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

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, the time-consistent optimal monetary policy is regime-dependent linear interest rate rules in inflation and output gaps. This optimal interest rate rule converges to zero if monetary authority extremely concerns immediate macro stability. 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 during 1952-2007, the near-optimal one is more stabilizing than the non-optimal one