Optimal Monetary Policy with and without Debt

We derive optimal monetary policy rules when government debt may be a constraint for the monetary authority. We focus on an environment where fiscal policy is exogenous, setting taxes according to a rule that specifies the tax rate as a function of lagged debt. In the case where taxes do not adjust sufficiently to ensure the solvency of debt, then the monetary authority is burdened by debt sustainability. Under this scenario, optimal monetary policy is a ‘passive money rule’, setting the interest rate to weakly respond to inflation. We characterize analytically the optimal inflation coefficients under alternative specifications of the central bank loss function, using a simple Fisherian model, but also the canonical New Keynesian model. We show that the maturity structure of debt is a key variable behind optimal policy. When debt maturity is calibrated to US data, our model predicts that a simple inflation targeting rule where the inflation coefficient is 1 − 1 Maturity is a good approximation of the optimal policy. Lastly, our framework can also nest the case where fiscal policy adjusts taxes to satisfy the intertemporal debt constraint. In this scenario optimal monetary policy is an active policy rule. We contrast the properties of active and passive policies, using the analytical optimal policy rules derived from this framework of monetary/fiscal interactions.