I have spent a very very long time trying different parameter values and initial values in order to find the steady state of this model, but Matlab never likes it. Messages I got include: convergence problem, spurious convergence, Newton direction isn’t finite, Jacobian is singular, etc. Any help would be appreciated.

With even moderately sized models it is often useful to solve the steady state yourself. At first glance, your model seems nearly linear, so this should be doable. Have a look at how to write the steadystate.m file at dynare.org/manual/index_20.h … state-file