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Monetary Policy Interactions: The Policy Rate, Asset Purchases, and Optimal Policy with an Interest Rate Peg

We consider a New Keynesian model with a variable term premium and scope for central bank asset purchases to matter. Current and future asset purchase policies have varying effects on output. We derive an analytic expression for the central bank's loss function, which directly penalizes term premium fluctuations. We then analyze optimal monetary policy. A version of the Divine Coincidence holds with both the short-term rate and balance sheet as available tools. In response to credit market shocks, the balance sheet neutralizes them, and the policy rate is unchanged. In response to natural rate shocks, both the policy rate and balance sheet react, moving opposite. The balance sheet expands as the policy rate falls, or vice versa. Active balance sheet management can support a determinate rational expectations equilibrium even under a permanent interest rate peg. We explore the costs of fixing either the policy rate or the balance sheet.