Taylor rule and ZLB

How to set ZLB for Taylor’s linearized rule。In general, the interest rate is going to be greater than zero. If it is cross variable, then the interest rate is greater than 1. But how to set ZLB after linearization?Thank you very much for your comments and answers。

At first order, the nominal interest rate in steady state is the sum of net steady state inflation and the net real interest rate coming from the time preference rate (usually 1/\beta-1). In that case, the ZBL will bind if the deviation from the steady state is bigger than -(1/\beta-1+\pi). For example, if the net real interest rate per quarter is 1 percent and inflation is 0.5 percent, the ZLB will bind if the nominal interest rate decreases below its steady state of 1.5% by more than 1.5%.


dear jpfeifer.Under normal circumstances, steady-state inflation is set at 1. Therefore, does the nominal interest rate need to be greater than -1/beta after linearization.

No, that would imply a zero gross interest rate. The ZLB is on the net interest rate, i.e. -(1/\beta-1)

dear jpfeifer,thank you very much for your answer. I understand it.
best wishes.