Optimal monetary policy at the zero-interest-rate bound

What should a central bank do when faced with a weak aggregate demand even after reducing the short-term nominal interest rate to zero? To address this question, we solve a central bank's intertemporal loss-minimization problem, in which the non-negativity constraint on nominal interest rates is explicitly considered. We find that the optimal path is characterized by policy inertia, in the sense that a zero interest rate policy should be continued for a while even after the natural rate of interest returns to a positive level. By making such a commitment, the central bank is able to achieve higher expected inflation, lower long-term nominal interest rates, and a weaker domestic currency in the adverse periods when the natural rate of interest significantly deviates from a steady-state level.