On the optimality of interest rate smoothing

This paper studies some continuous-time cash-in-advance models in which interest rate smoothing is optimal. We consider both deterministic and stochastic models. In the stochastic case we obtain two results of independent interest: (i) we study what is, to our knowledge, the only version of the neoclassical model under uncertainty that can be solved in closed form in continuous time; and (ii) we show how to characterize the competitive equilibrium of a stochastic continuous time model that cannot be computed by solving a planning problem. We also discuss the scope for monetary policy to improve welfare in an economy with a suboptimal real competitive equilibrium, focusing on the particular example of an economy with externalities.