Hello,

There didn’t seem to be a separate topic on this and so I decided to create this topic, which would hopefully serve as a reference to anyone trying to do this.

I would like to ask what is the simplest way to model an interest rate peg/zlb in a linearized PF model? By a peg, I mean that I would like to hold the interest rate at the SS for T number of periods. The following simple expression works for a non-linear case:

R=ex* R_ss+(1-ex)(phi_pi* pi+phi_y* Y));

where ex is a shock equal to 1 for T number of periods. That means the interest rate remains at SS for duration of T.

Doing the same thing in a linear version of a model(while keeping in mind that the steady state is now zero) essentially getting rid of the R_ss*ex part does not work.

Another approach that I have seen does the following “trick”:

```
R = s1(-1);
s1 = s2(-1);
s2 = s3(-1);
s3 = s4(-1);
s4 = (phi_pi*pi(4) + phi_y*(Y(4)));
```

This code would technically peg the interest rate for 4 periods, however the interest rate then starts to exhibit some kind of an extra smoothness and tends to die out very slowly, which doesn’t make sense since it does not follow the behavior of inflation and output (which in my case) immediately go back to SS after the shock is over. The same thing should happen to the interest rate, but it doesn’t indicating an issue with this method. Also, in this case you don’t explicitly include a shock to keep the rate at the SS, which I thought could still work, but it doesn’t seem to be the case.

What is the simplest way to include a peg in a linearized PF model?

Thanks