Occbin applying in different regimes

Dear Professor,

We are currently exploring the implementation of the Occbin constraint to address the Zero Lower Bound (ZLB) scenario. We are trying to use the Occbin constraint to apply ZLB, specifically when the interest rate is below zero, we want to switch to QE regimes, while relaxing stay to the normal Taylor rule.

However, we are encountering some uncertainty regarding the feasibility of integrating this process within the Occbin constraint framework. Any guidance or insights you could provide on this matter would be immensely valuable to us.

Thank you sincerely for your assistance.

That seems like a standard OccBin application.

Dear Professor,

Thank you for your quick reply.

In our current model setup, we have incorporated two monetary equations: one used during standard economic conditions with the Taylor rule, and the other representing QE activated specifically during the ZLB period.

We are thinking of incorporating this idea into the code using Occbin; the code may look like this:

name ‘ZLB’;
bind r<0, QE equation;
relax r>0 Taylor rule.

We tried this in the code, but it seems like it doesn’t work. So we searched the forum, we found that in the most models on the Forum, they don’t have a specific equation tailored solely for ZLB. Instead, as we understand, they just allow the interest rate to drop below zero and observe the behaviour of the original model. So this raises our concern regarding how to correctly incorporate QE equation in the occbin_constraints block in Dynare.

We greatly appreciate any further insights or guidance you can provide on this matter.

Thank you once again for your assistance.

That type of setup does not work. You need to have an indicator when to leave the ZLB. You cannot use the actual interest rate because that one is fixed at 0. That’s why people rely on a notional nominal interest rate.

I see, but we have both long-run and short-run interest rates, as well as money in the model. When the model hits the ZLB, the long-run interest rate is still positive, and the other money equation works during the ZLB. So what we want to do is figure out how to add another money equation that works only during the ZLB period using occbin_constraints in Dynare

The only thing you need to figure out is how to determine which variable/condition in the baseline regime tells you that you entered the ZLB region and which variable/condition in the ZLB regime tells you that you have left the ZLB. Usually, you use a counterfactual short term interest rate for that.

we indeed use the nominal short-term interest rate rt as the variable to get in and get out the ZLB, specifically, rt<0.0625, enter the ZLB, and rt>0.0625, left the ZLB.

However, our confusion is we not only have the Taylor rule in our model but also have money in the model. Specifically, when rt>0.0625, we have the Taylor rule that affects the money supply. When rt<0.0625, Taylor rule is fixed, and we introduce another money supply equation that targets credit risk premium (mt=psi*(premium)+error). So when we use the OCCINB, what we want is how to switch from the Taylor rule plus normal money supply equation (mt=psi1*Mt+error) to the new money supply equation targeting credit risk premium (mt=psi*(premium)+error). We would like to know the feasibility of this case in Dynare.

Again, the critical question is how to keep track of how to leave the ZLB. You would need to keep track of the notional rtnot that would be set if the ZLB were not binding (and which causes the actual rt to be 0.0625. Once you have that, everything else works as always. You have a money supply equation for each regime, for which you use the bind and relax tags