I am building an NK model with search and matching frictions. My NK workhorse model works well and produces beautiful impulse responses. However, when I include the search and matching features, it causes collinearity. Although the code produces impulse responses, they are clearly not correct plus the theoretical moments report some NANs.
What I understand is that the collinearity is allocated in the price-setting equations. I have the strong belief that the problem is related to the definition of marginal cost since now it accounts for the frictions.
Could anyone give me some advice, please? I have tried to simplify Calvo equations but nothing has worked by now. Thanks!