On the Taylor Rule and Optimal Monetary Policy in a “Natural Rate” Model

This paper investigates the stabilizing role of monetary policy in a dynamic, stochastic general equilibrium model of the “natural rate”, in which non indexed nominal wages are periodically set by labor market “insiders”. This nominal distortion allows for nominal shocks to have temporary real effects, and thus, for monetary policy to be able to affect short run fluctuations in both inflation and real output. We derive and analyze optimal monetary policy in the presence of real and nominal shocks, and highlight the properties of the optimal monetary policy rule. The optimal policy rule is second best, as it cannot completely neutralize productivity shocks, and is associated with a tradeoff between the stabilization of inflation and output. We also demonstrate that the optimal policy can be replicated by a set of appropriately parametrized Taylor rules, according to which deviations of the current nominal interest rate from its “natural” rate, depend on deviations of inflation from target and output from its “natural” level. We prove that the optimal Taylor rule is not unique, as multiple sets of parameters are consistent with optimality. Provided that the monetary authorities attach a sufficiently low weight to deviations of output from its “natural” level, the optimal policy could also be replicated through a unique, appropriately parametrized Wicksell rule, according to which deviations of the nominal interest rate from its “natural” rate depend only on deviations of inflation from target. The optimal set of Taylor rules is a set of simple, but not too simple rules, as, the nominal interest rate must react to changes in the “natural” rate of interest, in addition to deviations of inflation from target, and output from its “natural”level.