My dynare output says that the ‘maximum number of iterations is reached’ which I think is due to my “max(expression1,expression2)” equation. I have tried to use the "maxit_= " before steady to solve the problem but it doesn’t fixthe problem (it actually seems like it stops after 10 iterations even when I have set it to for instance 100).

(By the way: The code runs fine without the max expression & I’m running the old 4.4.1 at the moment)

Yes, it works if I reduce the magnitude of the shock, but I’m interested in a large shock (so to reach the ZLB). But is there no solution due to the math or because it “doesn’t try hard enough” (i.e. that the number of iterations is too low?)

It’s hard to tell. Using 10000 iterations resulted in no success. My guess would be that there is a more fundamental problem as in the model being not determinate anymore if you are sufficiently long at the ZLB due to a high shock size.