Jermann Quadrini (2012) with collateral constraints

Hi all,
I think the main issue in this model is that the nominal prices (price of consumption goods and wages) are moving to a new equilibrium after the monetary shock. And Taylor rule breaks. I have attached the updated code and IRFs. I used the version of the Taylor rule, which only reacts to the output gap.

Does anyone have an intuition about why the price doesn’t return to equilibrium after the shock? Is it a feature of the model, or did I make a mistake somewhere?

simple_model.mod (9.5 KB)
simple_model_steadystate.m (4.7 KB)
main_output_gap.fig (175.8 KB)
qwd_output_gap.fig (64.7 KB)