is some kind of shock that hits multiple things at the same time, you can use this approach. Or maybe you can say the exogenous processes are different but the shocks are correlated. Y_t = A^1_t f(K^1_t, L^1_t), Y_t = A^2_t f(K^2_t, L^2_t), cor(e^{A1}_t, e^{A2}_t) \neq 0.

Is the model solved under perfect foresight?

I have the same shock (exo-) variable entering two different stochastic processes (productivity, transfers) with different magnitudes to match what I observe in the data.

No, it is not. I have come across that, as I also wanted to experiment with a ZLB constraint. Is there a way to combine the stochastic productivity shock and a perfect foresight transfer shock/ZLB?

I would model the transfer shock as a sequence of news shock and the TFP shock as a separate shock. You can use the simult_-function to simulate a shock combination. See DSGE_mod/RBC_news_shock_model.mod at master · JohannesPfeifer/DSGE_mod · GitHub

Makes sense to me, I will give that a try. Thank you very much for your advice!