Implementation of Optimal Monetary Policy

Optimal monetary policy analysis can be viewed as a constrained optimization problem: the policymaker chooses a competitive equilibrium allocation that maximizes social welfare among the set of all feasible competitive equilibrium allocations. Part of the solution to this problem is a monetary policy rule that determines how variables that are under direct control of the policymaker -- the monetary policy instruments -- are set. An optimal policy rule is said to implement the optimal allocation if, conditional on the policy rule, the allocation is the unique rational expectations equilibrium of the economy. For a simple monetary model, we study the implementation of full-commitment and Markov-perfect policies when the policymaker uses a money-stock instrument. For a local approximation of the economy, we show that both policy rules implement the respective optimal allocations. We also show that the results for local approximations do not necessarily extend to a global analysis of the economy: the Markov-perfect policy rule is not implementable, and there is no proof that the full-commitment policy rule is implementable