An Interest Rate Rule to Uniquely Implement the Optimal Equilibrium in a Liquidity Trap

We propose a new interest rate rule that implements the optimal equilibrium and eliminates all indeterminacy in a canonical New Keynesian model in which the zero lower bound on nominal interest rates (ZLB) is binding. The rule commits to zero nominal interest rates for a length of time that increases in proportion to how much past inflation has deviated - either upward or downward - from its optimal level. Once outside the ZLB, interest rates follow a standard Taylor rule. Following the Taylor principle outside the ZLB is neither necessary nor sufficient to ensure uniqueness of equilibria. Instead, the key principle is to respond strongly enough to deviations of past inflation from optimal levels by sufficiently increasing the amount of time interest rates are promised to be kept at zero.