A growing body of evidence finds that policy reaction functions vary substantially over different periods in the United States. This paper explores how moving to an environment in which monetary and fiscal regimes evolve according to a Markov process can change the impacts of policy shocks. In one regime monetary policy follows the Taylor principle and taxes rise strongly with debt; in another regime the Taylor principle fails to hold and taxes are exogenous. An example shows that a unique bounded non-Ricardian equilibrium exists in this environment. A computational model illustrates that because agents' decision rules embed the probability that policies will change in the future, monetary and tax shocks always produce wealth effects. When it is possible that fiscal policy will be unresponsive to debt at times, active monetary policy (like a Taylor rule) in one regime is not sufficient to insulate the economy against tax shocks in that regime and it can have the unintended consequence of amplifying and propagating the aggregate demand effects of tax shocks. The paper also considers the implications of policy switching for two empirical issues.