Ok, so I solved Chen et al. (2012)'s model on my own with gensys. To make sure that my output is correct, I solved the simple 2 period NK model in dynare and then in Gensys to make sure that I get equivalent results. Their model does output a unique equilibrium. My model which gives me the unit root in dynare does not yield unique equilibria. Hence, their is something wrong in my setup, which I have to identify.
I find it puzzling, because this model is a reduced form of theirs. What I differ in their specification is that I exclude sticky wages, capital utilization and I used Rotemberg AC instead of Calvo pricing. Something about the segmentation must be interfering with my specification.
In any case though, there doesn’t appear to be a fundamental problem with their model.