Is it possible to compute optimal simple rules for the case of multiple shocks in Dynare? i.e., can we compute OSR when two shocks hit the economy simultaneously?

The general answer is yes. Dynare allows you to have an arbitrary shock variance matrix with multiple shocks. It finds the optimal policy given the ergodic distribution of shocks. What exactly do you have in mind? Perfectly correlated shocks?

Thank you for your response Professor. I had uncorrelated shocks in mind. When I specify non-zero standard deviations for multiple shocks and give the OSR command, I get optimal policy. There is a corresponding variance-covariance matrix as well. Is it for both shocks or one?

Yes, it’s for all shocks. But if you only specify shock standard deviations, it will simply be a diagonal matrix.

Yes, I understand that the matrix will be diagonal as the correlation between shocks is 0. Is this a problem?

No, if that’s what you want, i.e. uncorrelated shocks.