AbstractIn a fixed‐regime context, it has been established since the work of Leeper (1991) that a determinate and unique equilibrium can be achieved under both monetary dominance (characterized by an active monetary policy and a passive fiscal policy) and fiscal dominance (characterized by an active fiscal policy and a passive monetary policy) regimes yield a determinate unique equilibrium. In this paper, we generalize this well‐established policy‐mix taxonomy to regime‐switching models, and show that switches from monetary dominance to fiscal dominance regimes (and vice versa) render the economy indeterminate for standard parameter values. We apply our results to the important case of the exit from the zero lower bound (ZLB), where monetary policy is inherently passive. Contrary to the fixed‐regime prediction, the economy switching between the ZLB in a fiscally led regime and a monetary dominance regime is robustly indeterminate, making the coordination of agents' beliefs hard for anchoring expected inflation. Finally, we propose a direction toward which the perspective of the fiscal theory of the price level can be made consistent with a unique stable equilibrium.