Optimal Monetary Policy and Term Structure in a Continuous-Time DSGE Model

Abstract

We study optimal monetary policy, macro dynamics and their implications on the term structure of interest rates in a continuous-time New Keynesian model. With a quadratic cost function and regime-dependent monetary discount rates facing the central bank, the time-consistent optimal monetary policy is regime-dependent linear interest rate rules in inflation and output gaps. The optimal interest rate rules and the equilibrium dynamics of inflation and output gap form a regime-dependent term structure model. We take the model to the US data and find that the Fed had followed two distinct interest rate rules, one is not optimal while the other is near-optimal with a large monetary discount rate. The macro dynamics are more stable under the near-optimal policy rule than the non-optimal one.