Timing for interest bearing central bank liability

General DSGE Modeling
1

Dear Forum,
in my model I have an interest bearing (R_t^{CB}) central bank liability. I also have government bond remunerated at policy rate (R_t) following a Taylor rule. I set the interest rate on central bank liability as a constant spread from the policy rate i.e.
R_t^{CB} = R_t - SPR^{CB}.
The problem is I get BK condition violation when I use the above expression. If I use the next period policy rate i.e. if R_t^{CB} = \mathbb{E}_tR_{t+1} - SPR^{CB}, the model works. I have checked removing interest rate of the liability and the model works without any issue. Hence, the BK condition violation is definitely due to the setting of R_t^{CB}. Can anyone shed some light on this timing issue? Why the model should work with expected one-period ahead policy rate but not same period policy rate?

2
  1. Which type of BK violation do you get? Indeterminacy or instability?
  2. Usually I would suspect a timing error somewhere in the model extension that you “fix” by messing with the timing of the spread.