We study how determinacy and expectational stability (E-stability) of rational expectations equilibrium may be affected by monetary policy when the cost channel of monetary policy matters. We focus on both instrumental Taylor-type rules and optimal target rules. We show that standard instrument rules can easily induce indeterminacy and expectational instability when the cost channel is present. Overall, a naïve application of the traditional Taylor principle in this setting could be misleading. Regarding optimal rules, we find that "expectational-based rules" do not always induce determinate and E-stable equilibrium. This result stands in contrast to the findings of Evans and Honkapohja (2003) for the baseline "New Keynesian" model. Yet, a policy that it is a source of instability under learning in the baseline new keynesian model, i.e. "fundamental rule" under commitment, is a possible antidote when the cost channel is active.