I tried to reproduce Gertler and Karidi 2011, which reported that the BK condition was not satisfied

This is my code, NKGK.mod is the same model as NKKK.mod. NKGK.mod wrote an additional steadystate file, which can solve the steadystate, but when stochastic simulation, it shows that the BK condition is not satisfied. If NKKK is directly substituted into the steady-state value, the random simulation can be carried out smoothly. GK.zip (6.2 KB)

I get the same BK error for both files. The updated steady state file works with Dynare 5.4.
NKGK_steadystate.m (2.7 KB)

I run it, and there are still cases where the BK condition is not satisfied.

As I said, there is a consistent BK error across all files. So you should debug the timing. I only provided the steady state file to allow you upgrading to Dynare 5.4.