Issues with the steady state and ZLB

Perfect foresight simulations
1

Dear all,

I am trying to set the steady state for a perfect foresight simulation with ZLB but I am running into troubles. I don’t know how to set the steady state, I must be doing something wrong but at this point I have tried several things. I thought the constraint was the issue, but I get the same issue even setting alpha = -i. Any tips on this? The point, later on, would be to have a demand shock that brings i to ZLB.
forward_zlb_ss.mod (1.1 KB)

Thank you so much in advance!

2

What is the constraint

    i >= 0  ⟂  alpha >= 0;

supposed to represent in words? It does not tell us what i is in case the ZLB is non-binding.

3

Alpha should be the shadow price of violating the constraint i<0. I just don’t seem to find a way to introduce it, and Occbin doesn’t work when I have tried to run it.

4

Then what governs alpha? Usually, the ZLB is: follow a Taylor rule as long as i>0, set i=0 and alpha>0 otherwise. You are missing the part where alpha=0. Saying i>0 is not sufficient to pin down its value.