Policy functions with third order approximation

At third order, there is an uncertainty correction. For that reason, simulations without shocks will not converge to the deterministic steady state, but rather to the “stochastic steady state” or “ergodic mean in the absence of shocks”. This is expected behavior. For details, you can have a look at the Appendix to Born/Pfeifer (2014): “Risk Matters: A comment” at aeaweb.org/articles.php?doi=10.1257/aer.104.12.4231 and [Simult_ and nonzero IRFs in higher-order approximations)