I have written a symmetric two country model and solved it using a 2nd order approximation with pruning turned on. I use the simult_ function to calculate impulse responses given a one time shock at t=1. Somehow the variables for the home and foreign country converge to different steady states. Is this a signal that there is something wrong with the model?

There is still symmetry in the sense that, if I shock home exogenous variables, the foreign variables converge to the same steady state as the home variables do when I shock foreign exogenous variables in the same way.

Put alternatively, there is symmetry but the shocks have permanent effects.

It’s hard to tell, but it is not unheard of for shocks in open economy model to have permanent effects. See e.g. Mulit capital economy with bonds for the intuition

Thank you for your reply. One weird thing is that this seems to happen also in a 3rd order approximation. Heathcote and Perri (2016, IMF ER) claim that the 3rd order approximation should resolve the non-stationarity issues in open economy models with incomplete markets.

Higher order may solve the issue in SMOPEC models. I am not sure what happens in two-country models where the Jensen’s Inequality effect at third order affects both countries and may counteract each other.