Zero bound on nominal interest rates and optimal monetary policy

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. Given an adverse shock to aggregate demand, we compute the optimal path of short-term nominal interest rates under the assumption that the central bank has the ability to make a credible commitment about the future path of short-term nominal interest rates. We find that the optimal path is history dependent, in the sense that a zero interest rate policy should be continued for a while even after the economy returns to normal. By making such a commitment, the central bank is able to achieve higher expected inflation, lower long-term nominal interest rates, and weaker domestic currency in the adverse periods when the natural rate of interest significantly deviates from a normal level. We provide a numerical example to show that this channel of monetary policy transmission is quantitatively important.