Optimal Interest Rate Smoothing under Model Ambiguity

We first show that monetary certainty is a sufficient condition for an interest rate smoothing rule to be optimal even under preferences for model robustness on the part of private agents. We then derive the necessary and sufficient condition for a stochastic (but stationary) monetary policy to reproduce the equilibrium of the real economy and compute the optimal (constant) level of the nominal interest rate. The condition implies a monetary policy conducted in such a way that the effects of shocks due to the randomness of the money growth rate on private agents' optimal consumption are nullified. We also provide some positive empirical evidence as to the realism of this condition for the U.S. economy in recent years. We show that, without model ambiguity, the coefficient of risk aversion must, at the empirical level, be unrealistically large so as to make a constant interest rate rule optimal. Introducing a preference for robustness decreases the required risk aversion coefficient dramatically.